ArbitrageThe practice of taking advantage of a price differential between two or more markets: Combinations of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. An arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, a risk-free profit. If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium or arbitrage free market.

Conditions for arbitrageArbitrage is possible when one of three conditions is met:

The same asset does not trade at the same price on all markets ("the law of one price"). Two assets with identical cash flows do not trade at the same price. An asset with a known price in the future does not today trade at its future price

discounted at the risk-free interest rate (or, the asset does not have negligible costs of storage; as such, for example, this condition holds for grain but not for securities).

In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. "True" arbitrage requires that there be no market risk involved. Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other.

ExamplesSuppose that the exchange rates (after taking out the fees for making the exchange) in London are £5 = $10 = ¥1000 and the exchange rates in Tokyo are ¥1000 = £6 = $12. Converting ¥1000 to $12 in Tokyo and converting that $12 into ¥1200 in London, for a profit of ¥200, would be arbitrage. In reality, this "triangle arbitrage" is so simple that it almost never occurs. But more complicated foreign exchange arbitrages, such as the spot-forward arbitrage (see interest rate parity) are much more common.

Exchange-traded fund arbitrage - Exchange Traded Funds allow authorized participants to exchange back and forth between shares in underlying securities held by the fund and shares in the fund itself, rather than allowing the buying and selling of shares in the ETF directly with the fund sponsor. ETFs trade in the open market, with prices set by market demand. An ETF may trade at a premium or discount to the value of the underlying assets. When a significant enough premium appears, an arbitrageur will buy the underlying securities, convert them to shares in the ETF, and sell them in the open market. When a discount appears, an arbitrageur will do the reverse. In this way, the arbitrageur makes a low-risk profit, while fulfilling a useful function in the ETF marketplace by keeping ETF prices in line with their underlying value.

Some types of hedge funds make use of a modified form of arbitrage to profit. Rather than exploiting price differences between identical assets, they will purchase and sell securities, assets and derivatives with similar characteristics, and hedge any significant differences between the two assets. Any difference between the hedged positions represents any remaining risk (such as basis risk) plus profit; the belief is that there remains some difference which, even after hedging most risk, represents pure profit. For example, a fund may see that there is a substantial difference between U.S. dollar debt and local currency debt of a foreign country, and enter into a series of

matching trades (including currency swaps) to arbitrage the difference, while simultaneously entering into credit default swaps to protect against country risk and other types of specific risk.

Price convergenceArbitrage has the effect of causing prices in different markets to converge. As a result of arbitrage, the currency exchange rates, the price of commodities, and the price of securities in different markets tend to converge to the same prices, in all markets, in each category. The speed at which prices converge is a measure of market efficiency. Arbitrage tends to reduce price discrimination by encouraging people to buy an item where the price is low and resell it where the price is high, as long as the buyers are not prohibited from reselling and the transaction costs of buying, holding and reselling are small relative to the difference in prices in the different markets.

Arbitrage moves different currencies toward purchasing power parity. As an example, assume that a car purchased in America is cheaper than the same car in Canada. Canadians would buy their cars across the border to exploit the arbitrage condition. At the same time, Americans would buy US cars, transport them across the border, and sell them in Canada. Canadians would have to buy American Dollars to buy the cars, and Americans would have to sell the Canadian dollars they received in exchange for the exported cars. Both actions would increase demand for US Dollars, and supply of Canadian Dollars, and as a result, there would be an appreciation of the US Dollar. Eventually, if unchecked, this would make US cars more expensive for all buyers, and Canadian cars cheaper, until there is no longer an incentive to buy cars in the US and sell them in Canada. More generally, international arbitrage opportunities in commodities, goods, securities and currencies, on a grand scale, tend to change exchange rates until the purchasing power is equal.

In reality, of course, one must consider taxes and the costs of travelling back and forth between the US and Canada. Also, the features built into the cars sold in the US are not exactly the same as the features built into the cars for sale in Canada, due, among other things, to the different emissions and other auto regulations in the two countries. In addition, our example assumes that no duties have to be paid on importing or exporting cars from the USA to Canada. Similarly, most assets exhibit (small) differences between countries, and transaction costs, taxes, and other costs provide an impediment to this kind of arbitrage.

RisksArbitrage transactions in modern securities markets involve fairly low risks. Generally it is impossible to close two or three transactions at the same instant; therefore, there is the possibility that when one part of the deal is closed, a quick shift in prices makes it impossible to close the other at a profitable price. There is also counter-party risk that the other party to one of the deals fails to deliver as agreed; though unlikely, this hazard is serious because of the large quantities one must trade in order to make a profit on small price differences. These risks become magnified when leverage or borrowed money is used.

Another risk occurs if the items being bought and sold are not identical and the arbitrage is conducted under the assumption that the prices of the items are correlated or predictable. In the extreme case this is risk arbitrage, described below. In comparison to the classical quick arbitrage transaction, such an operation can produce disastrous losses.

In the 1980s, risk arbitrage was common. In this form of speculation, one trades a security that is clearly undervalued or overvalued, when it is seen that the wrong valuation is about to be corrected by events. The standard example is the stock of a company, undervalued in the stock market, which is about to be the object of a takeover bid; the price of the takeover will more truly reflect the value of the company, giving a large profit to those who bought at the current price—if the merger goes through as predicted. Traditionally, arbitrage transactions in the securities markets involve high speed and low risk. At some moment a price difference exists, and the problem is to execute two or three balancing transactions while the difference persists (that is, before the other arbitrageurs act). When the transaction involves a delay of weeks or months, as above, it may entail considerable risk if borrowed money is used to magnify the reward through leverage. One way of reducing the risk is through the illegal use of inside information, and in fact risk arbitrage with regard to leveraged buyouts was associated with some of the famous financial scandals of the 1980s such as those involving Michael Milken and Ivan Boesky.

Types of arbitrage

Merger arbitrageAlso called risk arbitrage, merger arbitrage generally consists of buying the stock of a company that is the target of a takeover while shorting the stock of the acquiring company.

Usually the market price of the target company is less than the price offered by the acquiring company. The spread between these two prices depends mainly on the probability and the timing of the takeover being completed as well as the prevailing level of interest rates.

The bet in a merger arbitrage is that such a spread will eventually be zero, if and when the takeover is completed. The risk is that the deal "breaks" and the spread massively widens.

Convertible bond arbitrageA convertible bond is a bond that an investor can return to the issuing company in exchange for a predetermined number of shares in the company.

A convertible bond can be thought of as a corporate bond with a stock call option attached to it. The price of a convertible bond is sensitive to three major factors:

Interest rate. When rates move higher, the bond part of a convertible bond tends to move lower, but the call option part of a convertible bond moves higher (and the aggregate tends to move lower).

Stock price. When the price of the stock the bond is convertible into moves higher, the price of the bond tends to rise.

Credit spread. If the creditworthiness of the issuer deteriorates (e.g. rating downgrade) and its credit spread widens, the bond price tends to move lower, but, in many cases, the call option part of the convertible bond moves higher (since credit spread correlates with volatility).

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Convertible arbitrage consists of buying a convertible bond and hedging two of the three factors in order to gain exposure to the third factor at a very attractive price.

For instance an arbitrageur would first buy a convertible bond, then sell fixed income securities or interest rate futures (to hedge the interest rate exposure) and buy some credit protection (to hedge the risk of credit deterioration). Eventually what he'd be left with is something similar to a call option on the underlying stock, acquired at a very low price. He could then make money either selling some of the more expensive options that are openly traded in the market or delta hedging his exposure to the underlying shares.

Depository receiptsA depository receipt is a security that is offered as a "tracking stock" on another foreign market. For instance a Chinese company wishing to raise more money may issue a depository receipt on the New York Stock Exchange, as the amount of capital on the local exchanges is limited. These securities, known as ADRs (American Depositary Receipt) or GDRs (Global Depositary Receipt) depending on where they are issued are typically considered "foreign" and therefore trade at a lower value when first released. However, they are exchangeable into the original security (known as fungibility) and actually have the same value. In this case there is a spread between the perceived value and real value, which can be extracted. Since the ADR is trading at a value lower than what it is worth, one can purchase the ADR and expect to make money as its value converges on the original. However there is a chance that the original stock will fall in value too, so by shorting it you can hedge that risk.Regulatory arbitrageRegulatory arbitrage is where a regulated institution takes advantage of the difference between its real (or economic) risk and the regulatory position. For example, if a bank, operating under the Basel I accord, has to hold 8% capital against default risk, but the real risk of default is lower, it is profitable to securitise the loan, removing the low risk loan from its portfolio. On the other hand, if the real risk is higher than the regulatory risk then it is profitable to make that loan and hold on to it, provided it is priced appropriately.

This process can increase the overall riskiness of institutions under a risk insensitive regulatory regime, as described by Alan Greenspan in his October 1998 speech on The Role of Capital in Optimal Banking Supervision and Regulation.

In economics, regulatory arbitrage (sometimes, tax arbitrage) may be used to refer to situations when a company can choose a nominal place of business with a regulatory, legal or tax regime with lower costs. For example, an insurance company may choose to locate in Bermuda due to preferential tax rates and policies for insurance companies. This can occur particularly where the business transaction has no obvious physical location: in the case of many financial products, it may be unclear "where" the transaction occurs.

Arbitrage pricing theoryArbitrage pricing theory (APT), in Finance, is a general theory of asset pricing that has become influential in the pricing of shares.

APT holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of

period price discounted at the rate implied by model. If the price diverges, arbitrage should bring it back into line.

The theory was initiated by the economist Stephen Ross in 1976.

The APT model

If APT holds, then a risky asset can be described as satisfying the following relation:

where E(rj) is the risky asset's expected return, RPk is the risk premium of the factor, rf is the risk-free rate, Fk is the macroeconomic factor, bjk is the sensitivity of the asset to factor k, also called factor loading, and εj is the risky asset's idiosyncratic random shock with mean zero.

That is, the uncertain return of an asset j is a linear relationship among n factors. Additionally, every factor is also considered to be a random variable with mean zero.

Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of factors may never surpass the total number of assets (in order to avoid the problem of matrix singularity),

Arbitrage and the APTArbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets and thereby making a risk free profit; sees Rational pricing.Arbitrage in expectationsThe APT describes the mechanism whereby arbitrage by investors will bring an asset which is mispriced, according to the APT model, back into line with its expected price. Note that under true arbitrage, the investor locks-in a guaranteed payoff, whereas under APT arbitrage as described below, the investor locks-in a positive expected payoff. The APT thus assumes "arbitrage in expectations" - i.e. that arbitrage by investors will bring asset prices back into line with the returns expected by the model portfolio theory.Arbitrage mechanicsIn the APT context, arbitrage consists of trading in two assets – with at least one being mispriced. The arbitrageur sells the asset which is relatively too expensive and uses the proceeds to buy one which is relatively too cheap.

Under the APT, an asset is mispriced if its current price diverges from the price predicted by the model. The asset price today should equal the sum of all future cash flows discounted at the APT rate, where the expected return of the asset is a linear function of various factors, and sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

A correctly priced asset here may be in fact a synthetic asset - a portfolio consisting of other correctly priced assets. This portfolio has the same exposure to each of the macroeconomic factors as the mispriced asset. The arbitrageur creates the portfolio by identifying x correctly

priced assets (one per factor plus one) and then weighting the assets such that portfolio beta per factor is the same as for the mispriced asset.

When the investor is long the asset and short the portfolio (or vice versa) he has created a position which has a positive expected return (the difference between asset return and portfolio return) and which has a net-zero exposure to any macroeconomic factor and is therefore risk free (other than for firm specific risk). The arbitrageur is thus in a position to make a risk free profit:

Where today's price is too low:

The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate. The arbitrageur could therefore: Today: 1 short sell the portfolio 2 buy the mispriced-asset with the proceeds. At the end of the period: 1 sell the mispriced asset 2 use the proceeds to buy back the portfolio 3 pocket the difference.

Where today's price is too high:

The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at less than this rate. The arbitrageur could therefore: Today: 1 short sell the mispriced-asset 2 buy the portfolio with the proceeds. At the end of the period: 1 sell the portfolio 2 use the proceeds to buy back the mispriced-asset 3 pocket the difference.

Relationship with the capital asset pricing model

The APT along with the capital asset pricing model (CAPM) is one of two influential theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in its assumptions. It allows for an explanatory (as opposed to statistical) model of asset returns. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM can be considered a "special case" of the APT in that the securities market line represents a single-factor model of the asset price, where Beta is exposed to changes in value of the Market.

Additionally, the APT can be seen as a "supply side" model, since its beta coefficients reflect the sensitivity of the underlying asset to economic factors. Thus, factor shocks would cause structural changes in the asset's expected return, or in the case of stocks, in the firm's profitability.

On the other side, the capital asset pricing model is considered a "demand side" model. Its results, although similar to those in the APT, arise from a maximization problem of each investor's utility

function, and from the resulting market equilibrium (investors are considered to be the "consumers" of the assets).

Using the APT

Identifying the factorsAs with the CAPM, the factor-specific Betas are found via a linear regression of historical security returns on the factor in question. Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors - the number and nature of these factors is likely to change over time and between economies. As a result, this issue is essentially empirical in nature. Several a priori guidelines as to the characteristics required of potential factors are, however, suggested:

their impact on asset prices manifests in their unexpected movements they should represent undiversifiable influences (these are, clearly, more likely to be

macroeconomic rather than firm-specific in nature) timely and accurate information on these variables is required the relationship should be theoretically justifiable on economic grounds

Chen, Roll and Ross identified the following macro-economic factors as significant in explaining security returns:

surprises in inflation; surprises in GNP as indicted by an industrial production index; surprises in investor confidence due to changes in default premium in corporate

bonds; surprise shifts in the yield curve.

As a practical matter, indices or spot or futures market prices may be used in place of macro-economic factors, which are reported at low frequency (e.g. monthly) and often with significant estimation errors. Market indices are sometimes derived by means of factor analysis. More direct "indices" that might be used are:

short term interest rates; the difference in long-term and short term interest rates; a diversified stock index such as the S&P 500 or NYSE Composite Index; oil prices gold or other precious metal prices Currency exchange rates

APT and asset management

Covered interest arbitrage

Covered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency. The

proceeds of the investment are only known exactly if the financial instrument is risk-free and only pays interest once, on the date of the forward sale of foreign currency. Otherwise, some foreign exchange risk remains.

Similar trades using risky foreign currency bonds or even foreign stock may be made, but the hedging trades may actually add risk to the transaction, e.g. if the bond defaults the investor may lose on both the bond and the forward contract.

ExampleIn this example the investor is based in the United States and assumes the following prices and rates: spot USD/EUR = $1.2000, forward USD/EUR for 1 year delivery = $1.2300, dollar interest rate = 4.0%, euro interest rate = 2.5%.

Exchange USD 1,200,000 into EUR 1,000,000 Buy EUR 1,000,000 worth of euro-denominated bonds Sell EUR 1,025,000 via a 1 year forward contract, to receive USD 1,260,750, i.e. agree to

exchange the euros back into US dollars in 1 year at today's forward price. This set of transactions can be viewed as having an effective dollar interest rate of

(1,260,750/1,200,000)-1 = 5.1% Alternatively, if the USD 1,200,000 were borrowed at 4%, USD 1,248,000 would be

owed in 1 year, leaving an arbitrage profit of 1,260,750 - 1,248,000 = USD 12,750 in 1 year.

ModelsFinancial models such as interest rate parity and the cost of carry model assume that no such arbitrage profits could exist in equilibrium, thus the effective dollar interest rate of investing in any currency will equal the effective dollar rate for any other currency, for risk-free instruments.Efficient market hypothesisIn finance, the efficient market hypothesis (EMH) asserts that financial markets are "informationally efficient", or that prices on traded assets, e.g., stocks, bonds, or property, already reflect all known information and therefore are unbiased in the sense that they reflect the collective beliefs of all investors about future prospects. Professor Eugene Fama at the University of Chicago Graduate School of Business developed EMH as an academic concept of study through his published Ph.D. thesis in the early 1960s at the same school.

The efficient market hypothesis states that it is not possible to consistently outperform the market by using any information that the market already knows, except through luck. Information or news in the EMH is defined as anything that may affect prices that is unknowable in the present and thus appears randomly in the future.

AssumptionsBeyond the normal utility maximizing agents, the efficient market hypothesis requires that agents have rational expectations; that on average the population is correct (even if no one person is) and whenever new relevant information appears, the agents update their expectations appropriately.

Note that it is not required that the agents be rational (which is different from rational expectations; rational agents act coldly and achieve what they set out to do). EMH allows that when faced with new information, some investors may overreact and some may underreact. All that is required by the EMH is that investors' reactions be random and follow a normal distribution pattern so that the net effect on market prices cannot be reliably exploited to make an abnormal profit, especially when considering transaction costs (including commissions and

spreads). Thus, any one person can be wrong about the market — indeed, everyone can be — but the market as a whole is always right.

There are three common forms in which the efficient market hypothesis is commonly stated — weak form efficiency, semi-strong form efficiency and strong form efficiency, each of which have different implications for how markets work.

Weak-form efficiency

No excess returns can be earned by using investment strategies based on historical share prices or other financial data.

Weak-form efficiency implies that Technical analysis techniques will not be able to consistently produce excess returns, though some forms of fundamental analysis may still provide excess returns.

In a weak-form efficient market current share prices are the best, unbiased, estimate of the value of the security. Theoretical in nature, weak form efficiency advocates assert that fundamental analysis can be used to identify stocks that are undervalued and overvalued. Therefore, keen investors looking for profitable companies can earn profits by researching financial statements.

Semi-strong form efficiency

Share prices adjust within an arbitrarily small but finite amount of time and in an unbiased fashion to publicly available new information, so that no excess returns can be earned by trading on that information.

Semi-strong form efficiency implies that Fundamental analysis techniques will not be able to reliably produce excess returns.

To test for semi-strong form efficiency, the adjustments to previously unknown news must be of a reasonable size and must be instantaneous. To test for this, consistent upward or downward adjustments after the initial change must be looked for. If there are any such adjustments it would suggest that investors had interpreted the information in a biased fashion and hence in an inefficient manner.

Strong-form efficiency

Share prices reflect all information and no one can earn excess returns. If there are legal barriers to private information becoming public, as with insider

trading laws, strong-form efficiency is impossible, except in the case where the laws are universally ignored. Studies on the U.S. stock market have shown that people do trade on inside information.[citation needed]

To test for strong form efficiency, a market needs to exist where investors cannot consistently earn excess returns over a long period of time. Even if some money managers are consistently observed to beat the market, no refutation even of strong-form efficiency follows: with tens of thousands of fund managers worldwide[citation

needed], even a normal distribution of returns (as efficiency predicts) should be expected to produce a few dozen "star" performers.

Arguments concerning the validity of the hypothesis

Some observers dispute the notion that markets behave consistently with the efficient market hypothesis, especially in its stronger forms. Some economists, mathematicians and market practitioners cannot believe that man-made markets are strong-form efficient when there are prima facie reasons for inefficiency including the slow diffusion of information, the relatively great power of some market participants (e.g. financial institutions), and the existence of apparently sophisticated professional investors. The way that markets react to surprising news is perhaps the most visible flaw in the efficient market hypothesis. For example, news events such as surprise interest rate changes from central banks are not instantaneously taken account of in stock prices, but rather cause sustained movement of prices over periods from hours to months.

Only a privileged few may have prior knowledge of laws about to be enacted, new pricing controls set by pseudo-government agencies such as the Federal Reserve banks, and judicial decisions that effect a wide range of economic parties. The public must treat these as random variables, but actors on such inside information can correct the market, but usually in discrete manner to avoid detection.

Another observed discrepancy between the theory and real markets is that at market extremes what fundamentalists might consider irrational behaviour is the norm: in the late stages of a bull market, the market is driven by buyers who take little notice of underlying value. Towards the end of a crash, markets go into free fall as participants extricate themselves from positions regardless of the unusually good value that their positions represent. This is indicated by the large differences in the valuation of stocks compared to fundamentals (such as forward price to earnings ratios) in bull markets compared to bear markets. A theorist might say that rational (and hence, presumably, powerful) participants should always immediately take advantage of the artificially high or artificially low prices caused by the irrational participants by taking opposing positions, but this is observably not, in general, enough to prevent bubbles and crashes developing. It may be inferred that many rational participants are aware of the irrationality of the market at extremes and are willing to allow irrational participants to drive the market as far as they will, and only take advantage of the prices when they have more than merely fundamental reasons that the market will return towards fair value. Behavioural finance explains that when entering positions market participants are not driven primarily by whether prices are cheap or expensive, but by whether they expect them to rise or fall. To ignore this can be hazardous: Alan Greenspan warned of "irrational exuberance" in the markets in 1996, but some traders who sold short new economy stocks that seemed to be greatly overpriced around this time had to accept serious losses as prices reached even more extraordinary levels. As John Maynard Keynes succinctly commented, "Markets can remain irrational longer than you can remain solvent."[citation

needed]

The efficient market hypothesis was introduced in the late 1960s. Prior to that, the prevailing view was that markets were inefficient. Inefficiency was commonly believed to exist e.g. in the United States and United Kingdom stock markets. However, earlier work by Kendall (1953) suggested that changes in UK stock market prices were random. Later work by Brealey and Dryden, and also by Cunningham found that there were no significant dependences in price changes suggesting that the UK stock market was weak-form efficient.

Further to this evidence that the UK stock market is weak form efficient, other studies of capital markets have pointed toward them being semi strong-form efficient. Studies by Firth (1976, 1979 and 1980) in the United Kingdom have compared the share prices existing after a takeover

announcement with the bid offer. Firth found that the share prices were fully and instantaneously adjusted to their correct levels, thus concluding that the UK stock market was semi strong-form efficient. The market's ability to efficiently respond to a short term and widely publicized event such as a takeover announcement cannot necessarily be taken as indicative of a market efficient at pricing regarding more long term and amorphous factors however.

Other empirical evidence in support of the EMH comes from studies showing that the return of market averages exceeds the return of actively managed mutual funds. Thus, to the extent that markets are inefficient, the benefits realized by seizing upon the inefficiencies are outweighed by the internal fund costs involved in finding them, acting upon them, advertising etc. These findings gave inspiration to the formation of passively managed index funds.[1]

It may be that professional and other market participants who have discovered reliable trading rules or stratagems see no reason to divulge them to academic researchers. It might be that there is an information gap between the academics who study the markets and the professionals who work in them. Some observers point to seemingly inefficient features of the markets that can be exploited e.g seasonal tendencies and divergent returns to assets with various characteristics. E.g. factor analysis and studies of returns to different types of investment strategies suggest that some types of stocks may outperform the market long-term (e.g in the UK, the USA and Japan).

Skeptics of EMH argue that there exists a small number of investors who have outperformed the market over long periods of time, in a way which is difficult to attribute luck, including Peter Lynch, Warren Buffett, George Soros, and Bill Miller. These investors' strategies are to a large extent based on identifying markets where prices do not accurately reflect the available information, in direct contradiction to the efficient market hypothesis which explicitly implies that no such opportunities exist. Among the skeptics is Warren Buffett who has argued that the EMH is not correct, on one occasion wryly saying "I'd be a bum on the street with a tin cup if the markets were always efficient"[citation needed] and on another saying "The professors who taught Efficient Market Theory said that someone throwing darts at the stock tables could select stock portfolio having prospects just as good as one selected by the brightest, most hard-working securities analyst. Observing correctly that the market was frequently efficient, they went on to conclude incorrectly that it was always efficient."[citation needed] Adherents to a stronger form of the EMH argue that the hypothesis does not preclude - indeed it predicts - the existence of unusually successful investors or funds occurring through chance. They also argue that presentation of anecdotal evidence of star-performers to cast doubt on the hypothesis is rife with survivorship bias.

However, importantly, in 1962 Warren Buffett wrote: "I present this data to indicate the Dow as an investment competitor is no pushover, and the great bulk of investment funds in the country are going to have difficulty in bettering, or... even matching, its performance. Our portfolio is very different from that of the Dow. Our method of operation is substantially different from that of mutual funds." [2]

The EMH and popular culture

Despite the best efforts of EMH proponents such as Burton Malkiel, whose book A Random Walk Down Wall Street (ISBN 0-393-32535-0) achieved best-seller status, the EMH has not caught the public's imagination. Popular books and articles promoting various forms of stock-picking, such as the books by popular CNBC commentator Jim Cramer and former Fidelity Investments fund manager Peter Lynch, have continued to press the more appealing notion that investors can "beat

the market." The theme was further explored in the recent The Little Book That Beats The Market (ISBN 0-471-73306-7) by Joel Greenblatt.

One notable exception to this trend is the recent book Wall Street Versus America (ISBN 1-59184-094-5), by investigative journalist Gary Weiss. In this caustic attack on Wall Street practices, Weiss argues in favor of the EMH and against stock-picking as an investor self-defense mechanism.

EMH is commonly rejected by the general public due to a misconception concerning its meaning. Many believe that EMH says that a security's price is a correct representation of the value of that business, as calculated by what the business's future returns will actually be. In other words, they believe that EMH says a stock's price correctly predicts the underlying company's future results. Since stock prices clearly do not reflect company future results in many cases, many people reject EMH as clearly wrong.

However, EMH makes no such statement. Rather, it says that a stock's price represents an aggregation of the probabilities of all future outcomes for the company, based on the best information available at the time. Whether that information turns out to have been correct is not something required by EMH. Put another way, EMH does not require a stock's price to reflect a company's future performance, just the best possible estimate of that performance that can be made with publicly available information. That estimate may still be grossly wrong without violating EMH.

An alternative theory: Behavioral Finance

Opponents of the EMH sometimes cite examples of market movements that seem inexplicable in terms of conventional theories of stock price determination, for example the stock market crash of October 1987 where most stock exchanges crashed at the same time. It is virtually impossible to explain the scale of those market falls by reference to any news event at the time. The explanation may lie either in the mechanics of the exchanges (e.g. no safety nets to discontinue trading initiated by program sellers) or the peculiarities of human nature.

Behavioural psychology approaches to stock market trading are among some of the more promising alternatives to EMH (and some investment strategies seek to exploit exactly such inefficiencies). A growing field of research called behavioral finance studies how cognitive or emotional biases, which are individual or collective, create anomalies in market prices and returns that may be inexplicable via EMH alone. However, how and if individual biases manifest inefficiencies in market-wide prices is still an open question. Indeed, the Nobel Laureate co-founder of the programme - Daniel Kahneman - announced his skepticism of resultant inefficiencies: "They're [investors] just not going to do it [beat the market]. It's just not going to happen."[3]

Ironically, the behaviorial finance programme can also be used to tangentially support the EMH - or rather it can explain the skepticism drawn by EMH - in that it helps to explain the human tendency to find and exploit patterns in data even where none exist. Some relevant examples of the Cognitive biases highlighted by the programme are: the Hindsight Bias; the Clustering illusion; the Overconfidence effect; the Observer-expectancy effect; the Gambler's fallacy; and the Illusion of control.

Immunization (finance)

In finance, interest rate immunization is a strategy that ensures that a change in interest rates will not affect the value of a portfolio. Similarly, immunization can be used to insure that the value of a pension fund's or a firm's assets will increase or decrease in exactly the opposite amount of their liabilities, thus leaving the value of the pension fund's surplus or firm's equity unchanged, regardless of changes in the interest rate.

Interest rate immunization can be accomplished by several methods, including cash flow matching, duration matching, and volatility and convexity matching. It can also be accomplished by trading in bond forwards, futures, or options.

Other types of financial risks, such as foreign exchange risk or stock market risk, can be immunized using similar strategies. If the immunization is incomplete, these strategies are usually called hedging. If the immunization is complete, these strategies are usually called arbitrage.

Cash flow matchingConceptually, the easiest form of immunization is cash flow matching. For example, if a financial company is obliged to pay 100 dollars to someone in 10 years, then it can protect itself by buying and holding a 10 year zero coupon bond that matures in 10 years and has a redemption value of $100. Thus the firm's expected cash inflows exactly match its expected cash outflows, and a change in interest rates will not affect the firm's ability to pay its obligations. Nevertheless, a firm with many expected cash flows can find that cash flow matching is difficult or expensive to achieve in practice.

Volatility matchingA more practical alternative immunization method is duration matching. Here the duration of the assets, or first derivative of the asset's price function with respect to the interest rate, is matched with the duration of the liabilities. To make the match more accurate, the convexity or second derivative of the assets and libilities, can also be matched.

Immunization in practiceImmunization can be done in a portfolio of a single asset type, such as government bonds, by creating long and short positions along the yield curve. It is usually possible to immunize a portfolio against the risk factors that are most prevalent. A principal component analysis of changes along the U.S. Government Treasury yield curve reveals that more than 90% of the yield curve shifts are parallel shifts, followed by a smaller percentage of slope shifts, and a very small percentage of curvature shifts. Using that knowledge, an immunized portfolio can be created by creating long positions with durations at the long and short end of the curve, and a matching short position with a duration in the middle of the curve. These positions protect against parallel shifts and slope changes, in exchange for exposure to curvature changes.

DifficultiesImmunization, if possible and complete, can protect against term mismatch but not against other kinds of financial risk such as default by the borrower (of a bond).Users of this technique include banks, insurance companies, pension funds, and bond brokers.The disadvantage associated with duration match is it assumes the duration of assets and liabilities are unchanged which is not true.

Interest rate parity

The interest rate parity is the basic identity that relates interest rates and exchange rates. The identity is theoretical, and usually follows from assumptions imposed in economics models. There is evidence that supports as well as rejects interest rate parity.Interest rate parity is an arbitrage condition, which says that the returns from borrowing in one currency, exchanging that currency for another currency and investing in interest-bearing instruments of the second currency, while simultaneously purchasing futures contracts to convert the currency back at the end of the investment period should be equal to the returns from purchasing and holding similar interest-bearing instruments of the first currency. If the returns are different, investors could theoretically arbitrage and make risk-free returns.Looked at differently, interest rate parity says that the spot and future prices for currency trades incorporate any interest rate differentials between the two currencies.Two versions of the identity are commonly presented in academic literature: covered interest rate parity and uncovered interest rate parity.

Covered interest rate parity

The basic covered interest parity (also called interest parity condition) is

where

is the domestic interest rate, ic is the interest rate in the foreign country,

F is forward exchange rate between domestic currency ($) and foreign currency (c), i.e. $/c, and

S is spot exchange rate between domestic currency ($) and foreign currency (c), i.e. $/c.

The covered interest parity states that the interest rate difference between two countries' currencies is equal to the percentage difference between the forward exchange rate and the spot exchange rate. The parity condition assumes that financial assets are perfectly mobile and similarly risky. If the parity condition does not hold, there exists an arbitrage opportunity. (see covered interest arbitrage and an example below).

Another way to express the interest rate parity is:

A more approximate version is sometimes given, although it is less correct for countries with highly volatile exchange rates:

An implication of this equation is that when the domestic interest rate is lower than the foreign interest rate, the forward price of the foreign currency will be below the spot price. Conversely, if

the domestic interest rate is above the foreign interest rate, then the forward price of the foreign currency will be above the spot price.

Covered interest arbitrage example

In short, assume that

.

This would imply that one dollar invested in the US < one dollar converted into a foreign currency and invested abroad. Such an imbalance would give rise to an arbitrage opportunity, where in one could borrow at the lower effective interest rate in US, convert to the foreign currency and invest abroad.

The following is a rudimentary example to understand covered interest rate arbitrage (CIA)

Consider the interest rate parity (IRP) equation,

Assume,

the 12-month interest rate in US is 5%, per annum the 12-month interest rate in UK is 8%, per annum the current Spot Exchange is 1.5 $/£ the current Forward Exchange is 1.5 $/£

From the given conditions it is clear that UK has a higher interest rate than the US. Thus the basic idea of covered interest arbitrage is to borrow in the country with lower interest rate and invest in the country with higher interest rate. All else being equal this would help you make money riskless. Thus,

Per the LHS of the interest rate parity equation above, a dollar invested in the US at the end of the 12-month period will be,

$1 · (1 + 5%) = $1.05

Per the RHS of the interest rate parity equation above, a dollar invested in the UK (after conversion into £ and back into $ at the end of 12-months) at the end of the 12-month period will be,

$1 · (1.5/1.5)(1 + 8%) = $1.08

Thus, one could carry out a covered interest rate (CIA) arbitrage as follows,

1. Borrow $1 from the US bank at 5% interest rate. 2. Convert $ into £ at current spot rate of 1.5$/£ giving 0.67£ 3. Invest the 0.67£ in the UK for the 12 month period

4. Purchase a forward contract on the 1.5$/£ (i.e. cover your position against exchange rate fluctuations)

At the end of 12-months

1. 0.67£ becomes 0.67£(1 + 8%) = 0.72£ 2. Convert the 0.72£ back to $ at 1.5$/£, giving $1.08 3. Pay off the initially borrowed amount of $1 to the US bank with 5% interest, i.e $1.05

Making an arbitrage profit of $1.08 − $1.05 = $0.03 or 3 cents per dollar.

Obviously, any such arbitrage opportunities in the market will close out almost immediately.

In the above example, any one or combination of the following may occur to re-establish the equilibrium of the IRP to close out the arbitrage opportunity,

US interest rates will go up

Forward exchange rates will go down

Spot exchange rates will go up

UK interest rates will go down

Uncovered interest rate parity

The uncovered interest rate parity postulates that

The equality assumes that the risk premium is zero, which is the case if investors are risk-neutral. If investors are not risk-neutral then the forward rate (Ft,t + 1) can differ from the expected future spot rate (Et[St + 1]), and covered and uncovered interest rate parities cannot both hold.

The uncovered parity is not directly testable in the absence of market expectations of future exchange rates. Moreover, the above rather simple demonstration assumes no transaction cost, equal default risk over foreign and domestic currency denominated assets, perfect capital flow and no simultaneity induced by monetary authorities. Note also that it is possible to construct the UIP condition in real terms, which is more plausible.

Uncovered interest parity exampleAn example for the uncovered interest parity condition: Consider an initial situation, where interest rates in the US (home country) and a foreign country (e.g. Japan) are equal. Except for exchange rate risk, investing in the US or Japan would yield the same return. If the dollar depreciates against the yen, an investment in Japan would become more profitable than a US-investment - in other words, for the same amount of yen, more dollars can be purchased. By investing in Japan and converting back to the dollar at the favorable exchange rate, the return

from the investment in Japan, in the dollar term, is higher than the return from the direct investment in the US. In order to persuade an Investor to invest in the US nonetheless, the dollar interest rate would have to be higher than the yen interest rate by an amount equal to the devaluation (a 20% depreciation of the dollar implies a 20% rise in the dollar interest rate).Note: Technically, a 20% depreciation in the dollar only results in an approximate rise of 20% in U.S. interest rates. The exact form is as follows: Change in spot rate (Yen/Dollar) equals the dollar interest rate minus the yen interest rate, with this expression being divided by one plus the yen interest rate.

Uncovered vs. covered interest parity exampleLet's assume you wanted to pay for something in Yen in a month's time. There are two ways to do this.

(a) Buy Yen forward 30 days to lock in the exchange rate. Then you may invest in dollars for 30 days until you must convert dollars to Yen in a month. This is called covering because you now have covered yourself and have no exchange rate risk.

(b) Convert spot to Yen today. Invest in a Japanese bond (in Yen) for 30 days (or otherwise loan Yen for 30 days) then pay your Yen obligation. Under this model, you are sure of the interest you will earn, so you may convert fewer dollars to Yen today, since the Yen will grow via interest. Notice how you have still covered your exchange risk, because you have simply converted to Yen immediately.

(c) You could also invest the money in dollars and change it for Yen in a month. According to the interest rate parity, you should get the same number of Yen in all methods. Methods (a) and (b) are covered while (c) is uncovered.

In method (a) the higher (lower) interest rate in the US is offset by the forward discount (premium).

In method (b) The higher (lower) interest rate in Japan is offset by the loss (gain) from converting spot instead of using a forward.

Method (c) is uncovered, however, according to interest rate parity, the spot exchange rate in 30 days should become the same as the 30 day forward rate. Obviously there is exchange risk because you must see if this actually happens.

General Rules: If the forward rate is lower than what the interest rate parity indicates, the appropriate strategy would be: borrow Yen, convert to dollars at the spot rate, and lend dollars.If the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be: borrow dollars, convert to Yen at the spot rate, and lend the Yen.

Cost of carry modelA slightly more general model, used to find the forward price of any commodity, is called the cost of carry model. Using continuously compounded interest rates, the model is:

where F is the forward price, S is the spot price, e is the base of the natural logarithms, r is the risk free interest rate, s is the storage cost, c is the convenience yield, and t is the time to delivery of the forward contract (expressed as a fraction of 1 year).For currencies there is no storage cost, and c is interpreted as the foreign interest rate. The currency prices should be quoted as domestic units per foreign units.If the currencies are freely tradeable and there are minimal transaction costs, then a profitable arbitrage is possible if the equation doesn't hold. If the forward price is too high, the arbitrageur sells the forward currency, buys the spot currency and lends it for time period t, and then uses the loan proceeds to deliver on the forward contract. To complete the arbitrage, the home currency is borrowed in the amount needed to buy the spot foreign currency, and paid off with the home currency proceeds of forward contract.

Similarly, if the forward price is too low, the arbitrageur buys the forward currency, borrows the foreign currency for time period t and sells the foreign currency spot. The proceeds of the forward contract are used to pay off the loan. To complete the arbitrage, the home currency from the spot transaction is lent and the proceeds used to pay for the forward contract.

Political arbitrageA trading strategy which involves using knowledge or estimates of future political activity to forecast and discount security values. For example, the major factor in the values of some foreign government bonds is the risk of default, which is a political decision taken by the country's government. The values of companies in war-sensitive sectors such as oil and arms are affected by political decisions to make war. In the UK, the government's decision to commission new housing to the east of London is likely to affect housebuilder company values.[citation needed]

Legal trading must be based on publicly available information. However there is a grey area involving lobbyists and market rumours. Like insider trading there is scope for conflicts of interest when political decision makers themselves are in positions to profit from private investments whose values are linked to their own public political actions.

TANSTAAFL

TANSTAAFL is an acronym for the adage "There Ain't No Such Thing As A Free Lunch," popularized by science fiction writer Robert A. Heinlein in his 1966 novel The Moon Is a Harsh Mistress, which discusses the problems caused by not considering the eventual outcome of an unbalanced economy. This phrase and book are popular with libertarians and economics textbooks. In order to avoid a double negative, the acronym "TINSTAAFL" is sometimes used instead, meaning "There Is No Such Thing As A Free Lunch".

The phrase refers to the once-common tradition of saloons in the United States providing a "free" lunch to patrons, who were required to buy at least one drink.[citation needed]

DetailsTANSTAAFL means that a person or a society cannot get something for nothing. Even if something appears to be free, there is always a cost to the person or to society as a whole even though that cost may be hidden or distributed. [1] For example, you may get complimentary food at a bar during "happy hour," but the bar owner bears the expense of your meal and will attempt to recover that expense somehow. Some goods may be nearly free, such as fruit picked in the wilderness, but usually some cost such as labor is incurred.

The idea that there is no free lunch at the societal level applies only when all resources are being used completely and appropriately, i.e., when economic efficiency prevails. If one individual or group gets something at no cost, somebody else ends up paying for it. If there appears to be no direct cost to any single individual, there is a social cost. Similarly, someone can benefit for "free" from an externality or from a public good, but someone has to pay the cost of producing these benefits.

To a scientist, TANSTAAFL means that the system is ultimately closed — there is no magic source of matter, energy, light, or indeed lunch, that cannot be eventually exhausted. Therefore the TANSTAAFL argument may also be applied to natural physical processes.

In mathematical finance, the term is also used as an informal synonym for the principle of no-arbitrage. This principle states that a combination of securities that has the same cash flows as another security must have the same net price.TANSTAAFL is sometimes used as a response to claims of the virtues of free software. Supporters of free software often counter that the use of the term "free" in this context is primarily a reference to a lack of constraint rather than a lack of cost.TANSTAAFL is the name of a snack bar in the Pierce dormitory of the University of Chicago. The name references the fact that the use of the term was popularized by Milton Friedman, the Nobel Prize–winning former University of Chicago professor.

Citations

In 1950, a New York Times columnist ascribed the phrase to economist (and Army General) Leonard P. Ayres of the Cleveland Trust Company. "It seems that shortly before the General's death [in 1946]... a group of reporters approached the general with the request that perhaps he might give them one of several immutable economic truisms which he had gathered from his long years of economic study... 'It is an immutable economic fact,' said the general, 'that there is no such thing as a free lunch.'"[2]

"Oh, 'tanstaafl'. Means 'There ain't no such thing as a free lunch.' And isn't," I added, pointing to a FREE LUNCH sign across room, "or these drinks would cost half as much. Was reminding her that anything free costs twice as much in the long run or turns out worthless."

o Manuel in The Moon Is a Harsh Mistress (1966), chapter 11, p. 162, by Robert A. Heinlein[3]

"There's no such thing as a free lunch." o popularized by economist Milton Friedman[4]; o Contrary to rumor, New York Mayor Fiorello LaGuardia did not say it in Latin in

1934; what he really said, in Italian, was "No more free lunch" (current references: linguistlist and a speech by George H. W. Bush; more references needed).

The book TANSTAAFL, the economic strategy for environmental crisis, by Edwin G. Dolan (Holt, Rinehart and Winston, 1971, ISBN 0-03-086315-5) may be the first published use of the term in the economics literature.

Malcolm Fraser, prime minister of Australia, was a fond user of this phrase [citation needed]. Spider Robinson's 2001 book 'The Free Lunch' draws its name from the TANSTAAFL

concept.

Triangle arbitrage

Triangle arbitrage (also known as triangular arbitrage) refers to taking advantage of a state of imbalance between three markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices.

Triangular arbitrage offers a risk-free profit (in theory), so opportunities for triangular arbitrage usually disappear quickly, as many people are looking for them.

Example

Suppose the exchange rate between:

the Canadian Dollar (CD$) and the US dollar (US$) is CD$1.13/US$1.00 in Canada (1 USD gets you CD$1.13)

the Australian Dollar (AU$) and the US dollar (US$) is AU$1.33/US$1.00 in Australia (1 USD gets you AU$1.33)

the Australian Dollar (AU$) and the Canadian Dollar (CD$) is AU$1.18/CD$1.00 (1 CD gets you AU$1.18)

Assuming that a US investor has US$10,000 to invest, he will:

1st) Buy Canadian Dollars with his US Dollars: US$10,000 * (CD$1.13/US$1) = CD$11,300

2nd) Buy Australian Dollars with his Canadian Dollars: CD$11,300 * (AU$1.18/CD$1.00) = AU$13,334

3rd) Buy US Dollars with his Australian Dollars: AU$13,334 / (AU$1.33/US$1.0000) = US$10,025

4th) Profit: US$25.00 Risk Free

Uncovered interest arbitrage

Uncovered interest arbitrage is a form of arbitrage where funds are transferred abroad to take advantage of higher interest in foreign monetary centers. It involves the conversion of the domestic currency to the foreign currency to make investment; and subsequent re-conversion of the fund from the foreign currency to the domestic currency at the time of maturity. A foreign exchange risk is involved due to the possible depreciation of the foreign currency during the period of the investment.

Value investingValue investing is a style of investment strategy from the so-called "Graham & Dodd" School. Followers of this style, known as value investors, generally buy companies whose shares appear underpriced by some forms of fundamental analysis; these may include shares that are trading at, for example, high dividend yields or low price-to-earning or price-to-book ratios.

The main proponents of value investing, such as Benjamin Graham and Warren Buffett, have argued that the essence of value investing is buying stocks at less than their intrinsic value.[1] The discount of the market price to the intrinsic value is what Benjamin Graham called the "margin of safety". The intrinsic value is the discounted value of all future distributions.

However, the future distributions and the appropriate discount rate can only be assumptions. Warren Buffett has taken the value investing concept even further as his thinking has evolved to where for the last 25 years or so his focus has been on "finding an outstanding company at a sensible price" rather than generic companies at a bargain price, this concept is important as you are actually buying into a business.

HistoryValue investing was established by Benjamin Graham and David Dodd, both professors at Columbia University and teachers of many famous investors. In Graham's book The Intelligent Investor, he advocated the important concept of margin of safety — first introduced in Security Analysis, a 1934 book he coauthored with David Dodd — which calls for a cautious approach to investing. In terms of picking stocks, he recommended defensive investment in stocks trading

below their tangible book value as a safeguard to adverse future developments often encountered in the stock market.

Further evolutionHowever, the concept of value (as well as "book value") has evolved significantly since the 1970s. Book value is most useful in industries where most assets are tangible. Intangible assets such as patents, software, brands, or goodwill are difficult to quantify, and may not survive the break-up of a company. When an industry is going through fast technological advancements, the value of its assets is not easily estimated. Sometimes, the production power of an asset can be significantly reduced due to competitive disruptive innovation and therefore its value can suffer permanent impairment. One good example of decreasing asset value is a personal computer. An example of where book value does not mean much is the service and retail sectors. One modern model of calculating value is the discounted cash flow model (DCF). The value of an asset is the sum of its future cash flows, discounted back to the present.

Value Investing Performance

Performance, value strategiesValue investing has proven to be a successful investment strategy. There are several ways to evaluate its success. One way is to examine the performance of simple value strategies, such as buying low PE ratio stocks, low price-to-cash-flow ratio stocks, or low price-to-book ratio stocks. Numerous academics have published studies investigating the effects of buying value stocks. These studies have consistently found that value stocks outperform growth stocks and the market as a whole.[2][3][4]

Performance, value investorsAnother way to examine the performance of value investing strategies is to examine the investing performance of well-known value investors. Simply examining the performance of the best known value investors would not be instructive, because investors do not become well known unless they are successful. This introduces a selection bias. A better way to investigate the performance of a group of value investors was suggested by Warren Buffett, in his May 17, 1984 speech that was published as The Superinvestors of Graham-and-Doddsville. In this speech, Buffett examined the performance of those investors who worked at Graham-Newman Corporation and were thus most influenced by Benjamin Graham. Buffett's conclusion is identical to that of the academic research on simple value investing strategies--value investing is, on average, successful in the long run.

During about a 25-year period (1965-90), published research and articles in leading journals of the value ilk were few. Warren Buffett once commented, "You couldn't advance in a finance department in this country unless you thought that the world was flat."[5]

Well Known Value InvestorsBenjamin Graham is regarded by many to be the father of value investing. Along with David Dodd, he wrote Security Analysis, first published in 1934. The most lasting contribution of this book to the field of security analysis was to emphasize the quantifiable aspects of security analysis (such as the evaluations of earnings and book value) while minimizing the importance of more qualitative factors such as the quality of a company's management. Graham later wrote The Intelligent Investor, a book that brought value investing to individual investors. Aside from Buffett, many of Graham's other students, such as William J. Ruane, Irving Kahn and Charles Brandes have gone on to become successful investors in their own right.

Graham's most famous student, however, was Warren Buffett, who ran successful investing partnerships before closing them in 1969 to focus on running Berkshire Hathaway. Charlie Munger joined Buffett at Berkshire Hathaway in the 1970s and has since worked as Vice Chairman of the company. Buffett has credited Munger with encouraging him to focus on long-term sustainable growth rather than on simply the valuation of current cash flows or assets.[6]

Another famous value investor is John Templeton. He first achieved investing success by buying shares of a number of companies in the aftermath of the stock market crash of 1929.

Martin J. Whitman is another well-regarded value investor. His approach is called safe-and-cheap, which was hitherto referred to as financial-integrity approach. Martin Whitman focuses on acquiring common shares of companies with extremely strong financial position at a price reflecting meaningful discount to the estimated NAV of the company concerned. Martin Whitman believes it is ill-advised for investors to pay much attention to the trend of macro-factors (like employment, movement of interest rate, GDP, etc.) not so much because they are not important as because attempts to predict their movement are almost always futile. Martin Whitman's letters to shareholders of his Third Avenue Value Fund (TAVF) are considered valuable resources "for investors to pirate good ideas" by another famous investor Joel Greenblatt in his book on special-situation investment "You Can Be a Stock Market Genius" (ISBN 0-684-84007-3)(pp 247)

Joel Greenblatt achieved annual returns at the hedge fund Gotham Capital of over 50% per year for 10 years from 1985 to 1995 before closing the fund and returning his investors' money. He is known for investing in special situations such as spin-offs, mergers, and divestitures. Edward Lampert is the chief of ESL Investments. He is best known for buying large stakes in Sears and Kmart and then merging the two companies.

Volatility arbitrageVolatility arbitrage (or vol arb) is a type of statistical arbitrage that is implemented by trading a delta neutral portfolio of an option and its underlier. The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility of the option's underlier. In volatility arbitrage, volatility is used as the unit of relative measure rather than price - that is, traders attempt to buy volatility when it is low and sell volatility when it is high.

OverviewTo an option trader engaging in volatility arbitrage, an option contract is a way to speculate in the volatility of the underlying rather than a directional bet on the underlier's price. If a trader buys options as part of a delta-neutral portfolio, he is said to be long volatility. If he sells options, he is said to be short volatility. So long as the trading is done delta-neutral, buying an option is a bet that the underlier's future realized volatility will be high, while selling an option is a bet that future realized volatility will be low. Because of put call parity, it doesn't matter if the options traded are calls or puts. This is true because put-call parity posits a risk neutral equivalence relationship between a call, a put and some amount of the underlier. Therefore, being long a delta neutral call results in the same returns as being long a delta neutral put.Forecast VolatilityTo engage in volatility arbitrage, a trader must first forecast the underlier's future realized volatility. This is typically done by computing the historic daily returns for the underlier for a given past sample such as 252 days, the number of trading days in a year. The trader may also use other factors, such as whether the period was unusually volatile, or if there are going to be

unusual events in the near future, to adjust his forecast. For instance, if the current 252-day volatility for the returns on a stock is computed to be 15%, but it's known that an important patent dispute will likely be settled in the next year, the trader may decide that the appropriate forecast volatility for the stock is 18%. That is, based on past movements and upcoming events, the stock is most likely to be 18% higher or lower from its current price one year from today.

Market (Implied) Volatility

As described in option valuation techniques, there are a number of factors that are used to determine the theoretical value of an option. However, in practice, the only two inputs to the model that change during the day are the price of the underlier and the volatility. Therefore, the theoretical price of an option can be expressed as:

where is the price of the underlier, and is the estimate of future volatility. Because the

theoretical price function is a monotonically increasing function of , there must be a

corresponding monotonically increasing function that expresses the volatility implied by the

option's market price , or

Or, in other words, when all other inputs including the stock price are held constant, there exists

no more than one implied volatility for each market price for the option.

Because implied volatility of an option can remain constant even as the underlier's value changes, traders use it as a measure of relative value rather than the option's market price. For instance, if a trader can buy an option whose implied volatility is 10%, it's common to say that the trader can "buy the option for 10%". Conversely, if the trader can sell an option whose implied volatility is 20%, it is said the trader can "sell the option at 20%".

For example, assume a call option is trading at $1.90 with the underlier's price at $45.50, yielding an implied volatility of 17.5%. A short time later, the same option might trade at $2.50 with the underlier's price at $46.36, yielding an implied volatility of 16.8%. Even though the option's price is higher at the second measurement, the option is still considered cheaper because the implied volatility is lower. The reason this is true is because the trader can sell stock needed to hedge the long call at a higher price.

MechanismArmed with a forecast volatility, and capable of measuring an option's market price in terms of implied volatility, the trader is ready to begin a volatility arbitrage trade. A trader looks for options where the implied volatility, is either significantly lower than or higher than the forecast realized volatility , for the underlier. In the first case, the trader buys the option and hedges with the underlier to make a delta neutral portfolio. In the second case, the trader sells the option and then hedges them.

Over the holding period, the trader will realize a profit on the trade if the underlier's realized volatility is closer to his forecast than it is to the market's forecast (i.e. the implied volatility). The profit is extracted from the trade through the continual re-hedging required to keep the portfolio delta neutral.

Fixed income arbitrageFixed-income arbitrage is an investment strategy generally associated with hedge funds, which consists of the discovery and exploitation of inefficiencies in the pricing of bonds, i.e. instruments from either public or private issuers yielding a contractually fixed stream of income.

Most arbitrageurs who employ this strategy trade globally.

In pursuit of their goal of both steady returns and low volatility, the arbitrageurs can focus upon interest rate swaps, US non-US government bond arbitrage, see US Treasury security, forward yield curves, and/or mortgage-backed securities.

The practice of fixed-income arbitrage in general has been compared to that of running in front of a steam roller to pick up nickels lying on the street [1].

Rational pricingRational pricing is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

Arbitrage mechanicsArbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.e. after transaction costs, storage costs, transport costs, dividends etc.) the arbitrageur "locks in" a risk free profit without investing any of his own money.

In general, arbitrage ensures that "the law of one price" will hold; arbitrage also equalises the prices of assets with identical cash flows, and sets the price of assets with known future cash flows.

The law of one priceThe same asset must trade at the same price on all markets ("the law of one price"). Where this is not true, the arbitrageur will:

buy the asset on the market where it has the lower price, and simultaneously sell it (short) on the second market at the higher price

deliver the asset to the buyer and receive that higher price pay the seller on the cheaper market with the proceeds and pocket the difference.

Assets with identical cash flowsTwo assets with identical cash flows must trade at the same price. Where this is not true, the arbitrageur will:

sell the asset with the higher price (short sell) and simultaneously buy the asset with the lower price

fund his purchase of the cheaper asset with the proceeds from the sale of the expensive asset and pocket the difference

deliver on his obligations to the buyer of the expensive asset, using the cash flows from the cheaper asset.

An asset with a known future-price

An asset with a known price in the future, must today trade at that price discounted at the risk free rate.

Note that this condition can be viewed as an application of the above, where the two assets in question are the asset to be delivered and the risk free asset.

(a) where the discounted future price is higher than today's price:

1. The arbitrageur agrees to deliver the asset on the future date (i.e. sells forward) and simultaneously buys it today with borrowed money.

2. On the delivery date, the arbitrageur hands over the underlying, and receives the agreed price.

3. He then repays the lender the borrowed amount plus interest. 4. The difference between the agreed price and the amount owed is the arbitrage profit.

(b) where the discounted future price is lower than today's price:

1. The arbitrageur agrees to pay for the asset on the future date (i.e. buys forward) and simultaneously sells (short) the underlying today; he invests the proceeds.

2. On the delivery date, he cashes in the matured investment, which has appreciated at the risk free rate.

3. He then takes delivery of the underlying and pays the agreed price using the matured investment.

4. The difference between the maturity value and the agreed price is the arbitrage profit.

It will be noted that (b) is only possible for those holding the asset but not needing it until the future date. There may be few such parties if short-term demand exceeds supply, leading to backwardation.

Fixed income securitiesRational pricing is one approach used in pricing fixed rate bonds. Here, each cash flow can be matched by trading in some multiple of a "risk free" government issue zero coupon bond with the corresponding maturity, or in a corresponding strip and ZCB.

Given that the cash flows can be replicated, the price of the bond, must today equal the sum of each of its cash flows discounted at the same rate as the corresponding government securities - i.e. the corresponding risk free rate (here, assuming similar credit worthiness). Were this not the case, arbitrage would be possible and would bring the price back into line with the price based on the government issued securities.

The pricing formula is as below, where each cash flow is discounted at the rate which matches that of the corresponding government zero coupon instrument:

Price =

Often, the formula is expressed as , using prices instead of rates, as prices are more readily available.

Pricing derivatives

A derivative is an instrument which allows for buying and selling of the same asset on two markets – the spot market and the derivatives market. Mathematical finance assumes that any imbalance between the two markets will be arbitraged away. Thus, in a correctly priced derivative contract, the derivative price, the strike price (or reference rate), and the spot price will be related such that arbitrage is not possible.

Futures

In a futures contract, for no arbitrage to be possible, the price paid on delivery (the forward price) must be the same as the cost (including interest) of buying and storing the asset. In other words, the rational forward price represents the expected future value of the underlying discounted at the risk free rate. Thus, for a simple, non-dividend paying asset, the value of the future/forward,

, will be found by discounting the present value at time to maturity by the rate of risk-free return .

This relationship may be modified for storage costs, dividends, dividend yields, and convenience yields; see futures contract pricing.

Any deviation from this equality allows for arbitrage as follows.

In the case where the forward price is higher:

1. The arbitrageur sells the futures contract and buys the underlying today (on the spot market) with borrowed money.

2. On the delivery date, the arbitrageur hands over the underlying, and receives the agreed forward price.

3. He then repays the lender the borrowed amount plus interest. 4. The difference between the two amounts is the arbitrage profit.

In the case where the forward price is lower:

1. The arbitrageur buys the futures contract and sells the underlying today (on the spot market); he invests the proceeds.

2. On the delivery date, he cashes in the matured investment, which has appreciated at the risk free rate.

3. He then receives the underlying and pays the agreed forward price using the matured investment. [If he was short the underlying, he returns it now.]

4. The difference between the two amounts is the arbitrage profit.

OptionsAs above, where the value of an asset in the future is known (or expected), this value can be used to determine the asset's rational price today. In an option contract, however, exercise is dependent on the price of the underlying, and hence payment is uncertain. Option pricing models therefore include logic which either "locks in" or "infers" this value; both approaches deliver identical results. Methods which lock-in future cash flows assume arbitrage free pricing, and those which infer expected value assume risk neutral valuation.

To do this, (in their simplest, though widely used form) both approaches assume a “Binomial model” for the behavior of the underlying instrument, which allows for only two states - up or down. If S is the current price, then in the next period the price will either be S up or S down. Here, the value of the share in the up-state is S × u, and in the down-state is S × d (where u and d are multipliers with d < 1 < u and assuming d < 1+r < u; see the binomial options model). Then, given these two states, the "arbitrage free" approach creates a position which will have an identical value in either state - the cash flow in one period is therefore known, and arbitrage pricing is applicable. The risk neutral approach infers expected option value from the intrinsic values at the later two nodes.

Although this logic appears far removed from the Black-Scholes formula and the lattice approach in the Binomial options model, it in fact underlies both models; see The Black-Scholes PDE. The assumption of binomial behaviour in the underlying price is defensible as the number of time steps between today (valuation) and exercise increases, and the period per time-step is increasingly short. The Binomial options model allows for a high number of very short time-steps (if coded correctly), while Black-Scholes, in fact, models a continuous process.

The examples below have shares as the underlying, but may be generalised to other instruments. The value of a put option can be derived as below, or may be found from the value of the call using put-call parity.

Arbitrage free pricing

Here, the future payoff is "locked in" using either "delta hedging" or the "replicating portfolio" approach. As above, this payoff is then discounted, and the result is used in the valuation of the option today.

Delta hedging

It is possible to create a position consisting of Δ calls sold and 1 share, such that the position’s value will be identical in the S up and S down states, and hence known with certainty (see Delta hedging). This certain value corresponds to the forward price above, and as above, for no arbitrage to be possible, the present value of the position must be its expected future value discounted at the risk free rate, r. The value of a call is then found by equating the two.

1) Solve for Δ such that:

value of position in one period = S up - Δ × (S up – strike price ) = S down - Δ × (S down – strike price)

2) solve for the value of the call, using Δ, where:

value of position today = value of position in one period ÷ (1 + r) = S current – Δ × value of call

The replicating portfolio

It is possible to create a position consisting of Δ shares and $B borrowed at the risk free rate, which will produce identical cash flows to one option on the underlying share. The position created is known as a "replicating portfolio" since its cash flows replicate those of the option. As shown, in the absence of arbitrage opportunities, since the cash flows produced are identical, the price of the option today must be the same as the value of the position today.

1) Solve simultaneously for Δ and B such that:

i) Δ × S up - B × (1 + r) = MAX ( 0, S up – strike price ) ii) Δ × S down - B × (1 + r) = MAX ( 0, S down – strike price )

2) solve for the value of the call, using Δ and B, where:

call = Δ × S current - B

Risk neutral valuation

Here the value of the option is calculated using the risk neutrality assumption. Under this assumption, the “expected value” (as opposed to "locked in" value) is discounted. The expected value is calculated using the intrinsic values from the later two nodes: “Option up” and “Option down”, with u and d as price multipliers as above. These are then weighted by their respective probabilities: “probability” p of an up move in the underlying, and “probability” (1-p) of a down move. The expected value is then discounted at r, the risk free rate.

1) solve for p

for no arbitrage to be possible in the share, today’s price must represent its expected value discounted at the risk free rate: S = [ p × (up value) + (1-p) ×(down value) ] ÷ (1+r) = [ p × S × u + (1-p) × S × d ] ÷ (1+r) then, p = [(1+r) - d ] ÷ [ u - d ]

2) solve for call value, using p

for no arbitrage to be possible in the call, today’s price must represent its expected value discounted at the risk free rate: Option value = [ p × Option up + (1-p)× Option down] ÷ (1+r) = [ p × (S up - strike) + (1-p)× (S down - strike) ] ÷ (1+r)

The risk neutrality assumption

Note that above, the risk neutral formula does not refer to the volatility of the underlying – p as solved, relates to the risk-neutral measure as opposed to the actual probability distribution of prices. Nevertheless, both Arbitrage free pricing and Risk neutral valuation deliver identical results. In fact, it can be shown that “Delta hedging” and “Risk neutral valuation” use identical formulae expressed differently. Given this equivalence, it is valid to assume “risk neutrality” when pricing derivatives.

SwapsRational pricing underpins the logic of swap valuation. Here, two counterparties "swap" obligations, effectively exchanging cash flow streams calculated against a notional principal amount, and the value of the swap is the present value (PV) of both sets of future cash flows "netted off" against each other.

Valuation at initiationTo be arbitrage free, the terms of a swap contract are such that, initially, the Net present value of these future cash flows is equal to zero; see swap valuation. For example, consider a fixed-to-floating Interest rate swap where Party A pays a fixed rate, and Party B pays a floating rate. Here, the fixed rate would be such that the present value of future fixed rate payments by Party A is equal to the present value of the expected future floating rate payments (i.e. the NPV is zero). Were this not the case, an Arbitrageur, C, could:

assume the position with the lower present value of payments, and borrow funds equal to this present value

meet the cash flow obligations on the position by using the borrowed funds, and receive the corresponding payments - which have a higher present value

use the received payments to repay the debt on the borrowed funds pocket the difference - where the difference between the present value of the loan and

the present value of the inflows is the arbitrage profit.

Subsequent valuationOnce traded, swaps can also be priced using rational pricing. For example, the Floating leg of an interest rate swap can be "decomposed" into a series of Forward rate agreements. Here, since the swap has identical payments to the FRA, arbitrage free pricing must apply as above - i.e. the value of this leg is equal to the value of the corresponding FRAs. Similarly, the "receive-fixed" leg of a swap, can be valued by comparison to a Bond with the same schedule of payments.

Pricing sharesThe Arbitrage pricing theory (APT), a general theory of asset pricing, has become influential in the pricing of shares. APT holds that the expected return of a financial asset, can be modelled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor specific beta coefficient:

where

E(rj) is the risky asset's expected return,

rf is the risk free rate,

Fk is the macroeconomic factor,

bjk is the sensitivity of the asset to factor k,

and εj is the risky asset's idiosyncratic random shock with mean zero.

The model derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by model. If the price diverges, arbitrage should bring it back into line. Here, to perform the arbitrage, the investor “creates” a correctly priced asset (a synthetic asset) being a portfolio which has the same net-exposure to each of the macroeconomic factors as the mispriced asset but a different expected return; see the APT article for detail on the construction of the portfolio. The arbitrageur is then in a position to make a risk free profit as follows:

Where the asset price is too low, the portfolio should have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate. The arbitrageur could therefore:

Today: short sell the portfolio and buy the mispriced-asset with the proceeds.

At the end of the period: sell the mispriced asset, use the proceeds to buy back the portfolio, and pocket the difference.

Where the asset price is too high, the portfolio should have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at less than this rate. The arbitrageur could therefore:

1. Today: short sell the mispriced-asset and buy the portfolio with the proceeds. 2. At the end of the period: sell the portfolio, use the proceeds to buy back the mispriced-

asset, and pocket the difference.

Note that under "true arbitrage", the investor locks-in a guaranteed payoff, whereas under APT arbitrage, the investor locks-in a positive expected payoff. The APT thus assumes "arbitrage in expectations" - i.e that arbitrage by investors will bring asset prices back into line with the returns expected by the model.

The Capital asset pricing model (CAPM) is an earlier, (more) influential theory on asset pricing. Although based on different assumptions, the CAPM can, in some ways, be considered a "special case" of the APT; specifically, the CAPM's Securities market line represents a single-factor model of the asset price, where Beta is exposure to changes in value of the Market.

Fundamental theorem of arbitrage-free pricing

In a general sense, the fundamental theorem of arbitrage/finance is a way to relate arbitrage opportunities with risk neutral measures that are equivalent to the original probability measure.

The fundamental theorem in a finite state market

In a finite state market, the fundamental theorem of arbitrage has two parts. The first part relates to existence of a risk neutral measure, while the second relates to the uniqueness of the measure (see Harrison and Pliska):

1. The first part states that there is no arbitrage if and only if there exists a risk neutral measure that is equivalent to the original probability measure.

2. The second part states that a market is complete if and only if there is a unique risk neutral measure that is equivalent to the original probability measure.

The fundamental theorem of pricing is a way for the concept of arbitrage to be converted to a question about whether or not a risk neutral measure exists.

The fundamental theorem in more general markets

When stock price returns follow a single Brownian motion, there is a unique risk neutral measure. When the stock price process is assumed to follow a more general semi-martingale (see Delbaen and Schachermayer), then the concept of arbitrage is too strong, and a weaker concept such as no free lunch with vanishing risk must be used to describe these opportunities in an infinite dimensional setting.

Capital asset pricing model

The Security Market Line, seen here in a graph, describes a relation between the beta and the asset's expected rate of return.

An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial Average over the last 3 years for monthly data.

The Capital Asset Pricing Model (CAPM) is used in finance to determine a theoretically appropriate required rate of return (and thus the price if expected cash flows can be estimated) of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM formula takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), in a number often referred to as beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in Economics (jointly with Harry Markowitz and Merton Miller) for this contribution to the field of financial economics.

The formula

The CAPM is a model for pricing an individual security (asset) or a portfolio. For individual security perspective, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

Individual security’s / beta = Market’s securities (portfolio) Reward-to-risk ratio Reward-to-risk ratio

,

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E(Ri), we obtain the Capital Asset Pricing Model (CAPM).

Where:

is the expected return on the capital asset

is the risk-free rate of interest

(the beta coefficient) the sensitivity of the asset returns to market returns, or also

,

is the expected return of the market

is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return). Note 1: the expected market rate of return is usually measured by looking at the arithmetic average of the historical returns on a market portfolio (i.e. S&P 500). Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

For the full derivation see Modern portfolio theory.

Asset pricing

Once the expected return, E(Ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate (E(Ri)), to establish the correct price for the asset.

In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation).

Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

Asset-specific required returnThe CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. The CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and diversificationThe risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by

including a greater number of assets in the portfolio. (specific risks "average out"); systematic risk (within one market) cannot. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as UK or US (more in case of developing markets because of higher asset volatilities) will render the portfolio sufficiently diversified to limit exposure to systemic risk only.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor.

The efficient frontier

The (Markowitz) efficient frontier

The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Because the unsystemic risk is diversifiable, the total risk of a portfolio can be viewed as beta.

The market portfolioAn investor might choose to invest a proportion of his or her wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund his or her purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset does not determine overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways:

1. By investing all of one's wealth in a risky portfolio, 2. or by investing a proportion in a risky portfolio and the remainder in cash (either

borrowed or invested).

For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2 will generally have the lower variance and hence be the more efficient of the two.

This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio.

Assumptions of CAPM

All investors have rational expectations. There are no arbitrage opportunities. Returns are distributed normally. Fixed quantity of assets. Perfectly efficient capital markets. Investors are solely concerned with level and uncertainty of future wealth Separation of financial and production sectors. Thus, production plans are fixed. Risk-free rates exist with limitless borrowing capacity and universal access. The Risk-free borrowing and lending rates are equal. No inflation and no change in the level of interest rate exists. Perfect information, hence all investors have the same expectations about security returns

for any given time period.

Shortcomings of CAPM

The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.

The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).

The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.

The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets. (Homogeneous expectations assumption)

The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.

The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.

The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll's Critique. Theories such as the Arbitrage Pricing Theory (APT) have since been formulated to circumvent this problem.

Because CAPM prices a stock in terms of all stocks and bonds, it is really an arbitrage pricing model which throws no light on how a firm's beta gets determined.

Modern portfolio theory

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Capital Market Line

Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced. The basic concepts of the theory

are Markowitz diversification, the efficient frontier, capital asset pricing model, the alpha and beta coefficients, the Capital Market Line and the Securities Market Line.

MPT models an asset's return as a random variable, and models a portfolio as a weighted combination of assets; the return of a portfolio is thus the weighted combination of the assets' returns. Moreover, a portfolio's return is a random variable, and consequently has an expected value and a variance. Risk, in this model, is the standard deviation of the portfolio's return.

Risk and rewardThe model assumes that investors are risk averse. This means that given two assets that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher returns must accept more risk. The exact trade-off will differ by investor based on individual risk aversion characteristics. The implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more favourable risk-return profile - i.e. if for that level of risk an alternative portfolio exists which has better expected returns.

Mean and varianceIt is further assumed that investor's risk / reward preference can be described via a quadratic utility function. The effect of this assumption is that only the expected return and the volatility (i.e. mean return and standard deviation) matter to the investor. The investor is indifferent to other characteristics of the distribution of returns, such as its skew. Note that the theory uses a historical parameter, volatility, as a proxy for risk, while return is an expectation on the future.

Recent innovations in portfolio theory, particularly under the rubric of Post-Modern Portfolio Theory (PMPT), have exposed many flaws in this total reliance on standard deviation as the investor's risk proxy.

Under the model:

Portfolio return is the proportion-weighted combination of the constituent assets' returns. Portfolio volatility is a function of the correlation of the component assets. The change in

volatility is non-linear as the weighting of the component assets changes.

Mathematically

In general:

Expected return:

Where R is return. Portfolio variance:

Portfolio volatility:

For a two asset portfolio:

Portfolio return:

Portfolio variance:

For a three asset portfolio, the variance is:

As can be seen, as the number of assets (n) in the portfolio increases, the calculation becomes “computationally intensive” - the number of covariance terms = n (n-1) /2. For this reason, portfolio computations usually require specialized software. These values can also be modeled using matrices; for a manageable number of assets, these statistics can be calculated using a spreadsheet.

DiversificationAn investor can reduce portfolio risk simply by holding instruments which are not perfectly correlated. In other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets. Diversification will allow for the same portfolio return with reduced risk. For diversification to work the component assets must not be perfectly correlated, i.e. correlation coefficient not equal to 1.

As the formula above shows, if all assets of a portfolio have a correlation of 0, the portfolio variance and hence volatility will be the weighted average of the individual instruments' volatilities. If correlation is less than zero, that is, the assets are inversely correlated, the portfolio's volatility is less than the weighted average of the volatilities, and vice-versa.

Capital allocation line

The Capital Allocation Line (CAL) is the line of expected return plotted against risk (standard deviation) that connects all portfolios that can be formed using a risky asset and a riskless asset. It can be proven that it is a straight line and that it has the following equation.

In this formula P is the risky portfolio, F is the riskless portfolio and C is a combination of portfolios P and F.

The efficient frontier

Efficient Frontier

Every possible asset combination can be plotted in risk-return space, and the collection of all such possible portfolios defines a region in this space. The line along the upper edge of this region is known as the efficient frontier (sometimes “the Markowitz frontier”). Combinations along this line represent portfolios for which there is lowest risk for a given level of return. Conversely, for a given amount of risk, the portfolio lying on the efficient frontier represents the combination offering the best possible return. Mathematically the Efficient Frontier is the intersection of the Set of Portfolios with Minimum Variance and the Set of Portfolios with Maximum Return.

The efficient frontier is illustrated above, with return μp on the y axis, and risk σp on the x axis; an alternative illustration from the diagram in the CAPM article is at right.

The efficient frontier will be convex – this is because the risk-return characteristics of a portfolio change in a non-linear fashion as its component weightings are changed. (As described above, portfolio risk is a function of the correlation of the component assets, and thus changes in a non-linear fashion as the weighting of component assets changes.) The efficient frontier is a parabola (hyperbola) when expected return is plotted against variance (standard deviation).

The region above the frontier is unachievable by holding risky assets alone. No portfolios can be constructed corresponding to the points in this region. Points below the frontier are suboptimal. A rational investor will hold a portfolio only on the frontier. 1

The risk-free asset

The risk-free asset is the (hypothetical) asset which pays a risk-free rate - it is usually proxied by an investment in short-dated Government securities. The risk-free asset has zero variance in returns (hence is risk-free); it is also uncorrelated with any other asset (by definition: since its variance is zero). As a result, when it is combined with any other asset, or portfolio of assets, the change in return and also in risk is linear.

Because both risk and return change linearly as the risk-free asset is introduced into a portfolio, this combination will plot a straight line in risk-return space. The line starts at 100% in cash and weight of the risky portfolio = 0 (i.e. intercepting the return axis at the risk-free rate) and goes through the portfolio in question where cash holding = 0 and portfolio weight = 1.

Mathematically

Using the formulae for a two asset portfolio as above:

Return is the weighted average of the risk free asset, f, and the risky portfolio, p, and is therefore linear:

Return =

Since the asset is risk free, portfolio standard deviation is simply a function of the weight of the risky portfolio in the position. This relationship is linear.

Standard deviation =

=

=

=

Portfolio leverage

An investor can add leverage to the portfolio by borrowing the risk-free asset. The addition of the risk-free asset allows for a position in the region above the efficient frontier. Thus, by combining a risk-free asset with risky assets, it is possible to construct portfolios whose risk-return profiles are superior to those on the efficient frontier.

An investor holding a portfolio of risky assets, with a holding in cash, has a positive risk-free weighting (a de-leveraged portfolio). The return and standard deviation will be lower than the portfolio alone, but since the efficient frontier is convex, this combination will sit above the efficient frontier – i.e. offering a higher return for the same risk as the point below it on the frontier.

The investor who borrows money to fund his/her purchase of the risky assets has a negative risk-free weighting -i.e a leveraged portfolio. Here the return is geared to the risky portfolio. This combination will again offer a return superior to those on the frontier.

The market portfolio

The efficient frontier is a collection of portfolios, each one optimal for a given amount of risk. A quantity known as the Sharpe ratio represents a measure of the amount of additional return (above the risk-free rate) a portfolio provides compared to the risk it carries. The portfolio on the efficient frontier with the highest Sharpe Ratio is known as the market portfolio, or sometimes the super-efficient portfolio; it is the tangency-portfolio in the above diagram.

This portfolio has the property that any combination of it and the risk-free asset will produce a return that is above the efficient frontier - offering a larger return for a given amount of risk than a portfolio of risky assets on the frontier would.

Capital market line

When the market portfolio is combined with the risk-free asset, the result is the Capital Market Line. All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier. (The market portfolio with zero cash weighting is on the efficient frontier; additions of cash or leverage with the risk-free asset in combination with the market portfolio are on the Capital Market Line. All of these portfolio represent the highest Sharpe ratios possible.)

The CML is illustrated above, with return μp on the y axis, and risk σp on the x axis.

One can prove that the CML is the optimal CAL and that its equation is:

Asset pricing

A rational investor would not invest in an asset which does not improve the risk-return characteristics of his existing portfolio. Since a rational investor would hold the market portfolio, the asset in question will be added to the market portfolio. MPT derives the required return for a correctly priced asset in this context.

Systematic risk and specific risk

Specific risk is the risk associated with individual assets - within a portfolio these risks can be reduced through diversification (specific risks "cancel out"). Systematic risk, or market risk, refers to the risk common to all securities - except for selling short as noted below, systematic risk cannot be diversified away (within one market). Within the market portfolio, asset specific risk will be diversified away to the extent possible. Systematic risk is therefore equated with the risk (standard deviation) of the market portfolio.

Since a security will be purchased only if it improves the risk / return characteristics of the market portfolio, the risk of a security will be the risk it adds to the market portfolio. In this context, the volatility of the asset, and its correlation with the market portfolio, is historically observed and is therefore a given (there are several approaches to asset pricing that attempt to price assets by modelling the stochastic properties of the moments of assets' returns - these are broadly referred to as conditional asset pricing models). The (maximum) price paid for any particular asset (and hence the return it will generate) should also be determined based on its relationship with the market portfolio.

Systematic risks within one market can be managed through a strategy of using both long and short positions within one portfolio, creating a "market neutral" portfolio.

Security characteristic line

The Security Characteristic Line (SCL) represents the relationship between the market return (rM) and the return of a given asset i (ri) at a given time t. In general, it is reasonable to assume that the SCL is a straight line and can be illustrated as a statistical equation:

where αi is called the asset's alpha coefficient and βi the asset's beta coefficient.

Capital asset pricing model

The asset return depends on the amount for the asset today. The price paid must ensure that the market portfolio's risk / return characteristics improve when the asset is added to it. The CAPM is a model which derives the theoretical required return (i.e. discount rate) for an asset in a market, given the risk-free rate available to investors and the risk of the market as a whole.

The CAPM is usually expressed:

β, Beta, is the measure of asset sensitivity to a movement in the overall market; Beta is usually found via regression on historical data. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average.

is the market premium, the historically observed excess return of the market over the risk-free rate.

Once the expected return, E(ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate to establish the correct price for the asset. (Here again, the theory accepts in its assumptions that a parameter based on past data can be combined with a future expectation.)

A more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. In theory, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued; it is undervalued for a too low price.

Mathematically

(1) The incremental impact on risk and return when an additional risky asset, a, is added to the market portfolio, m, follows from the formulae for a two asset portfolio. These results are used to derive the asset appropriate discount rate.

Risk =

Hence, risk added to portfolio =

but since the weight of the asset will be relatively low,

i.e. additional risk =

Return =

Hence additional return = (2) If an asset, a, is correctly priced, the improvement in risk to return achieved by adding it to the market portfolio, m, will at least match the gains of spending that money on an increased stake in the market portfolio. The assumption is that the investor will purchase the asset with

funds borrowed at the risk-free rate, Rf; this is rational if . Thus:

i.e. :

i.e. :

is the “beta”, β -- the covariance between the asset and the market compared to the variance of the market, i.e. the sensitivity of the asset price to movement in the market portfolio.

Securities market line

The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The X-axis represents the risk (beta), and the Y-axis represents the expected return. The market risk premium is determined from the slope of the SML.

The relationship between Beta & required return is plotted on the securities market line (SML) which shows expected return as a function of β. The intercept is the

risk-free rate available for the market, while the slope is . The Securities market line can be regarded as representing a single-factor model of the asset price, where Beta is exposure to changes in value of the Market. The equation of the SML is thus:

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.

The Security Market Line

Comparison with arbitrage pricing theory

The SML and CAPM are often contrasted with the Arbitrage pricing theory (APT), which holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor specific beta coefficient.

The APT is less restrictive in its assumptions: it allows for an explanatory (as opposed to statistical) model of asset returns, and assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors - the number and nature of these factors is likely to change over time and between economies.

Super-diversification

The highest degree of diversification occurs when institutional asset class funds are used to construct a financial portfolio. The term was first introduced in Wealth Without Worry by Jim Whiddon and Lance Alston (Brown Books, 2005) who apply the fundamental academic research of Eugene Fama and Professor Kenneth French. See also: diversification, efficient market hypothesis and market portfolio theory.

A super-diversified, asset class portfolio holds somewhere between 10,000 and 12,000 securities through a smaller number of institutional asset class funds.

Earnings response coefficient

Introduction

In financial economics, arbitrage pricing theory describes the theoretical relationship between information that is known to market participants about a particular equity (e.g., a common stock share of a particular company) and the price of that equity. Under the efficient market hypothesis, equity prices are expected in the aggregate to reflect all relevant information at a given time. Market participants with superior information are expected to exploit that information until share prices have effectively impounded the information. Therefore, in the aggregate, a portion of changes in a company's share price is expected to result from changes in the relevant information available to the market.

The earnings response coefficient, or ERC, expresses the relationship between equity returns and the unexpected portion (i.e., new information) of companies' earnings announcements.

The ERC is expressed mathematically as follows:

R = a + b(ern − u) + e

R = the expected return a = benchmark rate b = earning response coefficint (ern-u) = (actual earnings less expected earnings) = unexpected earnings e = random movement

Use & Debate

ERCs are used primarily in research in Accounting and Finance. In particular, ERCs have been used in research in Positive Accounting, a branch of Financial Accounting research, as they theoretically describe how markets react to different information events. Research in Finance has used ERCs to study, among other things, how different investors react to information events. (Hotchkiss & Strickland 2003)

There is some debate concerning the true nature and strength of the ERC relationship. As demonstrated in the above model, the ERC is generally considered to be the slope coefficient of a linear equation between unexpected earnings and equity return. However, certain research results suggest that the relationship is nonlinear.(Freeman & Tse 1992)

Fair value

Fair value, also called fair price, is a concept used in finance and economics, defined as a rational and unbiased estimate of the potential market price of a good, service, or asset, taking into account such factors as:

relative scarcity

perceived utility (economist's term for subjective value based on personal needs)

risk characteristics

replacement costs, or costs of close substitutes

production/distribution costs, including a cost of capital

In accounting, fair value is used as an estimate of the market value of an asset (or liability) for which a market price cannot be determined (usually because there is no established market for the asset). This is used for assets whose carrying value is based on mark-to-market valuations; for assets carried at historical cost, the fair value of the asset is not used.

Fair value vs market priceThere are two schools of thought about the relation between the market price and fair value in any kind of market, but especially with regards to tradable assets:

The efficient market hypothesis asserts that, in a well organized, reasonably transparent market, the market price is generally equal to or close to the fair value, as investors react quickly to incorporate new information about relative scarcity, utility, or potential returns in their bids; see also Rational pricing.

Behavioral finance asserts that the market price often diverges from fair value because of various, common cognitive biases among buyers or sellers. However, even proponents of behavioral finance generally acknowledge that behavioral anomalies that may cause such a divergence often do so in ways that are unpredictable, chaotic, or otherwise difficult to capture in a sustainably profitable trading strategy, especially when accounting for transaction costs.

Fair Value Measurements (US markets): Exposure Draft

The Financial Accounting Standards Board (FASB) issued Exposure Draft 1201-100 on June 23, 2004, to provide proposed guidance about how entities should determine fair value estimations for financial reporting purposes. The draft would apply broadly to financial and nonfinancial assets and liabilities measured at fair value under other authoritative accounting pronouncements. Absence of one single consistent framework for applying fair value measurements and developing a reliable estimate of a fair value in the absence of quoted prices has created inconsistencies and incomparability. The purpose of this exposure draft is to eliminate the inconsistencies by developing a solid framework to be used in any fair value measurements.

The draft suggests the following definition for fair value: the price at which an asset or liability could be exchanged in a current transaction between knowledgeable, unrelated willing parties. It notes that the price is an estimate in the absence of an actual exchange.

The exposure draft emphasizes the use of market inputs in valuing an asset or liability. The specific market inputs mentioned include: quoted prices, interest rates, yield curve, credit data, etc. Fair value is, by definition, derived from a current transaction which happens in an active market with knowledgeable and unrelated parties. When fair value is not available due to the lack of an actual transaction, it is logical to use information from an active market. However, sometimes quoted prices might not represent the best estimate of fair value.

The basis of the framework in the exposure draft centers on a fair value hierarchy. The hierarchy is suggested as a guide to determining what inputs to include in valuing an asset or liability at fair value. The hierarchy is broken down into three levels. Level One requires the use of quoted prices from an active market for identical assets or liabilities. To use this level, the entity must have immediate access to the market (could exchange in current condition). If more than one market is available, the exposure draft requires the use of the “most advantageous market.” Both the price and costs to do the transaction must be considered.

Level Two requires the use of quoted prices for similar assets or liabilities in active markets. While in Level One an entity is not permitted to make any change to the quoted price, an entity may make price adjustments, as necessary, in Level Two since the assets or liabilities are only similar, not identical. It is stated, however, that any adjustment must be objective. If the adjustment is not objective or there are no similar goods in the active market, an entity must measure the fair value based on Level Three. This level requires the use of valuation techniques. The draft suggests the use of the market, income, and cost approach, unless the use of all three produces undue costs and effort. If that is the case, an entity is to use the approach that produces the best approximation of the fair value. Inputs used to determine the value should be external to the entity. The entity may only rely on internal information if the cost and effort to obtain external information is too high.

A working draft has been established for the fair value exposure draft. The working draft was released for comment on October 21, 2005. One of the noticeable changes in the working draft compared to the exposure draft is the addition of two more levels in the fair value hierarchy. Level three has been adjusted to only include assets or liabilities that have observable inputs other than quoted prices. It is also explained that financial instruments must have an input that is observable over the entire term of the instrument. The addition of the additional levels helps to eliminate the ambiguity associated with the first exposure draft. Instruments that have inputs that are not directly observable, but have corroboration through other data, are considered level four. Level Five encompasses any remaining valuation that requires all entity inputs and no market inputs.

Homo economicus

Homo economicus, or Economic man, is the concept in some economic theories of man (that is, a human) as a rational and self-interested actor who desires wealth, avoids unnecessary labor, and has the ability to make judgments towards those ends.

History of the term

The term Economic Man was used for the first time in the late nineteenth century by critics of John Stuart Mill’s work on political economy.[1][2] Below is a passage from Mill’s work that those 19th-century critics were referring to:

"[Political economy] does not treat the whole of man’s nature as modified by the social state, nor of the whole conduct of man in society. It is concerned with him solely as a being who desires to possess wealth, and who is capable of judging the comparative efficacy of means for obtaining that end."

Later in the same work, Mill goes on to write that he is proposing “an arbitrary definition of man, as a being who inevitably does that by which he may obtain the greatest amount of necessaries, conveniences, and luxuries, with the smallest quantity of labour and physical self-denial with which they can be obtained.”

Although the term did not come into use until the 19th century, it is often associated with the ideas of 18th century thinkers like Adam Smith and David Ricardo. In The Wealth of Nations, Smith wrote:

"It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest."

This suggests the same sort of rational, self-interested, labor-averse individual that Mill proposes. Aristotle's Politics discussed the nature of self interest in Book II, Part V.

"Again, how immeasurably greater is the pleasure, when a man feels a thing to be his own; for surely the love of self is a feeling implanted by nature and not given in vain, although selfishness is rightly censured; this, however, is not the mere love of self, but the love of self in excess, like the miser's love of money; for all, or almost all, men love money and other such objects in a measure. And further, there is the greatest pleasure in doing a kindness or service to friends or guests or companions, which can only be rendered when a man has private property."

A wave of economists in the late 19th century—Francis Edgeworth, William Stanley Jevons, Leon Walras, and Vilfredo Pareto—built mathematical models on these assumptions. In the 20th century, Lionel Robbins’ rational choice theory came to dominate mainstream economics and the term Economic Man took on a more specific meaning of a person who acted rationally on complete knowledge out of self-interest and the desire for wealth.

The model

Homo economicus is a term used for an approximation or model of Homo sapiens that acts to obtain the highest possible well-being for himself given available information about opportunities

and other constraints, both natural and institutional, on his ability to achieve his predetermined goals. This approach has been formalized in certain social science models, particularly in economics.

Homo economicus is seen as "rational" in the sense that well-being as defined by the utility function is optimized given perceived opportunities. That is, the individual seeks to attain very specific and predetermined goals to the greatest extent with the least possible cost. Note that this kind of "rationality" does not say that the individual's actual goals are "rational" in some larger ethical, social, or human sense, only that he tries to attain them at minimal cost. Only naïve applications of the Homo economicus model assume that this hypothetical individual knows what is best for his long-term physical and mental health and can be relied upon to always make the right decision for himself. See rational choice theory and rational expectations for further discussion; the article on rationality widens the discussion.

As in social science in general, these assumptions are at best approximations. The term is often used derogatorily in academic literature, perhaps most commonly by sociologists, many of whom tend to prefer structural explanations to ones based on rational action by individuals.

The use of the Latin form Homo economicus is certainly long established; Persky (1995) traces it back to Pareto (1906) but notes that it may be older. The English term economic man can be found even earlier, in John Kells Ingram's A History of Political Economy (1888). The Oxford English Dictionary (O.E.D.) does not mention Homo economicus, but it is one of a number of phrases that imitate the scientific name for the human species. According to the O.E.D., the human genus name Homo is

Used with L. or mock-L. adjs. in names imitating Homo sapiens, etc., and intended to personify some aspect of human life or behaviour (indicated by the adj.). Homo faber ("feIb@(r)) [H. Bergson L'Evolution Créatrice (1907) ii. 151], a term used to designate man as a maker of tools.) Variants are often comic: Homo insipiens; Homo turisticus. (This is from the CD edition of 2002.)

Note that such forms should logically keep the capital for the "genus" name—i.e., Homo economicus rather than homo economicus. Actual usage is inconsistent.

Criticisms

Homo economicus bases his choices on a consideration of his own personal "utility function". Economic man is also amoral, ignoring all social values unless adhering to them gives him utility. Some believe such assumptions about humans are not only empirically inaccurate but unethical.

Consequently, the "homo economicus" assumptions have been criticized not only by economists on the basis of logical arguments, but also on empirical grounds by cross-cultural comparison. Economic anthropologists such as Marshall Sahlins[5], Karl Polanyi[6], Marcel Mauss[7] or Maurice Godelier[8] have demonstrated that in traditional societies, choices people make regarding production and exchange of goods follow patterns of reciprocity differ sharply from what the "homo oeconomicus" model postulates. Such systems have been termed gift economy rather than market economy. Criticisms of the "homo oeconomicus" model put forward from the standpoint of Christian ethics usually refer to thís traditional ethics of kinship-based reciprocity that held

together traditional societies. They typically tend to view the egoistic and amoral behavior of "homo oeconomicus" as unethical conduct that may be functional within a competitive market economy but is not in line with, but fundamentally running against human nature and ethics.

Economists Thorstein Veblen, John Maynard Keynes, Herbert Simon, and many of the Austrian School criticise Homo economicus as an actor with too great of an understanding of macroeconomics and economic forecasting in his decision making. They stress uncertainty and bounded rationality in the making of economic decisions, rather than relying on the rational man who is fully informed of all circumstances impinging on his decisions. They argue that perfect knowledge never exists, which means that all economic activity implies risk.

Empirical studies by Amos Tversky questioned the assumption that investors are rational. In 1995, Tversky demonstrated the tendency of investors to make risk-averse choices in gains, and risk-seeking choices in losses. The investors appeared as very risk-averse for small losses but indifferent for a small chance of a very large loss. This violates economic rationality as usually understood. Further research on this subject, showing other deviations from conventionally-defined economic rationality, is being done in the growing field of experimental or behavioral economics. Some of the broader issues involved in this criticism are studied in Decision Theory of which Rational Choice Theory is only a subset.

Other critics of the Homo economicus model of humanity, such as Bruno Frey, point to the excessive emphasis on extrinsic motivation (rewards and punishments from the social environment) as opposed to intrinsic motivation. For example, it is difficult if not impossible to understand how Homo economicus would be a hero in war or would get inherent pleasure from craftsmanship. Frey and others argue that too much emphasis on rewards and punishments can "crowd out" (discourage) intrinsic motivation: paying a boy for doing household tasks may push him from doing those tasks "to help the family" to doing them simply for the reward.

Altruistic economics rejects the model as unrealistically selfish, arguing that real people have friends to whom they are to a greater or lesser degree altruistic, so it relaxes the restriction that people's utility functions must be independent.

Other critics argue that the purely self-interested behavior of the Homo economicus reflects the behavior of the psycopath and not that of the average participant in the economy. As such the Homo economicus can be considered to be a purely theoretcial construct.

Another weakness is highlighted by sociologists, who argue that Homo economicus ignores an extremely important question, i.e., the origins of tastes and the parameters of the utility function by social influences, training, education, and the like. The exogeneity of tastes (preferences) in this model is the major distinction from Homo sociologicus, in which tastes are taken as partially or even totally determined by the societal environment (see below).

Further critics, learning from the broadly-defined psychoanalytic tradition, criticize the Homo economicus model as ignoring the inner conflicts that real-world individuals suffer, as between short-term and long-term goals (e.g., eating chocolate cake and losing weight) or between individual goals and societal values. Such conflicts may lead to "irrational" behavior involving inconsistency, psychological paralysis, neurosis, and/or psychic pain.

One criticism contends that the Homo economicus model works as a self-fulfilling prophecy if a group of people (a company, a society) accepts its premises, particularly the idea that individuals

only ever consider their personal utility function and that—as is often claimed—the "Invisible Hand" works to make these purely self-interested decisions promote the interest of society. Governance structures and social norms of such a group will effectively reward selfishness and discourage or ridicule deviant behavior like altruism, fairness, or teamwork; its idols will be those who most ruthlessly maximize their own utility function. This aspect has risen to wider attention in disciplines like organization science where extrinsic motivation has been found to be not nearly as effective with knowledge workers as it had been for traditional industries, creating a renewed interest in forms of motivation that do not fit into the Homo economicus model. This view however does not account for the fact that acting selfishly is not necessarily the same as acting in a self-interested manner, especially in social units in which altruistic and unselfish behavior is expected.

The clearest case of a self-fulfilling prophecy concerning Homo economicus has been in the teaching of economics. Several research studies have indicated that those students who take economics courses end up being more self-centered than before they took the courses. For example, they are less willing to co-operate with the other player in a "prisoner's-dilemma"-type game. See, for example, the article by Thomas Frank et al. (1993), cited below.

Some critics conclude from this that the "homo oeconomicus" construct is not so much a result of empirical research into human nature (which would have to take into account results of comparative, cross-cultural and historical research such as provided by economic anthropologists), but rather an implicitly prescriptive construct in line with the amoral rationality of modern monetary economies, in other words: not a result of empirical scientific inquiry but rather part of the ideology of liberalism. According to this view, traditionally held by many marxists, "homo oeceonomicus" functions as a complement of the idea of liberal natural law for life, liberty, and property, sharing the same ideological pattern of attributing social and individual features that are products of history and belong into a specific social structure (civil society) to human nature, thus making them look inborn, natural and ahistorical, thus unchangeable. Some marxists consider this false generalization as an ideological form necessary for maintaining the basic social structure of civil society, just as other forms of social organizations have their own form of ideology that places taboos on certain basic features of social organization in order to stabilize overall social structure.

It is also worth taking note of the fact that the economists believing in "homo oeconomicus" have been remarkably unsuccessful in creating "homo oeconomicus" in many so called developing countries, where people just don't seem to be ready to behave as the economists would like them to and would have expect them to according to their model.

Responses

Economists tend to disagree with these critiques, arguing that it may be relevant to analyze the consequences of enlightened egoism just as it may be worthwhile to consider altruistic or social behavior. Others argue that we need to understand the consequences of such narrow-minded greed even if only a small percentage of the population embraces such motives. Free riders, for example, would have a major negative impact on the provision of public goods. However, economists' supply and demand predictions might obtain even if only a significant minority of market participants act like Homo economicus. In this view, the assumption of Homo economicus can and should be simply a preliminary step on the road to a more sophisticated model.

Yet others argue that Homo economicus is a reasonable approximation for behavior within market institutions, since the individualized nature of human action in such social settings encourages individualistic behavior. Not only do market settings encourage the application of a simple cost/benefit calculus by individuals, but they reward and thus attract the more individualistic people. It can be difficult to apply social values (as opposed to following self-interest) in an extremely competitive market; a company that refuses to pollute (for example) may find itself bankrupt.

Defenders of the Homo economicus model see many critics of the dominant school as using a straw-man technique. For example, it is common for critics to argue that real people do not have cost-less access to infinite information and an innate ability to instantly process it. However, in advanced-level theoretical economics, scholars have found ways of addressing these problems, modifying models enough to more realistically depict real-life decision-making. For example, models of individual behavior under bounded rationality and of people suffering from envy can be found in the literature. It is primarily when targeting the limiting assumptions made in constructing undergraduate models that the criticisms listed above are valid. These criticisms are especially valid to the extent that the professor asserts that the simplifying assumptions are true and/or uses them in a propagandistic way.

The more sophisticated economists are quite conscious of the empirical limitations of the Homo economicus model. In theory, the views of the critics can be combined with the Homo economicus model to attain a more accurate model.

One problem with making the Homo economicus model more sophisticated is that sometimes the model becomes tautologically true, i.e., true by definition. If someone has a "taste" for variety, for example, it becomes difficult if not impossible to distinguish economic rationality from irrationality. In this case, the Homo economicus model may not add any new information at all to our economic understanding.

Homo sociologicus

Comparisons between economics and sociology have resulted in a corresponding term Homo sociologicus (introduced by German Sociologist Ralf Dahrendorf in 1958), to parody the image of human nature given in some sociological models that attempt to limit the social forces that determine individual tastes and social values. (The alternative or additional source of these would be biology.) Hirsch, Michaels, and Friedman (1990, p. 44) say that Homo sociologicus is largely a tabula rasa upon which societies and cultures write values and goals; unlike economicus, sociologicus acts not to pursue selfish interests but to fulfill social roles. This "individual" may appear to be all society and no individual. This suggests the need to combine the insights of Homo economicus models with those of Homo sociologicus models in order to create a synthesis, rather than rejecting one or the other.

Rational choice theory

Rational choice theory, also known as rational action theory, is a framework for understanding and often formally modeling social and economic behavior. It is the dominant theoretical paradigm in microeconomics. It is also central to modern political science and is used by scholars in other disciplines such as sociology. The 'rationality' described by rational choice theory is different from colloquial and most philosophical uses of rationality. Models of rational choice are very diverse but they share one thing in common. They all assume that individuals choose the

best action according to stable preference functions and constraints facing them. Most models have additional assumptions. Proponents of rational choice models do not claim that a model's assumptions are a full description of reality, only that good models can aid reasoning and provide help in formulating falsifiable hypotheses, whether intuitive or not. Successful hypotheses are those that survive empirical tests.

Rational choice theory is a successor of much older descriptions of rational behavior.[citation needed] It is widely used as an assumption of the behavior of individuals in microeconomic models and analysis. Although rationality cannot be directly empirically tested, empirical tests can be conducted on some of the results derived from the models. Over the last decades it has also become increasingly employed in social sciences other than economics, such as sociology and political science.[1] It has had far-reaching impacts on the study of political science, especially in fields like the study of interest groups, elections, behaviour in legislatures, coalitions, and bureaucracy (Dunleavy, 1991).

Models that rely on rational choice theory often adopt methodological individualism, the assumption that social situations or collective behaviors are the result of individual actions.

Actions, Assumptions, and Individual Preferences

Rational decision making entails choosing an action given one's preferences, the actions one could take, and expectations about the outcomes of those actions. Actions are often expressed as a set, for example a set of j exhaustive and exclusive actions:

For example, if a person is to vote for either Roger, Sara, or abstain, her set of possible voting actions is:

A = {Roger,Sara,abstain}

Individuals can also have similar sets of possible outcomes.

Rational choice theory makes two assumptions about individuals' preferences for actions. First, is the assumption of completeness, that is that all actions can be ranked in an order of preference (indifference between two or more is possible). Second, is the transitivity, the assumption that if action a1 is preferred to a2, and action a2 is preferred to a3, then a1 is preferred to a3.

Together these assumptions form the result that given a set of exhaustive and exclusive actions to chose from, an individual can rank them in terms of her preferences, and that her preferences are consistent.

An individual's preferences can also take forms:

Strict Preference occurs when an individual prefers a1 to a2, but not a2 to a1. In some models, a weak preference can be held in which an individual has a preference for at least aj, similar to the mathematical operator ≤.

Indifference occurs when an individual does not prefer a1 to a2, or a2 to a1.

In more complex models, other assumptions are often incorporated, such as the assumption of independence axiom. Also, with dynamic models that include decision-making over time, time inconsistency may affect an individual's preferences.

Other Assumptions

Often, to simplify calculation and facilitate testing, some possibly unrealistic assumptions are made about the world. These can include:

An individual has full or perfect information about exactly what will occur under any choice made. More complex models rely on probability to describe outcomes.

An individual has the cognitive ability, or time to weigh every choice against every other choice. Studies in to the limitations of this assumption are included in theories of bounded rationality.

Utility Maximization

Often preferences are described by their utility function or payoff function. This is an ordinal number an individual assigns over the available actions, such as:

The individual's preferences are then expressed as the relation between these ordinal assignments. For example, if an individual prefers the candidate Sara over Roger over abstaining, their preferences would have the relation:

Criticism

Both the assumptions and the behavioral predictions of rational choice theory have sparked criticism from various camps. Some people have developed models of bounded rationality, which hope to be more psychologically plausible without completely abandoning the idea that reason underlies decision-making processes. For a long time, a popular strain of critique was a lack of empirical basis, but experimental economics and experimental game theory have largely changed that critique (although they have added other critiques, mainly by demonstrating some human behavior that consistently deviates from rational choice theory).[citation needed]

In their 1994 piece, Pathologies of Rational Choice Theory, Green and Shapiro argue that the empirical outputs of rational choice theory have been limited. They contend that much of the applicable literature, at least in Political Science, was done with weak methods and that when corrected many of the empirical outcomes no longer hold. When taken in this perspective, Rational Choice Theory has provided very little to the overall understanding of political interaction - and is an amount certainly disproportionately weak relative to its appearance in the literature (Green and Shapiro, 1994).

Benefits of rational choice theory

Describing the decisions made by individuals as rational and utility maximizing may seem to be a tautological explanation of their behavior that provided very little new information. While there may be many reasons for a rational choice theory approach, two are important for the social sciences. First, assuming humans make decisions in a rational, rather than stochastic manner implies that their behavior can be modeled and thus predictions can be made about future actions. Second, the mathematical formality of rational choice theory models allows social scientists to derive results from their models that may have otherwise not been seen.

Rationality

Rationality as a term is related to the idea of reason, a word which following Webster's may be derived as much from older terms referring to thinking itself as from giving an account or an explanation. This lends the term a dual aspect. One aspect associates it with comprehension, intelligence, or inference, particularly when an inference is drawn in ordered ways (thus a syllogism is a rational argument in this sense). The other part associates rationality with explanation, understanding or justification, particularly if it provides a ground or a motive. 'Irrational', therefore, is defined as that which is not endowed with reason or understanding.

Rationality contra logic

A logical argument is sometimes described as "rational" if it is logically valid. However, rationality is a much broader term than logic, as it includes "uncertain but sensible" arguments based on probability, expectation, personal experience and the like, whereas logic deals principally with provable facts and demonstrably valid relations between them. For example, ad hominem arguments are logically unsound, but in many cases they may be rational. A simple philosophical definition of rationality refers to one's use of a "practical syllogism". For example,

I am cold If I close the window I will not be cold Therefore, I closed the window

We should note that standard form practical syllogisms follow a very specific format and are always valid if constructed correctly though they are not necessarily sound. There are several notable implications of such a definition. First, rationality is objective - it exists only when a valid practical syllogism is used. Second, a choice is either rational or it is not - there is no gradation since there is no gradation between valid and invalid arguments. Third, rationality only applies to actions - i.e., shutting the window is a rational thing to do if you are cold (assuming it is cold outside). Evidence bears on belief but not on rationality. All that is required for an action to be rational is that you believe that X and that that if X then Y so you do Y. Arguments about belief are couched in the terms valid and sound - logically you must believe something if the argument supporting it is sound. In some cases, such as religious belief, the argument may be valid but its soundness cannot be known for the truth of its premises cannot be known.

Rationality in the humanities and social sciences

In philosophy, rationality and reason are the key methods used to analyse the data gathered through systematically gathered observations. In economics, sociology, and political science, a decision or situation is often called rational if it is in some sense optimal, and individuals or organizations are often called rational if they tend to act somehow optimally in pursuit of their goals. Thus one speaks, for example, of a rational allocation of resources, or of a rational

corporate strategy. In this concept of "rationality", the individual's goals or motives are taken for granted and not made subject to criticism, ethical or otherwise. Thus rationality simply refers to the success of goal attainment, whatever those goals may be. Sometimes, in this context, rationality is equated with behavior that is self-interested to the point of being selfish. Sometimes rationality implies having complete knowledge about all the details of a given situation. It might be said that because the goals are not important in definition of rationality, it really only demands logical consistency in choice making. See rational choice theory.

Debates arise in these three fields about whether or not people or organizations are "really" rational, as well as whether it make sense to model them as such in formal models. Some have argued that a kind of bounded rationality makes more sense for such models. Others think that any kind of rationality along the lines of rational choice theory is a useless concept for understanding human behavior; the term homo economicus (economic man: the imaginary logically consistent but amoral being assumed in economic models) was coined largely in honor of this view.

Rationality is a central principle in artificial intelligence, where a rational agent is specifically defined as an agent which always chooses the action which maximises its expected performance, given all of the knowledge it currently possesses.

Theories of rationality

The German sociologist Max Weber proposed an interpretation of social action that distinguished between four different types of rationality. The first, which he called Zweckrational or purposive/instrumental rationality, is related to the expectations about the behavior of other human beings or objects in the environment. These expectations serve as means for a particular actor to attain ends, ends which Weber noted were "rationally pursued and calculated." The second type, Weber called Wertrational or value/belief-oriented. Here the action is undertaken for what one might call reasons intrinsic to the actor: some ethical, aesthetic, religious or other motive, independent of whether it will lead to success. The third type was affectual, determined by an actor's specific affect, feeling, or emotion - to which Weber himself said that this was a kind of rationality that was on the borderline of what he considered "meaningfully oriented." The fourth was traditional, determined by ingrained habituation. Weber emphasized that it was very unusual to find only one of these orientations: combinations were the norm. His usage also makes clear that he considered the first two as more significant than the others, and it is arguable that the third and fourth are subtypes of the first two. These kinds of rationality were ideal types.

The advantage in this interpretation is that it avoids a value-laden assessment, say, that certain kinds of beliefs are irrational. Instead, Weber suggests that a ground or motive can be given – for religious or affect reasons, for example — that may meet the criterion of explanation or justification even if it is not an explanation that fits the Zweckrational orientation of means and ends. The opposite is therefore also true: some means-ends explanations will not satisfy those whose grounds for action are 'Wertrational'.

Based on the premise that 'feelings of worthlessness' are a maladaptive byproduct of the evolution of rationality, Phil Roberts, Jr. has proposed a theory in which the rationality of an end is presumed to correlate with the comprehensiveness of its underlying considerations, and in which no concrete objective is presumed to be rational in any but a relative sense of the term. In addition to its ability to explain what morality is (a shared subconscious theory of rationality), Roberts has also demonstrated how his theory can be employed to address a number of rationality paradoxes,

including the paradox of rational irrationality, cognitive versus practical rationality conflict, the "rationality debate" (Cohen vs. Kahneman and Tversky) and the paradox of the Prisoner's Dilemma.[1]

Behavioral finance

Behavioral finance and behavioral economics are closely related fields which apply scientific research on human and social cognitive and emotional biases to better understand economic decisions and how they affect market prices, returns and the allocation of resources. The fields are primarily concerned with the rationality, or lack thereof, of economic agents. Behavioral models typically integrate insights from psychology with neo-classical economic theory. Behavioral Finance has become the theoretical basis for technical analysis.[1]

Behavioral analyses are mostly concerned with the effects of market decisions, but also those of public choice, another source of economic decisions with some similar biases.

History

During the classical period, economics had a close link with psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, an important text describing psychological principles of individual behavior; and Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Economists began to distance themselves from psychology during the development of neo-classical economics as they sought to reshape the discipline as a natural science, with explanations of economic behavior deduced from assumptions about the nature of economic agents. The concept of homo economicus was developed, and the psychology of this entity was fundamentally rational. Nevertheless, psychological explanations continued to inform the analysis of many important figures in the development of neo-classical economics such as Francis Edgeworth, Vilfredo Pareto, Irving Fisher and John Maynard Keynes.

Psychology had largely disappeared from economic discussions by the mid 20th century. A number of factors contributed to the resurgence of its use and the development of behavioral economics. Expected utility and discounted utility models began to gain wide acceptance, generating testable hypotheses about decision making under uncertainty and intertemporal consumption respectively. Soon a number of observed and repeatable anomalies challenged those hypotheses. Furthermore, during the 1960s cognitive psychology began to describe the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision making under risk and uncertainty to economic models of rational behavior. In Mathematical psychology, there is a longstanding interest in the transitivity of preference and what kind of measurement scale uitility consistutes (Luce, 2000).

Perhaps the most important paper in the development of the behavioral finance and economics fields was written by Kahneman and Tversky in 1979. This paper, 'Prospect theory: Decision Making Under Risk', used cognitive psychological techniques to explain a number of documented divergences of economic decision making from neo-classical theory. Further milestones in the development of the field include a well attended and diverse conference at the University of Chicago (see Hogarth & Reder, 1987), a special 1997 edition of the Quarterly Journal of Economics ('In Memory of Amos Tversky') devoted to the topic of behavioral economics and the award of the Nobel prize to Daniel Kahneman in 2002 "for having integrated insights from

psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."

Prospect theory is an example of generalized expected utility theory. Although not commonly included in discussions of the field of behavioral economics, generalized expected utility theory is similarly motivated by concerns about the descriptive inaccuracy of expected utility theory.

Behavioral economics has also been applied to problems of intertemporal choice. The most prominent idea is that of hyperbolic discounting, in which a high rate of discount is used between the present and the near future, and a lower rate between the near future and the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with some models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1, when t is the near future, but high at time t when t is the present and time t+1 the near future. As part of the discussion of hypberbolic discounting, has been animal and human work on Melioration theory and Matching Law of Richard Herrnstein. They suggest that behavior is not based on expected utility of on just previous reinforcement experience.

Methodology

At the outset behavioral economics and finance theories were developed almost exclusively from experimental observations and survey responses, though in more recent times real world data has taken a more prominent position. fMRI has also been used to determine which areas of the brain are active during various steps of economic decision making. Experiments simulating market situations such as stock market trading and auctions are seen as particularly useful as they can be used to isolate the effect of a particular bias upon behavior; observed market behavior can typically be explained in a number of ways, carefully designed experiments can help narrow the range of plausible explanations. Experiments are designed to be incentive compatible, with binding transactions involving real money the norm.

Key observations

There are three main themes in behavioral finance and economics (Shefrin, 2002):

Heuristics: People often make decisions based on approximate rules of thumb, not strictly rational analyses. See also cognitive biases and bounded rationality.

Framing: The way a problem or decision is presented to the decision maker will affect his action.

Market inefficiencies: There are explanations for observed market outcomes that are contrary to rational expectations and market efficiency. These include mispricings, non-rational decision making, and return anomalies. Richard Thaler, in particular, has written a long series of papers describing specific market anomalies from a behavioral perspective.

Recently, Barberis, Shleifer, and Vishny (1998), as well as Daniel, Hirshleifer, and Subrahmanyam (1998) have built models based on extrapolation (seeing patterns in random sequences) and overconfidence to explain security market over- and underreactions, though such models have not been used in the money management industry. These models assume that errors or biases are correlated across agents so that they do not cancel out in aggregate. This would be the case if a large fraction of agents look at the same signal (such as the advice of an analyst) or have a common bias.

More generally, cognitive biases may also have strong anomalous effects in aggregate if there is a social contamination with a strong emotional content (collective greed or fear), leading to more widespread phenomena such as herding and groupthink. Behavioral finance and economics rests as much on social psychology within large groups as on individual psychology. However, some behavioral models explicitly demonstrate that a small but significant anomalous group can also have market-wide effects (eg. Fehr and Schmidt, 1999).

Behavioral finance topics

Key observations made in behavioral finance literature include the lack of symmetry between decisions to acquire or keep resources, called colloquially the "bird in the bush" paradox, and the strong loss aversion or regret attached to any decision where some emotionally valued resources (e.g. a home) might be totally lost. Loss aversion appears to manifest itself in investor behavior as an unwillingness to sell shares or other equity, if doing so would force the trader to realise a nominal loss (Genesove & Mayer, 2001). It may also help explain why housing market prices do not adjust downwards to market clearing levels during periods of low demand.

Applying a version of prospect theory, Benartzi and Thaler (1995) claim to have solved the equity premium puzzle, something conventional finance models have been unable to do.

Presently, some researchers in experimental finance use experimental method, e.g. creating an artificial market by some kind of simulation software to study people's decision-making process and behavior in financial markets.

Behavioral finance models

Some financial models used in money management and asset valuation use behavioral finance parameters, for example

Thaler's model of price reactions to information, with three phases, underreaction-adjustment-overreaction, creating a price trend

One characteristic of overreaction is that the average return of asset prices following a series of announcements of good news is lower than the average return following a series of bad announcements. In other words, overreaction occurs if the market reacts too strongly or for too long (persistent trend) to news that it subsequently needs to be compensated in the opposite direction. As a result, assets that were winners in the past should not be seen as an indication to invest in as their risk adjusted returns in the future are relatively low compared to stocks that were defined as losers in the past.

The stock image coefficient

Criticisms of behavioral finance

Critics of behavioral finance, such as Eugene Fama, typically support the efficient market theory (though Fama may have reversed his position in recent years). They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies will eventually be priced out of the market or explained by appealing to market microstructure arguments. However, a distinction should be noted between individual biases and social biases;

the former can be averaged out by the market, while the other can create feedback loops that drive the market further and further from the equilibrium of the "fair price".

A specific example of this criticism is found in some attempted explanations of the equity premium puzzle. It is argued that the puzzle simply arises due to entry barriers (both practical and psychological) which have traditionally impeded entry by individuals into the stock market, and that returns between stocks and bonds should stabilize as electronic resources open up the stock market to a greater number of traders (See Freeman, 2004 for a review). In reply, others contend that most personal investment funds are managed through superannuation funds, so the effect of these putative barriers to entry would be minimal. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.

Behavioral economics topicsModels in behavioral economics are typically addressed to a particular observed market anomaly and modify standard neo-classical models by describing decision makers as using heuristics and being affected by framing effects. In general, behavioural economics sits within the neoclassical framework, though the standard assumption of rational behaviour is often challenged.

Critical conclusions of behavioral economicsCritics of behavioral economics typically stress the rationality of economic agents (see Myagkov and Plott (1997) amongst others). They contend that experimentally observed behavior is inapplicable to market situations, as learning opportunities and competition will ensure at least a close approximation of rational behavior.

Others note that cognitive theories, such as prospect theory, are models of decision making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.

Traditional economists are also skeptical of the experimental and survey based techniques which are used extensively in behavioral economics. Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys must be designed carefully to avoid systemic biases, strategic behavior and lack of incentive compatibility, and many economists are distrustful of results obtained in this manner due to the difficulty of eliminating these problems.

Rabin (1998) dismisses these criticisms, claiming that results are typically reproduced in various situations and countries and can lead to good theoretical insight. Behavioral economists have also incorporated these criticisms by focusing on field studies rather than lab experiments. Some economists look at this split as a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to overlap techniques and approaches in answering common questions. For example, many prominent behavioral economists are actively investigating neuroeconomics, which is entirely experimental and cannot be verified in the field.

Other proponents of behavioral economics note that neoclassical models often fail to predict outcomes in real world contexts. Behavioral insights can be used to update neoclassical equations, and behavioral economists note that these revised models not only reach the same correct predictions as the traditional models, but also correctly predict some outcomes where the traditional models failed.[verification needed]

Eugene Fama

Eugene Fama (born February 14, 1939) is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical.

He earned his undergraduate degree in French from Tufts University in 1960 and his MBA and Ph.D. from the Graduate School of Business at the University of Chicago in economics and finance. He has spent all of his teaching career at the University of Chicago.

His Ph.D. thesis, which concluded that stock price movements are unpredictable and follow a random walk, was published as the entire January, 1965 issue of the Journal of Business, entitled The Behavior of Stock Market Prices. That work was subsequently rewritten into a less technical article, Random Walks in Stock Market Prices, which was published in Financial Analysts Journal in 1966 and Institutional Investor in 1968.

His article The Adjustment of Stock Prices to New Information in the International Economic Review, 1969 (with several co-authors) was the first Event study that sought to analyze how stock prices respond to an event, using price data from the newly available CRSP database. This was the first of literally hundreds of such published studies.

Fama is most often thought of as the father of efficient market theory. In a ground-breaking article in the May, 1970 issue of the Journal of Finance, entitled Efficient Capital Markets: A Review of Theory and Empirical Work, Fama proposed two crucial concepts that have defined the conversation on efficient markets ever since. First, Fama proposed three types of efficiency: (1) strong-form; (ii) semi-strong form; and (iii) weak efficiency. Second, Fama demonstrated that the notion of market efficiency could not be rejected without an accompanying rejection of the model of market equilibrium (e.g. the price setting mechanism). This concept, known as the "joint hypothesis problem," has ever since vexed researchers.

In recent years, Fama has become controversial again, for a series of papers, co-written with Kenneth French, that cast doubt on the validity of the Capital Asset Pricing Model (CAPM), which posits that a stock's "beta" alone should explain its average return. These papers describe two factors above and beyond a stock's market beta which can explain differences in stock returns: market capitalization and "value". They also offer evidence that a variety of patterns in average returns, often labeled as "anomalies" in past work, can be explained with their 3 factor model.

Additionally, Fama co-authored the textbook The Theory of Finance with Nobel Memorial Prize in Economics winner Merton H. Miller. He is also the director of research of Dimensional Fund Advisors, Inc., an investment advising firm with $126 billion under management (as of 2006). One of his children, Eugene F. Fama Jr., is a vice president of the company.

Fama and French Three Factor Model

In the portfolio management field, Fama and French developed the highly successful three factor model to describe the market behavior.

CAPM uses a single factor, beta, to compare a portfolio with the market as a whole. But it oversimplifies the complex market. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a

high book-value-to-price ratio (customarily called value stocks; to be differentiated from growth stocks). They then added two factors to CAPM to reflect a portfolio's exposure to these two

classes:

Here r is the portfolio's return rate, Rf is the risk-free return rate, and Km is the return of the whole stock market. The "three factor" β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work. SMB and HML stand for "small [cap] minus big" and "high [book/price] minus low"; they measure the historic excess returns of small caps and "value" stocks over the market as a whole. By the way SMB and HML are defined, the corresponding coefficients bs and bv take values on a scale of roughly 0 to 1: bs = 1 would be a small cap portfolio, bs = 0 would be large cap, bv = 1 would be a portfolio with a high book/price ratio, etc. The Fama-French Three Factor model explains over 90% of stock returns. The signs of the coefficients suggested that small cap and value portfolios have higher expected returns--and arguably higher expected risk--than those of large cap and growth portfolios.[1]

The three factor model is gaining recognition in portfolio management. Morningstar.com classifies stocks and mutual funds based on these factors. Many studies show that the majority of actively managed mutual funds underperform broad indexes based on three factors if classified properly. This leads to more and more index funds and ETFs being offered based on the three factor model.

Finance

Finance is a field that studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. The term finance may thus incorporate any of the following:

The study of money and other assets; The management and control of those assets; Profiling and managing project risks; The science of managing money; As a verb, "to finance" is to provide funds for business or for an individual's large

purchases (car, home, etc.).

The activity of finance is the application of a set of techniques that individuals and organizations (entities) use to manage their financial affairs, particularly the differences between income and expenditure and the risks of their investments.

An entity whose income exceeds its expenditure can lend or invest the excess income. On the other hand, an entity whose income is less than its expenditure can raise capital by borrowing or selling equity claims, decreasing its expenses, or increasing its income. The lender can find a borrower, a financial intermediary, such as a bank or buy notes or bonds in the bond market. The lender receives interest, the borrower pays a higher interest than the lender receives, and the financial intermediary pockets the difference.

A bank aggregates the activities of many borrowers and lenders. A bank accepts deposits from lenders, on which it pays the interest. The bank then lends these deposits to borrowers. Banks allow borrowers and lenders, of different sizes, to coordinate their activity. Banks are thus compensators of money flows in space.

A specific example of corporate finance is the sale of stock by a company to institutional investors like investment banks, who in turn generally sell it to the public. The stock gives whoever owns it part ownership in that company. If you buy one share of XYZ Inc, and they have 100 shares outstanding (held by investors), you are 1/100 owner of that company. Of course, in return for the stock, the company receives cash, which it uses to expand its business in a process called "equity financing". Equity financing mixed with the sale of bonds (or any other debt financing) is called the company's capital structure.

Finance is used by individuals (personal finance), by governments (public finance), by businesses (corporate finance), etc., as well as by a wide variety of organizations including schools and non-profit organizations. In general, the goals of each of the above activities are achieved through the use of appropriate financial instruments, with consideration to their institutional setting.

Finance is one of the most important aspects of business management. Without proper financial planning a new enterprise is unlikely to be successful. Managing money (a liquid asset) is essential to ensure a secure future, both for the individual and an organization.

Personal finance

Questions in personal finance revolve around

How much money will be needed by an individual (or by a family) at various points in the future?

Where will this money come from (e.g. savings or borrowing)? How can people protect themselves against unforeseen events in their lives, and risk in

financial markets? How can family assets be best transferred across generations (bequests and inheritance)? How do taxes (tax subsidies or penalties) affect personal financial decisions?

Personal financial decisions may involve paying for education, financing durable goods such as real estate and cars, buying insurance, e.g. health and property insurance, investing and saving for retirement.

Personal financial decisions may also involve paying for a loan.

Business finance

In the case of a company, managerial finance or corporate finance is the task of providing the funds for the corporations' activities. For small business, this is referred to as SME finance. It generally involves balancing risk and profitability. Long term funds would be provided by ownership equity and long-term credit, often in the form of bonds. These decisions lead to the company's capital structure. Short term funding or working capital is mostly provided by banks extending a line of credit.

On the bond market, borrowers package their debt in the form of bonds. The borrower receives the money it borrows by selling the bond, which includes a promise to repay the value of the bond with interest. The purchaser of a bond can resell the bond, so the actual recipient of interest payments can change over time. Bonds allow lenders to recoup the value of their loan by simply selling the bond.

Another business decision concerning finance is investment, or fund management. An investment is an acquisition of an asset in the hopes that it will maintain or increase its value. In investment management - in choosing a portfolio - one has to decide what, how much and when to invest. In doing so, one needs to

Identify relevant objectives and constraints: institution or individual - goals - time horizon - risk aversion - tax considerations

Identify the appropriate strategy: active vs passive - hedging strategy Measure the portfolio performance

Financial management is duplicate with the financial function of the Accounting profession. However, Financial Accounting is more concerned with the reporting of historical financial information, while the financial decision is directed toward the future of the firm.

Shared Services

There is currently a move towards converging and consolidating Finance provisions into shared services within an organization. Rather than an organization having a number of separate Finance departments performing the same tasks from different locations a more centralized version can be created.

Finance of states

Country, state, county, city or municipality finance is called public finance. It is concerned with

Identification of required expenditure of a public sector entity Source(s) of that entity's revenue The budgeting process Debt issuance (municipal bonds) for public works projects

Financial economics

Financial economics is the branch of economics studying the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. Financial economics concentrates on influences of real economic variables on financial ones, in contrast to pure finance.

It studies:

Valuation - Determination of the fair value of an asset o How risky is the asset? (identification of the asset appropriate discount rate) o What cash flows will it produce? (discounting of relevant cash flows) o How does the market price compare to similar assets? (relative valuation)

o Are the cash flows dependent on some other asset or event? (derivatives, contingent claim valuation)

Financial markets and instruments o Commodities - topics o Stocks - topics o Bonds - topics o Money market instruments- topics o Derivatives - topics

Financial institutions and regulation

Financial mathematics

Financial mathematics is the main branch of applied mathematics concerned with the financial markets. Financial mathematics is the study of financial data with the tools of mathematics, mainly statistics. Such data can be movements of securities—stocks and bonds etc.—and their relations. Another large subfield is insurance mathematics.

Experimental finance

Experimental finance aims to establish different market settings and environments to observe experimentally and analyze agents' behavior and the resulting characteristics of trading flows, information diffusion and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance can study to what extent existing financial economics theory makes valid predictions, and attempt to discover new principles on which such theory can be extended. Research may proceed by conducting trading simulations or by establishing and studying the behaviour of people in artificial competitive market-like settings.

Insider trading

Insider trading is the trading of a corporation's stock or other securities (e.g. bonds or stock options) by corporate insiders such as officers, key employees, directors, or holders of more than ten percent of the firm's shares.[1] Insider trading may be perfectly legal, but the term is frequently used to refer to a practice, illegal in many jurisdictions, in which an insider or a related party trades based on material non-public information obtained during the performance of the insider's duties at the corporation, or otherwise misappropriated.[2]

All insider trades must be reported in the United States. Many investors follow the summaries of insider trades, published by the United States Securities and Exchange Commission (SEC), in the hope that mimicking these trades will be profitable. Legal "insider trading" may not be based on material non-public information. Illegal insider trading in the US requires the participation (perhaps indirectly) of a corporate insider or other person who is violating his fiduciary duty or misappropriating private information, and trading on it or secretly relaying it.

Insider trading is believed to raise the cost of capital for securities issuers, thus decreasing overall economic growth.[3]

Illegal insider trading

Rules against insider trading on material non-public information exist in most jurisdictions around the world, though the details and the efforts to enforce them vary considerably. The United States, the United Kingdom, and Canada are viewed as the countries who have the strictest laws and make the most serious efforts to enforce them.[4]

According to the U.S. SEC, corporate insiders are a company's officers, directors and any beneficial owners of more than ten percent of a class of the company's equity securities. Trades made by these types of insiders in the company's own stock, based on material non-public information, are considered to be fraudulent since the insiders are violating the trust or the fiduciary duty that they owe to the shareholders. The corporate insider, simply by accepting employment, has made a contract with the shareholders to put the shareholders' interests before their own, in matters related to the corporation. When the insider buys or sells based upon company owned information, he is violating his contract with the shareholders.

For example, illegal insider trading would occur if the chief executive officer of Company A learned (prior to a public announcement) that Company A will be taken over, and bought shares in Company A knowing that the share price would likely rise.

Liability for insider trading violations cannot be avoided by passing on the information in an "I scratch your back, you scratch mine" or quid pro quo arrangement, as long as the person receiving the information knew or should have known that the information was company property. For example, if Company A's CEO did not trade on the undisclosed takeover news, but instead passed the information on to his brother-in-law who traded on it, illegal insider trading would still have occurred.[5]

A newer view of insider trading, the "misappropriation theory" is now part of US law. It states that anyone who misappropriates (steals) information from their employer and trades on that information in any stock (not just the employer's stock) is guilty of insider trading. For example, if a journalist who worked for Company B learned about the takeover of Company A while performing his work duties, and bought stock in Company A, illegal insider trading might still have occurred. Even though the journalist did not violate a fiduciary duty to Company A's shareholders, he might have violated a fiduciary duty to Company B's shareholders (assuming the newspaper had a policy of not allowing reporters to trade on stories they were covering).[6]

Proving that someone has been responsible for a trade can be difficult, because traders may try to hide behind nominees, offshore companies, and other proxies. Nevertheless, the U.S. Securities and Exchange Commission prosecutes over 50 cases each year, with many being settled administratively out of court. The SEC and several stock exchanges actively monitor trading, looking for suspicious activity.

Not all trading on information is illegal inside trading, however. For example, while dining at a restaurant, you hear the CEO of Company A at the next table telling the CFO that the company will be taken over, and then you buy the stock, you wouldn't be guilty of insider trading unless there was some closer connection between you, the company, or the company officers.

Since insiders are required to report their trades, others often track these traders, and there is a school of investing which follows the lead of insiders. This is of course subject to the risk that an insider is making a buy specifically to increase investor confidence, or making a sell for reasons unrelated to the health of the company (e.g. a desire to diversify or buy a house).

As of December 2005 companies are required to announce times to their employees as to when they can safely trade without being accused of trading on inside information.

American insider trading law

The United States has been the leading country in prohibiting insider trading deemed illegal. Thomas Newkirk and Melissa Robertson of the SEC, summarize the development of U.S. insider trading laws.[7]

U.S. insider trading prohibitions are based on English and American common law prohibitions against fraud. In 1909, well before the Securities Exchange Act was passed, the United States Supreme Court ruled that a corporate director who bought that company’s stock when he knew it was about to jump up in price committed fraud by buying while not disclosing his inside information.

Section 17 of the Securities Act of 1933[8] contained prohibitions of fraud in the sale of securities which were greatly strengthened by the Securities Exchange Act of 1934.[9]

Section 16(b) of the Securities Exchange Act of 1934 prohibits short-swing profits (from any purchases and sales within any six month period) made by corporate directors, officers, or stockholders owning more than 10% of a firm’s shares. Under Section 10(b) of the 1934 Act, SEC Rule 10b-5, prohibits fraud related to securities trading.

The Insider Trading Sanctions Act of 1984 and the Insider Trading and Securities Fraud Enforcement Act of 1988 provide for penalties for illegal insider trading to be as high as three times the profit gained or the loss avoided from the illegal trading.[10]

S.E.C. regulation FD ("Full Disclosure") requires that if a company intentionally discloses material non-public information to one person, it must simulataneously disclose that information to the public at large. In the case of an unintentional disclosure of material non-public information to one person, the company must make a public disclosure "promptly."[11]

Insider trading, or similar practices, are also regulated by the SEC under its rules on takeovers and tender offers under the Williams Act.

Much of the development of insider trading law has resulted from court decisions. In SEC v. Texas Gulf Sulphur Co. (1966), a federal circuit court stated that anyone in possession of inside information must either disclose the information or refrain from trading.

In 1984, the Supreme Court of the United States ruled in the case of Dirks v. SEC that tippees (receivers of second-hand information) are liable if they had reason to believe that the tipper had breached a fiduciary duty in disclosing confidential information and the tipper received any personal benefit from the disclosure. (Since Dirks disclosed the information in order to expose a fraud, rather than for personal gain, nobody was liable for insider trading violations in his case.)

The Dirks case also defined the concept of "constructive insiders," who are lawyers, investment bankers and others who receive confidential information from a corporation while providing services to the corporation. Constructive insiders are also liable for insider trading violations if the corporation expects the information to remain confidential, since they acquire the fiduciary duties of the true insider.

In United States v. Carpenter (1986) the U.S. Supreme Court cited an earlier ruling while unanimously upholding mail and wire fraud convictions for a defendant who received his information from a journalist rather than from the company itself.

"It is well established, as a general proposition, that a person who acquires special knowledge or information by virtue of a confidential or fiduciary relationship with another is not free to exploit that knowledge or information for his own personal benefit but must account to his principle for any profits derived therefrom."

However, in upholding the securities fraud (insider trading) convictions, the justices were evenly split.

In 1997 the U.S. Supreme Court adopted the misappropriation theory of insider trading in United States v. O'Hagan, 521 U.S. 642, 655 (1997),. O'Hagan was a partner in a law firm representing Grand Met, while it was considering a tender offer for Pillsbury Co. O'Hagan used this inside information by buying call options on Pillsbury stock, resulting in profits of over $4 million. O'Hagan claimed that neither he nor his firm owed a fiduciary duty to Pillsbury, so that he did not commit fraud by purchasing Pillsbury options.[12]

The Court rejected O'Hagan's arguments and upheld his conviction.

The "misappropriation theory" holds that a person commits fraud "in connection with" a securities transaction, and thereby violates 10(b) and Rule 10b-5, when he misappropriates confidential information for securities trading purposes, in breach of a duty owed to the source of the information. Under this theory, a fiduciary's undisclosed, self-serving use of a principal's information to purchase or sell securities, in breach of a duty of loyalty and confidentiality, defrauds the principal of the exclusive use of the information. In lieu of premising liability on a fiduciary relationship between company insider and purchaser or seller of the company's stock, the misappropriation theory premises liability on a fiduciary-turned-trader's deception of those who entrusted him with access to confidential information.

The Court specifically recognized that a corporation’s information is its property: "A company's confidential information...qualifies as property to which the company has a right of exclusive use. The undisclosed misappropriation of such information in violation of a fiduciary duty...constitutes fraud akin to embezzlement – the fraudulent appropriation to one's own use of the money or goods entrusted to one's care by another."

In 2000, the SEC enacted Rule 10b5-1, which defined trading "on the basis of" inside information as any time a person trades while aware of material nonpublic information — so that it is no defense for one to say that she would have made the trade anyway. This rule also created an affirmative defense for pre-planned trades.

In May of 2007, representatives Brian Baird and Louise Slaughter introduced a bill entitled the "Stop Trading on Congressional Knowledge Act, or STOCK Act." that would hold congressional and federal employees liable for stock trades they made using information they gained through their jobs. The bill would also seek to regulate so called "Political Intelligence" firms that research government activities and sell the information to financial managers.[13]

Security analysis and insider trading

Security analysts gather and compile information, talk to corporate officers and other insiders, and issue recommendations to traders. Thus their activities may easily cross legal lines if they are not especially careful. The CFA Institute in its code of ethics states that analysts should make every effort to make all reports available to all the broker's clients on a timely basis. Analysts should never report material nonpublic information, except in an effort to make that information available to the general public. Nevertheless, analysts' reports may contain a variety of information that is "pieced together" without violating insider trading laws, under the mosaic theory. This information may include non-material nonpublic information as well as material public information, which may increase in value when properly compiled and documented.

Arguments for legalizing insider trading

Some economists and legal scholars (e.g. Henry Manne, Milton Friedman, Thomas Sowell, Daniel Fischel, Frank H. Easterbrook) argue that laws making insider trading illegal should be revoked. They claim that insider trading based on material nonpublic information benefits investors, in general, by more quickly introducing new information into the market.

Milton Friedman, laureate of the Nobel Memorial Prize in Economics, said: "You want more insider trading, not less. You want to give the people most likely to have knowledge about deficiencies of the company an incentive to make the public aware of that." Friedman did not believe that the trader should be required to make his trade known to the public, because the buying or selling pressure itself is information for the market.[14]

Other critics argue that insider trading is a victimless act: A willing buyer and a willing seller agree to trade property which the seller rightfully owns, with no prior contract (according to this view) having been made between the parties to refrain from trading if there is asymmetric information.

Legalization advocates also question why activity that is similar to insider trading is legal in other markets, such as real estate, but not in the stock market. For example, if a geologist knows there is a high likelihood of the discovery of petroleum under Farmer Smith's land, he may be entitled to make Smith an offer for the land, and buy it, without first telling Farmer Smith of the geological data. Of course there are also circumstances when the geologist could not legally buy the land without disclosing the information, e.g. when he had been hired by Farmer Smith to assess the geology of the farm.

Advocates of legalization make free speech arguments. Punishment for communicating about a development pertinent to the next day's stock price might seem to be an act of censorship [1]. Nevertheless, if the information being conveyed is proprietary information and the corporate insider has contracted to not expose it, he has no more right to communicate it than he would to tell others about the company's confidential new product designs, formulas, or bank account passwords.

There are very limited laws against "insider trading" in the commodities markets, if, for no other reason, than that the concept of an "insider" is not immediately analogous to commodities themselves (e.g., corn, wheat, steel, etc.). However, analogous activities such as front running are illegal under U.S. commodity and futures trading laws. For example, a commodity broker can be charged with fraud if he or she receives a large purchase order from a client (one likely to affect the price of that commodity) and then purchases that commodity before executing the client's order in order to benefit from the anticipated price increase.

Legal differences among jurisdictions

The US and the UK vary in the way the law is interpreted and applied with regard to insider trading.

In the UK, the relevant laws are the Financial Services Act 1986 and the Financial Services and Markets Act 2000, which defines an offense of Market Abuse.[15] It is not illegal to fail to trade based on inside information (whereas without the inside information the trade would have taken place), since from a practical point of view this is too difficult to enforce. It is often legal to deal ahead of a takeover bid, where a party deliberately buys shares in a company in the knowledge that it will be launching a takeover bid.[citation needed]

Japan enacted its first law against insider trading in 1988. Roderick Seeman says: "Even today many Japanese do not understand why this is illegal. Indeed, previously it was regarded as common sense to make a profit from your knowledge."[16]

In accordance with EU Directives, Malta enacted the Financial Markets Abuse Act in 2002, which effectively replaced the Insider Dealing and Market Abuse Act of 1994.

The "Objectives and Principles of Securities Regulation"[17] published by the International Organization of Securities Commissions (IOSCO) in 1998 and updated in 2003 states that the three objectives of good securities market regulation are (1) investor protection, (2) ensuring that markets are fair, efficient and transparent, and (3) reducing systemic risk. The discussion of these "Core Principles" state that "investor protection" in this context means "Investors should be protected from misleading, manipulative or fraudulent practices, including insider trading, front running or trading ahead of customers and the misuse of client assets." More than 85 percent of the world's securities and commodities market regulators are members of IOSCO and have signed on to these Core Principles.

The World Bank and International Monetary Fund now use the IOSCO Core Principles in reviewing the financial health of different country's regulatory systems as part of these organization's financial sector assessment program, so laws against insider trading based on non-public information are now expected by the international community. Enforcement of insider trading laws varies widely from country to country, but the vast majority of jurisdictions now outlaw the practice, at least in principle.

Market anomaly

A market anomaly (or inefficiency) is a price and/or return distortion on a financial market.

It is usually related to:

either structural factors (unfair competition, lack of market transparency, ...) or behavioral biases by economic agents (see behavioral economics)

It sometimes refers to phenomena contradicting the efficient market hypothesis. There are anomalies in relation to the economic fundamentals of the equity, technical trading rules, and economic calendar events.

Microeconomics

Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold.

Microeconomics examines how these decisions and behaviours affect the supply and demand for goods and services, which determines prices, and how prices, in turn, determine the supply and demand of goods and services.[2][3]

Macroeconomics, on the other hand, involves the "sum total of economic activity, dealing with the issues of growth, inflation, and unemployment and with national economic policies relating to these issues"[4] and the effects of government actions (e.g., changing taxation levels) on them.[5] Particularly in the wake of the Lucas critique, much of modern macroeconomic theory has been built upon 'microfoundations' — i.e. based upon basic assumptions about micro-level behaviour.

Overview

One of the goals of microeconomics is to analyze market mechanisms that establish relative prices amongst goods and services and allocation of limited resources amongst many alternative uses. Microeconomics analyzes market failure, where markets fail to produce efficient results, as well as describing the theoretical conditions needed for perfect competition. Significant fields of study in microeconomics include markets under asymmetric information, choice under uncertainty and economic applications of game theory. Also considered is the elasticity of products within the market system.

Assumptions and definitions

The theory of supply and demand usually assumes that markets are perfectly competitive. This implies that there are many buyers and sellers in the market and none of them have the capacity to significantly influence prices of goods and services. In many real-life transactions, the assumption fails because some individual buyers or sellers or groups of buyers or sellers do have the ability to influence prices. Quite often a sophisticated analysis is required to understand the demand-supply equation of a good. However, the theory works well in simple situations.

Mainstream economics does not assume a priori that markets are preferable to other forms of social organization. In fact, much analysis is devoted to cases where so-called market failures lead to resource allocation that is suboptimal by some standard (highways are the classic example, profitable to all for use but not directly profitable for anyone to finance). In such cases, economists may attempt to find policies that will avoid waste directly by government control, indirectly by regulation that induces market participants to act in a manner consistent with optimal welfare, or by creating "missing markets" to enable efficient trading where none had previously existed. This is studied in the field of collective action. It also must be noted that "optimal welfare" usually takes on a Paretian norm, which in its mathematical application of Kaldor-Hicks Method, does not stay consistent with the Utilitarian norm within the normative side of economics which studies collective action, namely public choice. Market failure in positive economics (microeconomics) is limited in implications without mixing the belief of the economist and his or her theory.

The demand for various commodities by individuals is generally thought of as the outcome of a utility-maximizing process. The interpretation of this relationship between price and quantity demanded of a given good is that, given all the other goods and constraints, this set of choices is that one which makes the consumer happiest.

Modes of operation

It is assumed that all firms are following rational decision-making, and will produce at the profit-maximizing output. Given this assumption, there are four categories in which a firm's profit may be considered.

A firm is said to be making an economic profit when its average total cost is less than the price of each additional product at the profit-maximizing output. The economic profit is equal to the quantity output multiplied by the difference between the average total cost and the price.

A firm is said to be making a normal profit when its economic profit equals zero. This occurs where average total cost equals price at the profit-maximizing output.

If the price is between average total cost and average variable cost at the profit-maximizing output, then the firm is said to be in a loss-minimizing condition. The firm should still continue to produce, however, since its loss would be larger if it were to stop producing. By continuing production, the firm can offset its variable cost and at least part of its fixed cost, but by stopping completely it would lose the entirety of its fixed cost.

If the price is below average variable cost at the profit-maximizing output, the firm should go into shutdown. Losses are minimized by not producing at all, since any production would not generate returns significant enough to offset any fixed cost and part of the variable cost. By not producing, the firm loses only its fixed cost. By losing this fixed cost the company faces a challenge. It must either exit the market or remain in the market and risk a complete loss.

Market failure

In microeconomics, the term "market failure" does not mean that a given market has ceased functioning. Instead, a market failure is a situation in which a given market does not efficiently organize production or allocate goods and services to consumers. Economists normally apply the term to situations where the inefficiency is particularly dramatic, or when it is suggested that non-market institutions would provide a more desirable result. On the other hand, in a political context, stakeholders may use the term market failure to refer to situations where market forces do not serve the "public interest," a subjective assessment that is often made on social or moral grounds.

The four main types or causes of market failure are:

Monopolies or other cases of abuse of market power where a "single buyer or seller can exert significant influence over prices or output"). Abuse of market power can be reduced by using antitrust regulations.[6]

Externalities, which occur in cases where the "market does not take into account the impact of an economic activity on outsiders." There are positive externalities and negative externalities.[6] Positive externalities occur in cases such as when a television program on family health improves the public's health. Negative externalities occur in cases such as when a company’s processes pollutes air or waterways. Negative externalities can be reduced by using government regulations, taxes, or subsidies, or by using property rights to force companies and individuals to take the impacts of their economic activity into account.

Public goods such as national defence[6] and public health initiatives such as draining mosquito-breeding marshes. For example, if draining mosquito-breeding marshes was left to the private market, far fewer marshes would probably be drained. To provide a good supply of public goods, nations typically use taxes that compel all residents to pay for these public goods (due to scarce knowledge of the positive externalities to third parties/social welfare); and

Cases where there is asymmetric information or uncertainty (information inefficiency).[6] Information asymmetry occurs when one party to a transaction has more or better information than the other party. Typically it is the seller that knows more about the product than the buyer, but this is not always the case. Buyers in some markets have better information than the Sellers. For example, used-car salespeople may know whether a used car has been used as a delivery vehicle or taxi, information that may not be available to buyers. An example of a situation where the buyer may have better information than the seller would be an estate sale of a house, as required by a last will and testament. A real estate broker purchasing this house may have more information about the house than the family members of the deceased.

This situation was first described by Kenneth J. Arrow in a seminal article on health care in 1963 entitled "Uncertainty and the Welfare Economics of Medical Care," in the American Economic Review. George Akerlof later used the term asymmetric information in his 1970 work The Market for Lemons. Akerlof noticed that, in such a market, the average value of the commodity tends to go down, even for those of perfectly good quality, because the buyer has no way of knowing whether the product they are buying will turn out to be a "lemon" (a defective product).

Opportunity cost

Although opportunity cost can be hard to quantify, the effect of opportunity cost is universal and very real on the individual level. In fact, this principle applies to all decisions, not just economic ones. Since the work of the German economist Friedrich von Wieser, opportunity cost has been seen as the foundation of the marginal theory of value.

Opportunity cost is one way to measure the cost of something. Rather than merely identifying and adding the costs of a project, one may also identify the next best alternative way to spend the same amount of money. The forgone profit of this next best alternative is the opportunity cost of the original choice. A common example is a farmer that chooses to farm his land rather than rent it to neighbors, wherein the opportunity cost is the forgone profit from renting. In this case, the farmer may expect to generate more profit himself. Similarly, the opportunity cost of attending university is the lost wages a student could have earned in the workforce, rather than the cost of

tuition, books, and other requisite items (whose sum makes up the total cost of attendance). The opportunity cost of a vacation in the Bahamas might be the down payment money for a house.

Note that opportunity cost is not the sum of the available alternatives, but rather the benefit of the single, best alternative. Possible opportunity costs of the city's decision to build the hospital on its vacant land are the loss of the land for a sporting center, or the inability to use the land for a parking lot, or the money that could have been made from selling the land, or the loss of any of the various other possible uses—but not all of these in aggregate. The true opportunity cost would be the forgone profit of the most lucrative of those listed.

One question that arises here is how to assess the benefit of dissimilar alternatives. We must determine a dollar value associated with each alternative to facilitate comparison and assess opportunity cost, which may be more or less difficult depending on the things we are trying to compare. For example, many decisions involve environmental impacts whose dollar value is difficult to assess because of scientific uncertainty. Valuing a human life or the economic impact of an Arctic oil spill involves making subjective choices with ethical implications.

The supply and demand model describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). The graph depicts a right-shift in demand from D1 to D2 along with the consequent increase in price and quantity required to reach a new market-clearing equilibrium point on the supply curve (S).

Applied microeconomics

Applied microeconomics includes a range of specialized areas of study, many of which draw on methods from other fields. Industrial organization and regulation examines topics such as the entry and exit of firms, innovation, role of trademarks. Law and economics applies microeconomic principles to the selection and enforcement of competing legal regimes and their relative efficiencies. Labor economics examines wages, employment, and labor market dynamics. Public finance (also called public economics) examines the design of government tax and expenditure policies and economic effects of these policies (e.g., social insurance programs). Political economy examines the role of political institutions in determining policy outcomes. Health economics examines the organization of health care systems, including the role of the health care workforce and health insurance programs. Urban economics, which examines the

challenges faced by cities, such as are sprawl, air and water pollution, traffic congestion, and poverty, draws on the fields of urban geography and sociology. The field of financial economics examines topics such as the structure of optimal portfolios, the rate of return to capital, econometric analysis of security returns, and corporate financial behavior. The field of economic history examines the evolution of the economy and economic institutions, using methods and techniques from the fields of economics, history, geography, sociology, psychology, and political science.

Random walk hypothesis

The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices of the stock market cannot be predicted. It has been described as 'jibing' with the efficient market hypothesis. Investors, economists, and other financial behaviorists have historically accepted the random walk hypothesis. They have run several tests and continue to believe that stock prices are completely random because of the efficiency of the market.

The term was popularized by the 1973 book, A Random Walk Down Wall Street, by Burton Malkiel, currently a Professor of Economics and Finance at Princeton University.

Testing the hypothesis

Burton G. Malkiel, an economist professor at Princeton University and writer of A Random Walk Down Wall Street, performed a test where his students were given a hypothetical stock that was initially worth fifty dollars. The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests. Malkiel then took the results in a chart and graph form to a chartist (a person who “seeks to predict future movements by seeking to interpret past patterns on the assumption that ‘history tends to repeat itself’”) (Keane 11). The chartist told Malkiel that they needed to immediately buy the stock. When Malkiel told him it was based purely on flipping a coin, the chartist was very unhappy. This indicates that the market and stocks could be just as random as flipping a coin.

The random walk hypothesis was also applied to NBA basketball. Psychologists made a detailed study of every shot the Philadelphia 76ers made over one and one-half seasons of basketball. The psychologists found no positive correlation between the previous shots and the outcomes of the shots afterwards. Economists and believers in the random walk hypothesis apply this to the stock market. The actual lack of correlation of past and present can be easily seen. If a stock goes up one day, no stock market participant can accurately predict that it will rise again the next. Just as a basketball player with the “hot hand” can miss his or her next shot, the stock that seems to be on the rise can fall at any time, making it completely random.

A non-random walk hypothesis

There are other economists, professors, and investors who believe that the market is predictable to some degree. The people believe that there are trends and incremental changes in the prices and when looking at them, one can determine whether the stock is on the rise or fall. There have been key studies done by economists and a book has been written by two professors of economics that try to prove the random walk hypothesis wrong.

Martin Weber, a leading researcher in behavioral finance, has done many tests and studies on finding trends in the stock market. In one of his key studies, he observed the stock market for ten years. Over those ten years, he looked at the market prices and looked for any kind of trends. He found that stocks with high price increases in the first five years tended to become under-performers in the following five years. Weber and other believers in the non-random walk hypothesis cite this as a key contributor and contradictor to the random walk hypothesis.

Another test that Weber ran that contradicts the random walk hypothesis was finding stocks that have had an upward revision for earnings outperform other stocks in the forthcoming six months. With this knowledge, investors can have an edge in predicting what stocks to pull out of the market and which stocks — the stocks with the upward revision — to leave in. Martin Weber’s studies detract from the random walk hypothesis, because according to Weber there are trends and other tips to predicting the stock market.

Professors Andrew W. Lo and A. Craig MacKinlay, professors of Finance at the MIT Sloan School of Management and the University of Pennsylvania, respectively, have also tried to prove the random walk theory wrong. They wrote the book A Non-Random Walk Down Wall Street, which goes through a number of tests and studies that try to prove there are trends in the stock market and that they are somewhat predictable. They try to prove it with what is called the simple volatility-based specification test, which is an equation that states:

where

Xt is the price of the stock at time t μ is an arbitrary drift parameter εt is a random disturbance term.

With this equation, they have been able to put in stock prices over the last number of years, and figure out the trends that have unfolded (Non-Random 19). They have found small incremental changes in the stocks throughout the years. Through these changes, Lo and MacKinlay believe that the stock market is predictable, thus contradicting the random walk hypothesis.

Random walk hypothesis vs. market trends

The hypothesis does have its detractors. Research in behavioral finance has shown that some phenomena, for example market trends, might in some cases contradict that hypothesis.

Profs. Andrew W. Lo of MIT and A. Craig MacKinlay set about to prove the theory wrong with their paper and synonymous book, A Non-Random Walk Down Wall St., published in 1999 by the Princeton University Press. They argue that the random walk does not exist and that even the casual observer can look at the many stock and index charts generated over the years and see the trends. If the market were random, it is argued, there would never be the many long rises and declines so clearly evident in those charts. Subscribers to the random walk hypothesis counter-argue that past performance cannot be indicative of future performance in a semi-strong market economy.

Prediction Company, started by chaos physicists Norman Packard and Doyne Farmer, has been attempting to predict the stock market since 1991. So far, they have proved moderately successful.[1]

Post-modern portfolio theory

This article discusses in detail the application of post-modern portfolio theory1 (PMPT) to risk/return analysis and describes its theoretical and practical benefits over Modern Portfolio Theory (“MPT”), also referred to as Mean-Variance Analysis (“MVA”). And like MPT, PMPT proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced.

Overview

It has been a generation since Harry Markowitz laid the foundations and built much of the structure of what we now know as MPT, the greatest contribution of which is the establishment of a formal risk/return framework for investment decision-making. By defining investment risk in quantitative terms, Markowitz gave investors a mathematical approach to asset selection and portfolio management. But as Markowitz himself and William F. Sharpe, the other giant of MPT acknowledge, there are important limitations to the original MPT formulation.

"Under certain conditions the MVA can be shown to lead to unsatisfactory predictions of (investor) behavior. Markowitz suggests that a model based on the semi-variance would be preferable; in light of the formidable computational problems, however, he bases his (MVA) analysis on the mean and the standard deviation2."

The causes of these “unsatisfactory” aspects of MPT are the assumptions that 1) variance of portfolio returns is the correct measure of investment risk, and 2) the investment returns of all securities and portfolios can be adequately represented by the normal distribution. Stated another way, MPT is limited by measures of risk and return that do not always represent the realities of the investment markets.

Recent advances in portfolio and financial theory, coupled with today’s increased electronic computing power, have overcome these limitations. The resulting expanded risk/return paradigm is known as Post-Modern Portfolio Theory, or PMPT. Thus, MPT becomes nothing more than a (symmetrical) special case of PMPT.

Introduction to PMPT

As already stated, standard deviation3 and the normal distribution are a major practical limitation: they are symmetrical. Using standard deviation implies that better-than-expected returns are just as risky as those returns that are worse than expected. Furthermore, using the normal distribution to model the pattern of investment returns makes investment results with more upside than downside returns appear more risky than they really are, and vice-versa for returns with more a predominance of downside returns. The result is that using traditional MPT techniques for measuring investment portfolio construction and evaluation frequently distorts investment reality.

It has long been recognized that investors typically do not view as risky those returns above the minimum they must earn in order to achieve their investment objectives. They believe that risk has to do with the bad outcomes (i.e., returns below a required target), not the good outcomes

(i.e., returns in excess of the target) and that losses weigh more heavily than gains. This view has been noted by researchers in finance, economics and psychology, including Sharpe (1964). "Under certain conditions, the mean-variance approach can be shown to lead to unsatisfactory predictions of behavior. Markowitz suggests that models based on semi-variance would be preferable; in light of the formidable computational problems, however, he bases his analysis on the variance and standard deviation."

The Tools of PMPT

In 1987 The Pension Research Institute at San Francisco State University developed the practical mathematical algorithms of PMPT that are in use today. These methods provide a framework that recognizes investors' preferences for upside over downside volatility. At the same time, a more robust model for the pattern of investment returns, the three-parameter lognormal distribution4, was introduced.

Downside risk

Downside risk (DR) is measured by target semi-deviation (the square root of target semi-variance) and is termed downside deviation. It is expressed in percentages and therefore allows for rankings in the same way as standard deviation.

An intuitive way to view downside risk is the annualized standard deviation of returns below the target. Another is the square root of the probability-weighted squared below-target returns. The squaring of the below-target returns has the effect of penalizing large failures much more severely than small failures. This is consistent with observations made on the behavior of individual decision-making under uncertainty.

where

d is downside deviation (commonly known in the finacial community as 'downside risk'). Note: By extension, d2 = downside variance.

t is the annual target return, or MAR

r is the random variable representing the return for the distribution of annual returns f(r),

f(r) is a the three-parameter lognormal distribution

For the reasons provided below, this continuous formula is preferred over a simpler discrete version that determines the standard deviation of below-target periodic returns taken from the return series.

1. The continuous form permits all subsequent calculations to be made using annual returns which is the natural way for investors to specify their investment goals. The discrete form requires monthly returns for there to be sufficient data points to make a meaningful calculation, which in turn requires converting the annual target into a monthly target. This significantly affects the amount of risk that is identified. For example, a goal of earning 1% each and every month results in greater risk than the (apparently) equivalent goal of earning 12% each and every year.

2. A second reason for strongly preferring the continuous form to the discrete form has been proposed by Sortino & Forsey (1996): "Before we make an investment, we don't know what the outcome will be... After the investment is made, and we want to measure its performance, all we know is what the outcome was, not what it could have been. To cope with this uncertainty, we assume that a reasonable estimate of the range of possible returns, as well as the probabilities associated with estimation of those returns...In statistical terms, the shape of [this] uncertainty is called a probability distribution. In other words, looking at just the discrete monthly or annual values does not tell the whole story."

Using the observed points to create a distribution is a staple of conventional performance measurement. For example, monthly returns are used to calculate a fund's mean and standard deviation. Using these values and the properties of the normal distribution, we can make statements such as the likelihood of losing money (even though no negative returns may actually have been observed), or the range within which two-thirds of all returns lies (even though the returns identified in this way do not necessarily have to have actually occurred). Our ability to make these statements comes from the process of assuming the continuous form of the normal distribution and certain of its well-known properties.

In PMPT an analogous process is followed: 1. Observe the monthly returns, 2. Fit a distribution that permits asymmetry to the observations, 3. Annualize the monthly returns, making sure the shape characteristics of the distribution are retained, 4. Apply integral calculus to the resultant distribution to calculate the appropriate statistics.

Sortino ratio

The Sortino ratio measures returns adjusted for the target and downside risk. It is defined as:

where,

r = the annualized rate of return,

t = the target return,

d = downside risk.

This ratio replaces the traditional Sharpe ratio as a means for ranking investment results. The following table shows risk-adjusted ratios for several major indexes using both

Sortino and Sharpe ratios. The data cover the five years 1992-1996 and are based on monthly total returns. The Sortino ratio is calculated against a 9.0% target.

IndexSortino Ratio

Sharpe Ratio

90-day T-bill -1.00 0.00

Lehman Aggregate -0.29 0.63

MSCI EAFE -0.05 0.30

Russell 2000 0.55 0.93

S&P 500 0.84 1.25

As an example of the different conclusions that can be drawn using these two ratios, notice how the Lehman Aggregate and MSCI EAFE compare - the Lehman ranks higher using the Sharpe ratio whereas EAFE ranks higher using the Sortino ratio. In many cases, manager or index rankings will be different, depending on the risk-adjusted measure used. These patterns will change again for different values of t. For example, when t is close to the risk-free rate, the Sortino Ratio for T-Bill's will be higher than that for the S&P 500, while the Sharpe ratio remains unchanged.

Volatility skewness

Volatility skewness is another portfolio-analysis statistic introduced by Rom and Ferguson under the PMPT rubric. It measures the ratio of a distribution's percentage of total variance from returns above the mean, to the percentage of the distribution's total returns from returns below the mean. Thus, if a distribution is symmetrical (i.e., normal, as is assumed under MPT), it has a volatility skewness of 1.00. Values greater than 1.00 indicate positive skewness; values less than 1.00 indicate negative skewness. While closely correlated with the traditional statistical measure of skewness (viz., the third moment of a distribution), the authors of PMPT argue that their volatility skewness measure has the advantage of being intuitively more understandable to non-statisticians who are the primary practical users of these tools.

The importance of skewness lies in the fact that the more non-normal (i.e., skewed) a return series is, the more its true risk will be distorted by traditional MPT measures such as the Sharpe ratio. Thus, with the recent advent of hedging and derivative strategies, which are asymmetrical by design, MPT measures are essentially useless, while PMPT is

able to capture significantly more of the true information contained in the returns under consideration. This being said, as the following table shows, many of the common market indices and the returns of stock and bond mutual funds cannot themselves always be assumed to be accurately represented by the normal distribution. This fact is also not well understood by many practitioners.

IndexUpside

Skewness(%)Downside Skewness(%) Volatility Skewness

Lehman Aggregate 32.35 67.65 0.48

Russell 2000 37.19 62.81 0.59

S&P 500 38.63 61.37 0.63

90-day T-Bill 48.26 51.74 0.93

MSCI EAFE 54.67 45.33 1.21

Conclusion

PMPT is able to assist investment practitioners more accurately create optimal investment strategies and evaluate the true performance of investment managers, mutual funds and other portfolios, without the restrictions imposed by MPT.

Sharpe ratio

The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the mean excess return per unit of risk in an investment asset or a trading strategy. Since its revision made by the original author in 1994, it is defined as:

,

where R is the asset return, Rf is the return on a benchmark asset, such as the risk free rate of return, E[R − Rf] is the expected value of the excess of the asset return over the benchmark return, and σ is the standard deviation of the excess return (Sharpe 1994).

Note, if Rf is a constant risk free return throughout the period,

. Sharpe's 1994 revision acknowledged that the risk free

rate changes with time. Prior to this revision the definition was assuming a constant Rf.

The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken. When comparing two assets each with the expected return E[R] against the same benchmark with return Rf, the asset with the higher Sharpe ratio gives more return for the same risk. Investors are often advised to pick investments with high Sharpe ratios.

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

This ratio was developed by William Forsyth Sharpe in 1966. Sharpe originally called it the "reward-to-variability" ratio in before it began being called the Sharpe Ratio by later academics and financial professionals. Recently, the (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during evaluation periods of declining markets (Scholz 2007).

Examples

Suppose the asset has an expected return of 15%. We typically do not know the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%. Finally, suppose the risk-free rate of return, Rf, has been constant at 4%. Then the Sharpe ratio will be 1.10 (R = 0.15, Rf = 0.04, and σ = 0.10).

As a guide post, one could substitute in the longer term return of the S&P500 as 10%. The risk-free return of bonds could be about 4%. And the average standard deviation of the S&P500 is about +/- 16%. Doing the math, we get that the average, long-term Sharpe ratio of the US market is about 0.375. But we should note that if one were to calculate the ratio over, for example, three-year rolling periods, then the Sharpe ratio would vary dramatically.

Sortino ratio

The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target, or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. It is thus a more realistic measure of risk-adjusted returns than the Sharpe.

The ratio is calculated as

,

where R is the asset or porfolio return; T is the target or required rate of return for the investment strategy under consideration, (T was originally known as the minimum acceptable return, or MAR); DR is the downside risk. The downside risk is the target semideviation = square root of the target semivariance (TSV). TSV is a the return distribution's lower-partial moment of degree 2 (LPM2).

Thus, the ratio is the actual rate of return in excess of the investor's target rate of return, per unit of downside risk.

The ratio was created by Brian M. Rom [1] in 1986 as an element of Investment Technologies' [2] Post-Modern Portfolio Theory portfolio optimization software.

Cost of carry

The cost of carry is the cost of "carrying" or holding a position. If long the cost of interest paid on a margin account, or if short the cost of paying dividends, or opportunity cost the cost of purchasing a particular security rather than an alternative. For most investments, the cost of carry generally refers to the risk-free interest rate that could be earned by investing currency in a theoretically safe investment vehicle such as a money market account minus any future cash-flows that are expected from holding an equivalent instrument with the same risk (generally expressed in percentage terms and called the convenience yield). Storage costs (generally expressed as a percentage of the spot price) should be added to the cost of carry for physical commodities such as corn, wheat, or gold.

The cost of carry model expresses the forward price (or, as an approximation, the futures price) as a function of the spot price and the cost of carry.

where F is the forward price, S is the spot price, e is the base of the natural logarithms, r is the risk-free interest rate, s is the storage cost, c is the convenience yield, and t is the time to delivery of the forward contract (expressed as a fraction of 1 year).

The same model in currency markets is known as interest rate parity.

For example, a US investor buying a Standard and Poor's 500 e-mini futures contract on the Chicago Mercantile Exchange could expect the cost of carry to be the prevailing risk-free interest rate (around 3% as of June, 2005) minus the expected dividends that one could earn from buying each of the stocks in the S&P 500 and receiving any dividends that they might pay, since the e-mini futures contract is a proxy for the underlying stocks in the S&P 500. Since the contract is a futures contract and settles at some forward date, the actual values of the dividends may not yet be known so the cost of carry must be estimated.

No-arbitrage boundsIn financial mathematics, No-arbitrage bounds are mathematical relationships specifying simple limits on derivative prices. Normally, these are found by simple arguments based on the payouts of the security in question, without specifying any sort of Distribution on any of the asset returns involved.

Lack of arbitrage explains some rather obvious questions in option pricing, such that the value of a call option will never rise above the underlying stock price itself. However, the most frequent nontrivial example of no-arbitrage bounds is put-call parity for option prices.

The Arbitrage Pricing TheoryIntroduction The economist Stephen Ross PhD developed a more generalized Modern Portfolio Theory [MPT] model called Arbitrage Pricing Theory (APT). 

DefinitionAPT is based upon somewhat less restrictive assumptions than CAPM and results in the conclusion that there are multiple factors representing systematic risk.  The APT incorporates the fact that different securities react in varying degrees to unexpected changes in systematic factors other than just beta to the market portfolio.The risk-free return plus the expected return for exposure to each source of systematic risk times the beta coefficient to that risk is what determines the expected rate of return for a given security.An important point for physicians to keep in mind is that the APT focuses on unexpected changes for its systematic risk factors. The financial markets are viewed as a discounting mechanism, with prices established for various securities reflecting investors’ expectations about the future, so any excess return for an expected change will be arbitraged away (i.e., the price of that risk will be bid down to zero). For example, market prices already reflect physician and other investors’ expectations about GNP growth, so prices of assets should only react to the extent that GNP growth either exceeds or falls short of expectations (i.e., an unexpected change in GNP growth).

A Rhetorical Interrogative?And so - we can ask - why do medical professionals and their advisors go wrong in making passive asset allocation decisions using MPT?   The problem has less to do with the limitations of CAPM or APT as theories and more to do with how these theories are applied in the real world.The basic premise behind the various MPT models is that both return and risk measures are the expectations assessed by the investor.   Too often, however, decisions are made based on what investors see in their rear view mirror rather than what lies on the road ahead of them.In other words, while modern portfolio theory is geared towards assessing expected future returns and risk, investors and financial professionals all too often simply rely on historical data rather than develop a forecast of expected future returns and risks.While it is clearly difficult for physicians and all investors to accurately forecast future returns or betas, whether they are for the market as a whole or an individual security, there is no reason to believe that simply using historical data will be any more accurate.  One major shortcoming of modern portfolio theory as it is commonly applied today is the fact that historical relationships between different securities are unstable.  And, it would seem that a physician or other healthcare provider should not rely on historical averages to establish a passive asset allocation.  Of course, the use of unstable historical returns in modern portfolio theories clearly violates the rule-of-thumb related to the dangers of projecting forward historical averages; MPT is nonetheless an important concept for medical professionals to understand as a result of its frequent use by investment professionals. Furthermore, MPT has helped focus investors on two extremely critical elements of investing that are central to successful investment strategies: First, MPT offers the first framework for investors to build a diversified portfolio.   Second, the important conclusion that can be drawn from MPT is that diversification does in fact help reduce portfolio risk.

Conclusion MPT approaches are generally consistent with the first investment rule of thumb, “understand and diversify risk to the extent possible.”  Additionally, the risk/return tradeoff (i.e., higher returns are generally consistent with higher risk) central to MPT based strategies has helped investors recognize that if it looks too good to be true, it probably is. What are your thoughts - and experiences - in the matter? 

CAPM - Another Portfolio Pricing Model to ConsiderIntroductionCAPM is an economic model based upon the idea that there is a single portfolio representing all investments (i.e., the market portfolio) at the point of the optimal portfolio on the CML and a single source of systematic risk, beta, to that market portfolio.   The resulting conclusion is that there should be a “fair” return physician investors should expect to receive given the level of risk (beta) they are willing to assume.  Thus, the excess return, or return above the risk-free rate, that may be expected from an asset is equal to the risk-free return plus the excess return of the market portfolio times the sensitivity of the asset’s excess return to the market portfolio excess return.Beta then, is a measure of the sensitivity of an asset’s returns to the market as a whole.  A particular security’s beta depends on the volatility of the individual security’s returns relative to the volatility of the market’s returns, as well as the correlation between the security’s returns and the markets returns. Thus, while a stock may have significantly greater volatility than the market, if that stock’s returns are not highly correlated with the returns of the overall market (i.e., the stock’s returns are independent of the overall market’s returns) then the stock’s beta would be relatively low.A beta in excess of 1.0 implies that the security is more exposed to systematic risk than the overall market portfolio, and likewise, a beta of less 1.0 means that the security has less exposure to systematic risk than the overall market.The CAPM uses beta to determine the Security Market Line or SML.  The SML determines the required or expected rate of return given the security’s exposure to systematic risk, the risk-free rate, and the expected return for the market as a whole. The SML is similar in concept to the Capital Market Line, although there is a key difference.  Both concepts capture the relationship between risk and expected returns. However, the measure of risk used in determining the CML is standard deviation, whereas the measure of risk used in determining the SML is beta.  

Conclusion The CML estimates the potential return for a diversified portfolio relative to an aggregate measure of risk (i.e., standard deviation), while the SML estimates the return of a single security relative to its exposure to systematic risk. Now, if this is the essence of the Capital Asset Pricing Model, what are the arguments against CAPM?

Understanding Modern Portfolio TheoryModern Portfolio Theory (MPT) is the basic economic model that establishes a linear relationship between the return and risk of an investment.  The tools of MPT are used as the basis for the passive asset mix, which involves setting a static mix of various types of investments or asset classes and rebalancing to that allocation target on a periodic basis.  

Introduction

According to MPT, when building a diversified investment portfolio, the goal should be to obtain the highest expected return for a given level of risk.  A key assumption underlying modern portfolio theory is that higher risk generally translates to higher expected returns.From the perspective of MPT, risk is defined simply as the variability of an investment’s returns.  While MPT is based upon the idea that expected volatility of returns is used, risk is measured by standard deviation of historical returns in practice. Standard deviation is a measure of the dispersion of a security’s returns, X1,…,Xn, around its mean (or average) return.  Often, standard deviation is calculated using monthly or quarterly data points, but is represented as an annualized number to correspond with annualized returns of various investments.  Now, let us assume Stock A has a mean return of 10.0 percent and a standard deviation of 7.5 percent. Then, approximately 68 percent of Stock A’s returns are within one standard deviation of the mean return, and 95 percent of Stock A’s returns are within 2 standard deviations.In other words, 68 percent of Stock A’s returns should be between 2.5 percent and 17.5 percent, and 95 percent of the returns for Stock A should be between negative 5.0 percent and 25.0 percent. However, a key assumption underlying this logic is that the returns for Stock A are normally distributed (i.e., including that the distribution curve of Stock A’s returns is symmetrical around the mean).Unfortunately, in reality security returns may not be symmetrically distributed and both the mean return and standard deviation of returns may shift dramatically over time. 

Sources of Risk There are many different sources of risk, but the two forms of risk hypothesized by Harry Markowitz Ph.D., father of MPT, were systematic risk and unsystematic risk.Systematic risk is sometimes referred to as non-diversifiable risk, since it affects the returns on all investments.  In alternate theories like the Capital Asset Pricing Model [CAPM], systematic risk is defined as sensitivity to the overall market. While Arbitrage Pricing Theory has several common macroeconomic and market factors that are considered sources of systematic risk.   Investors are generally unable to diversify systematic risk, since they cannot reduce their portfolio’s exposure to systematic risk by increasing the number of securities in their portfolio. In contrast, physicians diversifying an investment portfolio can reduce unsystematic risk, or the risk specific to a particular investment.  Sources of unsystematic risk include a stock’s company-specific risk and industry risk. For example, in addition to the risk of a falling stock market, physician investors in Merck also are exposed to risks unique to the pharmaceutical industry (e.g., healthcare reform), as well as the risks specific to Merck’s business practices (e.g., success of research and development efforts, patent time frames, etc). A physician investor can reduce unsystematic risk by building a portfolio of securities from numerous industries, countries, and even asset classes.  Thus, portfolio risk in MPT refers to the both systematic (non-diversifiable) and non-systematic (diversifiable) risk, but a basic conclusion of MPT is that no investor would be rational to take on non-systematic risk since this risk can be diversified away.

Conclusion MPT is the philosophy that higher returns correspond to higher risk, and that doctor investors typically desire to earn the highest return per a given level of risk.

The tradeoff between expected return and volatility of returns to make investment decisions is known as the mean-variance framework and is central concept in many of today’s passive asset allocation portfolio management principles. Now, is MPT as viable today - as when it was originally proposed?

Equity Price InfluencersThe equity markets react to the business cycle as it moves through standard phases.For example, coming out of a recession, when gross domestic product (GDP) is increasing, cyclicals do best, since consumers are fulfilling “pent-up demand” for big ticket items that could be deferred during tough economic times.  Conversely, as the economy turns down - so do cyclicals - often slightly ahead of the overall economy. As inflation heats up in a rising economy, companies can raise prices and profit at first as expenses stay constant.  But ultimately inflation raises interest rates and capital becomes more expensive, so companies have to spend more to borrow capital to finance growth. Gentle interest rate increases do not always make the stock market fall, but it will rise more slowly.  However, high interest rates and high inflation ultimately are negatives for the stock market. A bull market in stocks generally consists of three consecutive phases:• Monetary: Interest rates are falling, either naturally as inflation eases or with the help of a central bank, like the Federal Reserve, which can artificially lower short-term interest rates.• Earnings-Driven: Companies have been able to borrow capital cheaply and have spent the down-market time practicing efficiencies, so now they are geared up for growth. Consumers are buying, so earnings are beginning to flow through to the “bottom line.” • Speculative blowout: The markets are responding to the good earnings reports—sometimes beyond what is justified. P/E ratios begin to get very high relative to a normal market, and markets are “overbought.” Wary physicians and canny medical investors may want to sell stocks to take profits. According to Goldman Sachs Research, the stock market may peak while the overall economy is still in a growth phase. Since 1952, the S&P 500 peak has led the overall economy’s peak by about seven months. During down markets, high-dividend-paying stocks and stocks of companies that sell necessary goods or services, like utilities and food companies tend to hold their value. These are called defensive stocks.  

ConclusionFundamental analysis takes into consideration economic factors such as consumers’ ability to buy a company’s goods or services or the company’s borrowing needs at current rates.How has the recent economic and medical business cycle affected your investments?

ArbitrageBuy Low, Sell HighArbitrage is a method, or concept, that has been around for thousands of years, but there is still no set definition of what it is. Your stock broker may give you one definition, while a commodities broker may tell you it's something else. Heck, most investors have no clue what it's about.

The basic premise of the arbitrage theory is that investors (or speculators) force a profit making opportunity to exist. In its most simple form, the definition should look something like, "Buy in a cheap market and immediately sell in a more expensive market." A good example would be the farmers markets found in two different villages. John, an arbitrage junky, goes to the Cheap Village and sees that oranges are selling for $3 per bushel. Through the grapevine, he's heard that oranges sell for $3.50 in Expensive Village. John takes all his cash and buys oranges at $3 per bushel in Cheap Village, then walks to Expensive Village and immediately sells the oranges for $3.50 per bushel. This is basic arbitrage--John has created a

profit making opportunity of $0.50 per bushel. This theory has been used for a long time, at least conceptually. There are four keys to arbitrage, outlined as follows... Information: John had to know that the oranges were selling for $3 in Cheap Village and $3.50 in Expensive Village. Profit Opportunity: John had to see a profit making opportunity, that's the key motivation to arbitrage. Judgment: John had to use his judgment and determine the risk/reward factor. Decision: John had to make the decision whether to actually carry out his arbitrage scheme. These four keys seem obvious, but they're the result of many years of testing, discussion, thought, and evaluation. Stephen Ross initiated an important, and now infamous, arbitrage study in 1976. His study began with comparisons to the Capital Asset Pricing Model, where he pointed out that the CAPM only takes market risk into account when pricing securities. The obvious problem with the CAPM is that there are other considerable risks to securities pricing, such as the industry, sector, interest rates, and so on. Ross argued that the Arbitrage Pricing Theory is a multi-factor model and that it does account for non-market risks. The problem with the APT theory is that we don't know exactly what risks of what magnitude should be identified. For example, when pricing a stock, one investor may put heavy weight on interest rate risk, while another investor puts heavy weight on industry risk. For the theory to be validated, all investors would have to consider the same factors at the same magnitude. So in conclusion, there is still no set definition of arbitrage. Anyone will find several different definitions when checking dictionaries, encyclopedias, and financial glossaries. But to have a basic understanding of what the arbitrage theory represents, there are three important things to remember. Create a profit making opportunity. Buy in a cheap market, sell in an expensive market. Garbage in, garbage out; this relates to the APT and the fact that investors will put different weights on different factors.

Demystifying Hedge Funds Hedge funds may have an aura of exoticism and modernism, but their goals are as old as the art of investing itself. They seek a positive annual return (the higher the better), limited swings in value, and, above all else, capital preservation. They do so by using the best of what modern financial science can provide—rapid price discovery; massive mathematical and statistical processing; risk measurement and control techniques; and leverage and active trading in corporate equities, bonds, foreign exchange, futures, options, swaps, forwards, and other derivatives.Because of their nature, hedge funds are restricted to large-scale investors. Historically, they have attracted high-net-worth individuals and institutional investors, and the array of the latter has widened significantly in recent years to include pension funds, charities, universities, endowments, and foundations. Funds of funds are starting to introduce hedge funds to retail markets, but on a rather limited scale. Currently, there are about 8,500 hedge funds operating worldwide, managing over $1 trillion in assets. Quite a leap from the 2,800 hedge funds, managing $2.8 billion in assets in 1995, not to mention the amounts involved in the earliest hedge fund–type investments in the days of Aristotle (see Box 1).

Box 1It all began with olivesThe first recorded hedge fund–style investment was a "call option" trade and appears to have occurred about 2,500 years ago. Aristotle told the story of a poor philosopher, Thales, who

proved to doubters that he had developed a "financial device, which involves a principle of universal application," by making a profit from negotiating with owners of olive presses for the exclusive rights to use their equipment in the upcoming harvest. Olive press owners were happy to pass on the risks of future olive prices and to accept payment now as a hedge against a bad harvest later. As it turns out, Thales correctly predicted a bountiful harvest, and the demand for olive presses rose. He sold his rights to use the presses and made a profit. Thales's "call option" risked only his down payment. Although he did not invest in fields, workers, or olive presses, he participated actively in olive production by taking on a kind of risk olive growers and press owners were unable or unwilling to take—in the process enabling them to concentrate on growing and processing olives. They made a profit from their work, and he made a profit from his.Modern hedge fund history began with Alfred Winslow Jones, a sociologist and journalist who wrote about market behavior in the 1930s and 1940s and founded one of the first hedge funds in 1949. Jones's fund used leverage and short selling to "hedge" its stock portfolio against drops in stock prices. There was little widespread interest until 1966, when an article in Fortune magazine generated considerable interest by pointing out that Jones was earning 44 percent higher returns than the best-performing equity asset fund—even though he charged a fee equaling 20 percent of the fund's gain. By 1968, there were about 200 hedge funds, although many failed in the 1969–70 and 1973–74 market downturns. Hedge fund business really picked up in the 1990s, fueled mainly by new wealth generated during the 1990s equity bull market.

What is hedging?A few key features distinguish hedge funds from other investment vehicles: the focus on absolute returns, and the use of hedging, arbitrage, and leverage.Absolute versus relative returns. Over very long periods, buy-and-hold strategies almost always do well. The problem is the length of time and starting point: it can matter enormously when you buy. For example, over hundreds of years, stocks returns have averaged about 8 percent a year, but there can be several decades when stock prices don't increase in value at all. The Standard & Poor's (S&P) index, which fell sharply after reaching a peak in 1968, failed to return to its 1968 level in inflation-adjusted terms until 1992! Back in the 1970s, these swings in value prompted investment managers to focus on returns relative to benchmarks, such as the S&P 500 stock index. That way, good performance was expressed in terms of asset managers' performance relative to standard asset-class indices, and the better the relative performance, the more investors were attracted. In other words, managers attracted more investors—and were paid more money—even if the fund declined in value, so long as it did not decline as much as the benchmark index.In contrast, hedge fund managers focus on risk-adjusted absolute returns—that is, their objective is to maximize the increase in investment value per year rather than to simply perform better than the average. Consequently, most hedge fund managers are paid based on how much they increase investors' wealth—a percent of the return—not on how well they do relative to a benchmark, thus focusing their performance exclusively on positive returns. Although managers are also paid a 1 or 2 percent commission a year for assets under management, most of their compensation depends on delivering a positive absolute return. In addition, managers typically invest significant amounts of their own capital in the fund, which aligns their interests with the investors and discourages reckless risk taking. And, when used, a "high-water mark"—whereby capital losses have to be made up before a performance fee is paid—introduces a strong incentive toward capital preservation. In this context, minimizing swings in value and immunizing the hedge fund's portfolio from general swings in market values, through hedging, become key to long-term return maximization.

Hedging, arbitrage, and leverage. What is hedging? It is a technique aimed at protecting a portfolio against sharp movements in market values. It essentially implies buying and holding assets that have good long-term prospects while simultaneously selling assets that have doubtful prospects. The latter technique, short selling, involves borrowing someone else's shares of stock and selling them, with the intent to buy the shares back at a lower price and return them to the original lender. The difference between what the shares are sold for and what needs to be paid to buy them back is the profit. The development of market-traded stock and stock index futures, options, and related derivatives over the past half-century has created a near-infinite number of ways to engage in short selling and hedging (see Box 2).

Box 2 Basic hedge fund arbitrage strategiesConvertible arbitrage. A strategy in which managers purchase a portfolio of securities that are convertible into other kinds of securities. For example, corporate bonds are often convertible into equity shares of the issuing companies. Normally, the prices of the bonds and shares trade in a close relationship. Sometimes bond and stock market conditions cause the prices to get out of line. Hedge funds buy and sell the bonds and stocks simultaneously, pushing the prices back into line and profiting from market mispricing. Distressed securities. A strategy in which managers use borrowed funds to invest in the debt and equity of companies that are currently or recently in bankruptcy reorganization, or may declare bankruptcy in the near future.Event-driven/merger. A strategy in which managers invest in opportunities created by significant transactional events, such as spin-offs, mergers and acquisitions, bankruptcy reorganizations, recapitalizations, and share buybacks.Global macro. A strategy in which managers employ "top down" global approaches and may invest in any markets using any instruments to profit from inaccurately priced market movements resulting from shifts in world economies, geopolitical conditions, global supply and demand balances, or other large-scale changes.Long/short. Strategies in which managers take long positions in securities expected to rise in value and short positions in securities expected to fall in value in an effort to insulate the portfolio from market volatility. One example of this strategy is to build a portfolio made up of long positions in the strongest companies in an industry and corresponding short positions in the weakest companies.Market neutral. A category of long/short strategies in which managers invest the same amount of capital in offsetting long and short positions, maintaining a portfolio with zero or near-zero net market exposure.Volatility arbitrage. A strategy in which managers sell short-term call and put options to profit from option premium decay and volatility mean-reverting tendencies using index options and/or options on futures contracts.

The technique of arbitrage tries to profit from the fact that sometimes an asset trades at a different price in different markets at the same time. Because an asset should have the same price in all markets at the same time, a way to capture a low-risk profit is to sell the higher-priced asset in one market (sell it short) and buy the lower-priced asset (buy it long) in the other market. When the prices converge, an arbitrage profit can be captured by selling the formerly low-priced asset and buying back the formerly high-priced asset. A typical example of potential arbitrage opportunities is company bonds that are convertible into equity shares of the company.A hedge fund manager focuses on achieving absolute returns by finding as many profit opportunities as possible that are immune to market gyrations—in industry lingo, generating alpha (returns uncorrelated to market performance) rather than beta. Because these opportunities

often involve small trading margins, the use of leverage and prudent risk management seeks to achieve good returns with lower volatility. The key performance variable is risk-adjusted returns. The most widely used measure is the Sharpe ratio—the rate of the mean of the return to its standard deviation. Higher values mean the risk-adjusted return is higher, given a particular measure of risk.The bottom line is that hedge fund profits arise not from accurately predicting the direction of prices but from being able to identify transient pricing opportunities. To believe in the ability of hedge funds to be successful, one must disbelieve, or at least relax, the well-known efficient markets hypothesis, which says that on average no model projecting directional movements in asset prices will be significantly superior to tossing a coin. In fact, however, the operations of hedge funds may be viewed as promoting efficient markets: by actively seeking to eliminate market mispricing, hedge funds contribute to a faster and more efficient convergence of prices toward a market equilibrium, diminish market pricing errors, reduce price extremes, and can help to stabilize markets, "buying low and selling high."

Debunking hedge fund mythsIn recent years, there has been a lot of debate and hand wringing about hedge funds, their effects on global financial stability—especially since a major U.S. hedge fund had to be bailed out in 1998 (see Box 3)—and the degree of regulation or supervision to which they are subject. The reality is that these worries are overblown. Take two of the biggest myths.

Box 3 The LTCM debacleIn all markets there are failures, and hedge funds are not immune to them. The most famous case is that of Long-Term Capital Management (LTCM), a well-known hedge fund that lost all its capital in the fall of 1998. A sudden spike in market volatility in the summer of 1998 led to a very rapid increase in LTCM's losses, forcing its liquidation. In addition to the doubtful soundness of some of its strategies, LTCM's failure happened for two main reasons: risk management systems in LTCM and its banks were weak; and LTCM's investment positions had become too large relative to the total market volume in those assets. When prices turned against it, LTCM could not sell its holdings quickly enough. And as it engaged in fire-selling to adjust its portfolio, its losses snowballed. Because its positions were so large and were linked to so many other financial institutions, LTCM became a potential systemic risk, convincing the authorities to intervene.As a result of a thorough review of the hedge fund business following the LTCM failure, companies that interact with hedge funds have tightened counterparty risk management. And national and foreign financial regulatory institutions have upgraded their supervisory oversight of hedge funds. But perhaps even more important, there has been a rethinking within the hedge fund industry itself, with leading hedge fund companies establishing best practice guidelines for the industry. And follow-up evaluations, such as the one by the Financial Stability Forum in 2002, show that risk management discipline has increased and leverage has fallen.

Myth 1: Hedge funds can move financial markets for their own gain or cause market turmoil. After exhaustive analysis, the U.S. Securities and Exchange Commission (SEC) recently determined that there is little evidence that hedge funds can move markets, and several research studies have found no evidence that hedge funds were a cause of the Asian crisis or other world economic turmoil (Eichengreen and others, 1998). The unwinding of "carry trades" (borrowing at a low interest rate and lending at a higher one) did contribute to Europe's 1993 exchange rate mechanism crisis, the 1994–95 peso crisis, and the 1997–98 Asian crisis. But the key problem underlying these events was the misalignment of exchange rates with respect to their

fundamentals—not the intervention of financial market participants. In fact, the IMF study led by Eichengreen found that hedge funds, by being willing to take the risk of buying some of the assets that had already fallen significantly in price, contributed to limiting the downfall during the Asian crisis and advancing the recovery.The reality is that hedge fund activity makes financial markets more efficient and, in many cases, more liquid, as has been widely recognized by the U.S. Federal Reserve, the SEC, and the IMF. Not only do hedge funds contribute to the adjustments of markets when they overshoot, they also help banks and other creditors unbundle risks related to real economic activity by actively participating in the market of securitized financial instruments. And because hedge fund returns in many cases are less correlated with broader debt and equity markets, hedge funds offer more traditional investment institutions a way to reduce risk by providing portfolio diversification.Myth 2: Hedge funds are unregulated and unsupervised. The fact is that hedge funds in the United States are regulated and supervised directly or indirectly by seven U.S. government agencies (the Federal Reserve, the Department of Treasury, the SEC, the Commodity Futures Trading Commission, the National Futures Association, the Comptroller of the Currency, and the Federal Deposit Insurance Corporation) and by numerous international agencies.Here to stayIn sum, hedge funds are called hedge funds because they use a full array of hedging techniques to reduce portfolio volatility. They are becoming increasingly popular, as private ownership of capital expands worldwide and large-scale capital owners seek to preserve their wealth in volatile markets. In an effort to soothe worries about transparency and supervision, public authorities are trying to develop new approaches to meet the public's need for financial system stability and investor protection while enabling investors to enjoy the benefits that hedge funds bring to financial markets.

Sportsbook Arbitrage- The Basics I. Arbitrage with Sportsbook Bonuses – The BasicsWhat is arbitrage?Basically, sportsbook arbitrage is exploiting price differences in a market in order to guarantee a profit.Sports betting offers one of the easiest, low-risk way of using arbitrage to guarantee yourself a nice return on investment (ROI). A ROI which can be much higher than can be obtain from investing in the stock market. First, arbitrage opportunities only exist when a book offers a line that differs greatly from that offered at another book. This can occur when the line first comes out, due to the fact that the sports manager at one book disagrees with the linesmaker at another book. More commonly, however, is that the perceived value of a wager, like a stock, is ever changing. Lines are constantly changing, and the books that are slowest to adjust their lines to be with the rest of the market will be most vulnerable to sportsbook arbitrage opportunities. Second, sportsbook arbitrage opportunities do not last long, as there are many people trying to profit from the same mistake. Once a book realizes it is taking too much action on the bad side of a line, it will adjust that line and the sportsbook arbitrage will no longer exist. Lastly, if you are fortunate enough to be able to place a bet on the bad line, you should have no trouble “selling” it by betting on the other side of the event at another book. The greatest part about sportsbook arbitrage is you can take a negative-return arb and still make a nice profit, we will go over this later.How do you know if an arbitrage exists?It can be difficult at first to identify which lines at different sites will have a sportsbook arbitrage opportunity. If you are using American odds (as opposed to Decimal or Fractional odds), lines

will be portrayed using a plus or minus sign, followed by a number of 100 or higher. A line with a plus sign is used for the underdog. The number that follows indicates how much you will win if you place a $100 bet. For example, a line of +2000 means that for every $100 you wager you will win $200. Similarly, a minus sign is used for the favorite. The number that follows indicates how much you must bet to win $100. For example, a line of –200 means that you must wager $200 to win $100.

A sportsbook arbitrage exists whenever the positive line (on the underdog) is greater than the negative line (on the favorite).For example, let’s say Detroit plays Chicago and the line for which team is going to win (Known as the Moneyline or ML) at book A is -150 on Detroit and +140 on Chicago. At book B, they have -170 Detroit and +155 Chicago. Therefore, we have a situation where the positive line is greater than the negative one. In this case, -150 with Detroit at book A and +155 with Chicago at book B. If we placed a $500 bet on Detroit (-150) at book A, we would win $333.33. If we place $325 bet on Chicago (+155) at book B, we would win $503.75. Therefore, if Detroit wins we won $333.33 at book A but lost $325 at book B, for a total profit of $8.33. If Chicago wins, we win $503.75 at book B but lost $500 at book A, for a total profit of $3.75. So no matter what the result of the game, we guarantee we make something. Now 3 or 8 dollars doesn’t seem like it would be worth your time? However, we will always be playing with bonus money given to us from the various sportsbooks. We will go over this later, also. How many sportsbook arbs can be found a day?Generally, you will be limited by the amount of events available to bet on that day. You will mostly place bets on the larger well-known sports, like baseball, basketball, football, hockey, and soccer (which is a little trickier than the others)Basically:Number of books used Experience Bankroll size Events on given day Expect to have no troubles finding all the sportsbook arbs you need in a given day. Generally, only your bankroll will be your limiting factor.What time is best for finding sportsbook arbs?You can arb nearly 24 hours a day. You are slightly limited during the period of 11pm (Eastern Time) until late morning (Eastern Time). These are the time in which the betting exchanges don’t have as many available bets. Betting exchanges will be a major source of finding arbs.How many books should I use?Generally, you will use a couple of main books for covering your sportsbook arbs. These include Matchbook and Pinnacle. After these two, you will be obtaining bonuses from various online sportsbooks. Generally, you will attempt to work 1-3 bonuses, depending on your bankroll size.How much money do I need to get started?You could get started with a very small amount, as low as $500. This will allow you to work a lot of the smaller match-play bonuses at a lot of the UK sportsbooks. However, a better figure for getting started would be $5,000. This would allow you to go after bonuses that would require a deposit of a range of $500-$1,000. Once you are comfortable, a better figure to work with would be $10,000-$15,000. Then, you will be able to work off several bonuses for the max bonus amounts at the same time.How much money can I make and how much time will I need to invest.This is strongly dependent on bankroll size. At first, it will be slower, because you will be learning and spending more time double checking and being cautious. Once you catch on to the basic concepts, you will find yourself spending less and less time working on sportsbook arbitrage. It will get to the point where you run out of things to do fairly quickly. By the time you

get the hang of it, you will rarely invest more than one hour a day and be able to consistently bring in an extra $200-$500 a week. I have seen people make over $3,000 in their first month. This won’t bring in enough to do for a living, but can provide great extra income for those who don’t have a tremendous amount of free time.Why not just try and pick the winning bets instead?Sportsbook arbitrage isn’t very exciting because you are never risking any money on the games you bet on, you are basically doing a bunch of simple math problems to place your bets. Most people who try to bet on just one side of an event are rarely successful long-term. The ones that are invest nearly all of their time researching lines and statistics to make their bets. Even they can have losing years.So, why sportsbook arbitrage over handicapping? The reason is that sportsbook arbitrage gives you a guaranteed profit. While this isn’t as exciting as trying to pick the winner of a game, trust me, it feels good to win money on sports betting week-in and week-out. It is very nice to be able to bet on a game and not even care who wins or loses and yet still make money either way.ArbitrageDefinition: Arbitrage is the practice of taking advantage of price differences between markets. Stock brokers do this by buying in one country and immediately selling it in another for a profit. Arbitrage is used by some Internet entrepreneurs to take advantage of the price difference between some advertising keywords in AdWords and AdSense. The basic system is that someone buys a inexpensive AdWords campaign, such as "cheap widgets" for ten cents. The ads direct anyone clicking on them to a Web page that is optimized for a more expensive keyword, such as "expensive widgets" for five dollars per click. If even a fraction of people visiting "expensive-widgets.com" click on the ads, the arbitrageur has turned a reasonable profit. Although there is nothing explicitly forbidden about using arbitrage to profit from AdSense, it is often a technique employed by low quality content producers, and Google has shut down some very profitable accounts that were using this technique.

ARBITRAGE STRATEGIES:

1. Convertible Arbitrage involves purchasing a portfolio of convertible securities, generally convertible bonds, and hedging a portion of the equity risk by selling short the underlying common stock. Certain managers may also seek to hedge interest rate exposure under some circumstances. Most managers employ some degree of leverage, ranging from zero to 6:1. The equity hedge ratio may range from 30 to 100 percent. The average grade of bond in a typical portfolio is BB-, with individual ratings ranging from AA to CCC. However, as the default risk of the company is hedged by shorting the underlying common stock, the risk is considerably better than the rating of the unhedged bond indicates.

2. Distressed Securities strategies invest in, and may sell short, the securities of companies where the security’s price has been, or is expected to be, affected by a distressed situation. This may involve reorganizations, bankruptcies, distressed sales and other corporate restructurings. Depending on the manager’s style, investments may be made in bank debt, corporate debt, trade claims, common stock, preferred stock and warrants. Strategies may be sub-categorized as “high-yield” or “orphan equities.” Leverage may be used by some managers. Fund managers may run a market hedge using S&P put options or put options spreads.

3. Equity Market Neutral investing seeks to profit by exploiting pricing inefficiencies between related equity securities, neutralizing exposure to market risk by combining long and short positions. Typically, the strategy is based on quantitative models for selecting specific stocks with equal dollar amounts comprising the long and short sides of the portfolio. One example of this

strategy is to build portfolios made up of long positions in the strongest companies in several industries and taking corresponding short positions in those showing signs of weakness. Another variation is investing long stocks and selling short index futures.

4. Fixed Income: Arbitrage is a market neutral hedging strategy that seeks to profit by exploiting pricing inefficiencies between related fixed income securities while neutralizing exposure to interest rate risk. Fixed Income Arbitrage is a generic description of a variety of strategies involving investment in fixed income instruments, and weighted in an attempt to eliminate or reduce exposure to changes in the yield curve. Managers attempt to exploit relative mispricing between related sets of fixed income securities. The generic types of fixed income hedging trades include: yield-curve arbitrage, corporate versus Treasury yield spreads, municipal bond versus Treasury yield spreads and cash versus futures.

5. Merger Arbitrage, sometimes called Risk Arbitrage, involves investment in event-driven situations such as leveraged buy-outs, mergers and hostile takeovers. Normally, the stock of an acquisition target appreciates while the acquiring company’s stock decreases in value. These strategies generate returns by purchasing stock of the company being acquired, and in some instances, selling short the stock of the acquiring company. Managers may employ the use of equity options as a low-risk alternative to the outright purchase or sale of common stock. Most Merger Arbitrage funds hedge against market risk by purchasing S&P put options or put option spreads.

6. Relative Value Arbitrage attempts to take advantage of relative pricing discrepancies between instruments including equities, debt, options and futures. Managers may use mathematical, fundamental, or technical analysis to determine misvaluations. Securities may be mispriced relative to the underlying security, related securities, groups of securities, or the overall market. Many funds use leverage and seek opportunities globally. Arbitrage strategies include dividend arbitrage, pairs trading, options arbitrage and yield curve trading.

7. Volatility Arbitrage: Many derivatives, particular options, are sensitive to the levels of volatility in the market prices of securities. Volatility arbitrage strategies aim to directly exploit mis-pricings in volatility between options or between the relative volatility of options versus their underlying securities. Many of these strategies aim to be long volatility in order to make money when volatility increases but this must be carefully balanced against the cost of the option and the potential to lose money if volatility decreases. Managers typically employ sophisticated modeling and simulation tools to quantify, optimise and/or hedge their exposures. Funds in the sector may focus on single stock options, index options/futures and/or equity dispersion trading. Some funds may also focus on non-equity volatility or a combination of all of these.

8. Credit Long/Short: Credit long/short funds aim to achieve returns by identifying fundamental opportunities expressed through long or short positions in credit instruments. Returns, which can be correlated with movements in credit spread, are generated through both carry (income) and capital appreciation/depreciation.

9. Emerging Markets Credit: Emerging market credit funds focus on investing in credit risks in emerging markets. Political risk is often a major factor in determining the performance of these strategies. Funds may invest in sovereign focused risk, dollar denominated or Brady bonds only or include local sovereign debt, emerging markets corporate credit or distressed debt and trade finance.

Asset Backed Securities / Leveraged Finance10. Mortgage and Asset-Backed Credit : Mortgaged and asset-backed securities are secured by either high value collateral, usually hard assets like real estate, or high confidence cash flows, such as those arising from senior secured liabilities like bank loans. Hedge funds investing in these areas generally find opportunities either from analysis of the underlying credit characteristics of the assets or from the complexity of the structures which govern the coupon payments. Collateral types can include residential and commercial mortgages, pools of receivables or bank loans.

11.Distressed: Funds employing this strategy invest primarily in the debt of companies in financial distress or bankruptcy. Such securities typically trade at substantial discounts to par as existing investors often sell the debt of companies which start to experience financial distress or file for bankruptcy. These investors either cannot or do not wish to hold debt that is undergoing the procedural complexities of the bankruptcy or reorganisation process. Distressed managers seek to profit by buying debt below what they estimate to be its ultimate recovery value during or upon finalisation of the reorganisation process.

12. Event Driven: Event driven strategies focus on capturing price movements or anomalies generated by corporate events. Many funds are equity-oriented but more diversified funds may invest in credit as well as equities, although they typically hold more than 25% of their portfolios in equities.

Relative value arbitrage encompasses a number of sub-strategies. Generally, relative value managers seek to profit from the mis-pricings of related financial instruments; they use quantitative and qualitative analysis to identify securities, or spreads between securities, that deviate from their perceived fair value and/or historical norms. Relative value sub-strategies mainly include fixed income strategies. Fixed Income Relative ValueFixed income relative value funds trade a broad range of government bonds, swaps, money markets and swaption instruments. These funds sometimes have a small exposure to mortgages and credit but it is not their primary focus. 13. Mortgage Relative Value: Mortgage relative value funds focus on liquid mortgage securities. Hedge funds investing in these securities typically model the impact of changes in interest rates and other factors on the repayment or prepayment characteristics of an underlying pool of assets, and attempt to identify securities that are mis-priced relative to other mortgages in the market. They may hedge out exposure to interest rate fluctuations using Treasuries, swaps or other fixed income derivatives. These funds do not generally take any credit risk.

14. Municipal Bond Arbitrage: These funds focus on the municipal bond market in the US. Municipal bonds are issued by US states, municipalities or counties, in order to finance capital expenditures. Municipal bonds are exempt from federal taxes and from most state and local taxes. Municipal bond arbitrage funds seek to profit from tax rate arbitrage and non-economic selling, often by retail investors who make up the majority of the investors in the asset class.

15. Relative Value Diversified: The relative value diversified sector tends to include strategies that invest outside fixed income. Examples include commodity relative value funds, funds pursuing ADR/GDR arbitrage strategies and closed fund discount arbitrage. It should be noted that statistical arbitrage equity funds are typically categorised as either systematic non-trend under Trading or equity long/short under Equity Hedge.