MONEY & BANKINGTopics: Lesson 10 to 22 Risk Measuring & Evaluating RiskBonds & Bonds PricingYield to MaturityShift In Equilibrium /Bond and Source of BondTax Effect & Term StructureThe Liquidity Premium TheoryValuing Stock and Risk Role of Financial Intermediaries

RISK MEASURING AND EVALUATING

Risk is defined as the uncertainty of an asset's return over a given period. We usually think of risk as involving the possibility of a loss or a major hardship, like losing money in the stock market or being stranded on a deserted stretch of highway with a flat tire. But more generally risk just means uncertainty, a range of possible outcomes, not all of which are equally good.

Almost all people are risk averse (they have risk aversion), in that they hate to lose more than they love to win. A risk-averse person dislikes being exposed to risk, and will always refuse an even-money bet(such as a coin toss with $20 at stake) to the point of paying to avoid such bets. Buying insurance is a sign of risk aversion. Someone who is not risk-averse is either risk-neutral (indifferent between taking or not taking even-money bets) or risk-loving (will always accept such bets -- e.g., habitual gamblers).-- If returns on two assets are equal, risk-averse people will prefer the lower-risk asset---- increase in an asset's risk (relative to other assets)--> decreased demand for that asset,      increased demand for all other assets

Characteristics of risk Risk can be quantified. Risk arises from uncertainty about the future. Risk has to do with the future payoff to an investment, which is unknown. Our definition of risk refers to an investment or group of investments. Risk must be measured over some time horizon. Risk must be measured relative to some benchmark, not in isolation. If you want to know the risk associated with a specific investment strategy, the most

appropriate benchmark would be the risk associated with other investing strategies

II. MEASURING RISK

Conceptually, an asset's risk is the volatility of the asset's return. We can measure that volatility, or variability, of the asset's return as the* variance (average squared deviation from mean return) of the asset's yearly returns, or as the * standard deviation (typical deviation from mean, or average, return; equal to the square root of the variance).

* An alternative that involves only simple arithmetic is the average (absolute-value) deviation from the mean return, which produces a result not far from the standard deviation. The standard deviation is the preferred measure, however (one reason why is that it gives more weight to outliers, or large deviations. If we're risk-averse, then it makes sense to give extra weight to outliers.)

Two of the most crucial pieces of information about any financial asset are its mean return (relates to expected return) and the standard deviation of its year-to-year returns.

-- If the expected return is just a simple average of past returns, then it's very easy to compute. Alternatively, one might put a lot more weight on recent returns, or incorporate other information into one's expectations.

The expected value of an investment is defined as the probability-weighted sum of the possible values of an investment. The expected return on an investment is the expected value of future payouts, minus what you paid for the investment.  (To put it in percentage terms, we would then divide that amount by what you paid for the investment, then take it to the 1/n power (to get an annualized return), and multiply by 100%.)

Old bonus question, long since answered:Q: Suppose that a slot machine costs $1 to play once, and that the player has a 1 in 5,000 chance of a $1,000 payout, a 1 in 500 chance of a $100 payout, a 1 in 50 chance of a $10 payout, and otherwise nothing.  What is the expected payout from playing that slot machine?  Show your work.A: Expected payout, or Expected value = (Probability of $1000 payout)*($1,000 payout) + (Probability of $100 payout)*($100 payout) + (Probability of $10 payout)*($10 payout)= (1/5000)*($1000) + (1/500)*($100) + (1/50)*($10)= $0.20 + $0.20 + $0.20= $0.60.(That's the expected payout.  Since it costs $1 to play, your expected return from playing is minus forty cents.

Ex.: A company's stock has had the following yearly returns over the past five years: 5%, 15%, 10%, 2%, 8%

--> Mean return = simple average of those = (5+15+10+2+8)% / 5 = 40% / 5 = 8%

Deviations from mean = difference each year's return and the mean return (yearly return minus mean return)= -3%, 7%, 2%, -6%, 0%(calculated as 5% - 8%, 15% - 8%, 10% - 8%, 2% - 8%, 8% - 8%)

Absolute deviations from mean = absolute values of deviations= 3%, 7%, 2%, 6%, 0%

Average absolute deviation = simple average of absolute deviations= (3+7+2+6+0)% / 5

= 18% / 5= 3.6%/|\ | The standard deviation will be pretty close to this number, and only a bit more complicated to compute. It's the square root of the variance, which is the average squared deviation from the mean. So let's first compute the (population) variance, by taking the squares of those deviations from the mean (which were 3%, 7%, 2%, -6%, 0%), add them up, and divide by 5 (the number of observations):

Variance= (9% + 49% + 4% + 36% + 0%) / 5= 98% / 5= 19.6%.

Taking the square root of that gives us the standard deviation, which is4.4%.

So the standard deviation is very much like the average absolute deviation, except it tends to be a bit bigger. That first step of squaring all those deviations means that large deviations become magnified, and the final step of taking the square root of the average does not entirely undo that magnification.-- For example, consider two more stocks with an 8% mean return and yearly returns over a five-year period of (a) 4%, 12%, 4%, 12%, 8% and (b) 0%, 16%, 8%, 8%, 8%. The standard deviation is 3.6% for the first, 5.1% for the second.

{Nice to know: On an Excel spreadsheet, the command for the mean or average is =AVERAGE(range of cells or numbers), the command for standard deviation is =STDEV(range...), and the command for variance is =VAR(range...).}

Another useful measure of risk is value at risk, which is defined as the worst possible loss over a specific time horizon at a given probability. One can look at past returns and outcomes to form a prediction of how large a loss could occur and how likely it is to occur.-- Ex.: If you have $10,000 and want to invest it in an index fund of the stock market over the next year, then you might want to know your odds of losing half of your investment. If a 50% loss in a one-year period has occurred in four of the past 100 years, then you could say you have a 4% probability of losing $5,000 (i.e., 50% of $10,000).-- Value at risk is a helpful concept because it explains why risk-averse (or even risk-neutral) people would do things like go to casinos or play the lottery, where the expected return is negative and you're likely to lose money. The answer is that such people tend to budget just a small amount of money for casino gambling or lottery tickets, so they're not putting a lot at risk.

III. SOURCES OF RISK: IDIOSYNCRATIC AND SYSTEMATIC

Two types of risk:

(1) idiosyncratic (firm- or industry-specific, nonsystematic) -- unique to the individual firm or industry; can be diversified away-- Ex.: Nike stock, Philip Morris (tobacco) stock, New York municipal bonds-- Studies have shown that to eliminate nearly all of the company-specific, or non-systematic, risk in a stock portfolio, you need own maybe 30-40 stocks. The average mutual fund holds 130.

(2) systematic -- cannot be diversified away-- Ex.: stocks have systematic risk, because you can never be certain what will happen to those companies, and fluctuations in the current interest rate will raise or lower their resale prices (PDVs). Long-term bonds have systematic interest-rate risk as well.-- Risk that is unique to a particular class of asset, as opposed to a particular firm or industry, classifies as systematic risk. You can diversify by holding assets of many different types (e.g., stocks, bonds, real estate, cash), but you won't be able to eliminate the risk from your portfolio entirely.

Asset risk = idiosyncratic risk + systematic risk

In a well-diversified portfolio, there is no idiosyncratic (company- or industry-specific) risk. All of the risk is systematic, arising from the inherent riskiness of the individual components (stocks, bonds, etc.) of that portfolio.

The standard measure of systematic risk: beta: measures the sensitivity of an asset's return to changes in the average return on the entire market. Beta is a numerical measure (a regression coefficient, to be precise) of the mutual relationship between market return and asset's return. If beta is 1, then an increase in the market return of, say, 10% means that the asset will typically gain 10% as well (a market index fund has a beta of 1). If beta is 2, then a 10% increase in the market return typically means a 20% increase in the asset's return. In an "up" market, a high beta means a high, above-average return; but in a "down" market, high betas mean bigger-than-average losses. Some assets have negativebetas, meaning that they do poorly when the market does well and vice versa. Some examples:-- A stock-market index fund will have a beta of 1, because it holds the exact same stocks that go into the market average.-- Technology stocks and other new-industry stocks tend to have betas > 1.-- Utility stocks and those of long-established companies tend to have betas < 1.-- Long-term bonds seem to have a beta close to 0. (Stocks and bonds are substitutes, but both are affected about the same by things like changes in market interest rates.)-- Precious metals have a beta of less than 0. Their prices tend to go up when stock prices are down.

The greater an asset's risk, the greater the return it must offer to induce people to hold it and hence the greater its risk premium (the extra return on a risky asset, relative to the return on a risk-free asset like a Treasury bill). This concept will be explored more fully when we cover chapter 7 ("The Risk and Term Structure of Interest Rates").-- Ex.: Rock star David Bowie issued $55 million worth of bonds in early 1997. His capacity to repay was pretty good, because he had a large and steady stream of income from royalties, album sales, etc. It's unclear whether those royalties will rise or fall in the future, but it's a fairly safe bet that they'll be enough for him to make his bond payments. Still, it's not a completely safe bet, so compared with Treasury bonds of the same maturity length (10 years), the Bowie bonds should pay a higher interest rate. As indeed they did: the Bowie bonds paid 6.9% interest, and Treasury bonds at the time paid 6.4% interest. The difference, 0.5% (i.e., 50 basis points), was the risk premium on the Bowie bonds.---- Side note: Why did Bowie issue those bonds in the first place? Don't know. He may have wanted the money to finance some big new investment project, or, as the book suggests, he might just have wanted the sure thing of having $55 million right now instead of waiting for the money to trickle in the form of royalties and other income. So the book is suggesting that Bowie himself is risk-averse, because he gets $55 million now and will pay his bondholders out of that large-but-uncertain stream of future royalty income. If his royalties are less than expected and he can't make the bond payments, that's a bigger problem for the bondholders than for him.)

Risk Aversion and the Risk Premium

In economics and finance, we assume the people are risk averse. This means people do not like risk ALL ELSE BEING EQUAL. Consider the example above, with expected value of $1100 or a 10% expected return. Would you take investment 1 over the choice of a GUARANTEED 10% return? No, you would not. Furthermore, risk averse investors will prefer investment 2 to investment 1 since it has the same expected return, but a lower risk.

Risk aversion is a simple but powerful concept. It is a key building block to all modern asset pricing and portfolio theory in finance. If goes back to the core principle that risk requires compensation. To entice investors to buy securities with higher risky, the seller must offer is higher expected payoff. This is known as the risk premium. This also means that investments with higher expected payoffs also carry higher risk. This is the risk-return tradeoff. You don't get both low risk and high return.

BOND AND BOND PRICING

A debt investment in which an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate. Bonds are used by companies, municipalities, states and U.S. and foreign governments to finance a variety of projects and activities. Bonds are commonly referred to as fixed-income securities and are one of the three main asset classes, along with stocks and cash equivalents..

Investopedia Says:The indebted entity (issuer) issues a bond that states the interest rate (coupon) that will be paid and when the loaned funds (bond principal) are to be returned (maturity date). Interest on bonds is usually paid every six months (semi-annually). The main categories of bonds are corporate bonds, municipal bonds, and U.S. Treasury bonds, notes and bills, which are collectively referred to as simply "Treasuries."

Two features of a bond - credit quality and duration - are the principal determinants of a bond's interest rate. Bond maturities range from a 90-day Treasury bill to a 30-year government bond. Corporate and municipals are typically in the 3-10-year range.

Bond Prices

Here we look at four basic types of bonds: Interest rates apply to four types of credit market instruments:

zero coupon bond or discount bond

purchased at some price below its face value (or at a discount) entitles the owner to a face value payment at the maturity date.

There are no interest payments, hence the name "zero coupon bond."

U.S. Treasury Bills are an example of a zero coupon bond.

fixed-payment loan

provides the borrower with an amount of principal

the principal and interest are repaid with equal monthly payments for a certain period

each monthly payment is a combination of principal and interest

mortgages and car loans are fixed-payments loans

coupon bond

purchased at some price entitles the owner to fixed interest payments annually (coupon payments) until maturity

and a face value payment (or par value) at maturity

characterized by the issuer, the maturity, and the coupon rate, which is multiplied by the face value to determine the coupon payment

Note: your textbook focuses on annual payments, but in fact, almost all coupon bonds issued in the United States have semi-annual payments.

consol

purchased at some price entitles the owner to interest payments forever

the principal is never repaid

EXPLINATION

Zero-coupon Bonds

Because discount bonds have only one payment at maturity, it yield to maturity is easy to calculate and is similar to that of a simple loan. Most discount bonds have a maturity of LESS than one year, so the example below looks at such a case:

example 1: Consider a Treasury bill with 90 days to maturity, a price of $9875, and a face value of $10,000.

The current value is $9850, and the only future payment is $10,000 at maturity. However, we do not wait a year for this payment but only 90 days so we need to adjust the discounting for this.

The yield to maturity solves the following equation:

Solving for i,

This method is the convention in financial markets, known as the bond equivalent basis. If you use a financial calculator you may come up with a different answer. Here's why.

In general, the yield to maturity is found by the formula

where F is the face value, P is the bond price, and d is the days to maturity.

Fixed-Payment Loan

This case is more complicated due to the multiple payments through the life of the loan. Your textbook example uses a loan with annual payments on page 71. However, the most common forms of this type of loan are for monthly payments, like a mortgage, student loans or an auto loan. Loans with multiple payments during the year are a bit more complicated, as shown in the example below:

example 2: Suppose you take out a $15,000 car loan for 5 years, with monthly payments of $300.

The value of the loan today is $15,000. The future payments are $300 payments over the next 60 months.

The yield to maturity is the i that solves the following equation:

Note that since payments are monthly for 5 years, there are a total of 5 x 12 = 60 payment periods. Also, the yield to maturity, i, is expressed on an annual basis, so i/12 represents the monthly discount rate (note 1)

.

So how do we solve this for i? Well it is not easy, since there is no way to isolate i in this equation. It could be done by trial and error (trying values of i until the right-hand side of the equation is $15,000), but that is too time consuming. This problem is solved with the aid of a table, financial calculator, or spreadsheet programs that do this automatically. A financial calculator is not required for this course, so I provide loan or bond table when needed.

Consider the following loan table:

We are looking for a 5 year loan (shaded yellow), and a monthly payment of $300. Looking at the table above we see that at 7.5% yield to maturity, the payment is $300.57. So the yield to maturity is slightly under 7.5% (7.42% to be more precise).

Click below for the "high tech" ways to solve this example:

Financial Calculator: TI BA II+ Excel Spreadsheet

Coupon Bond

With the multiple interest payments involved, this case is similar to the fixed payment loan in its complexity. Again, your textbook example uses a coupon bond with annual coupon payments on page 121. However, all bonds issued in the United States have coupon payments semi-annually, or every 6 months, including Treasury notes, Treasury bonds, and corporate bonds. So the example below also uses 6-month payments.

example 3: Consider a 2-year Treasury note with a face value of $10,000, a coupon rate of 6%, and a price of $9750.

So the yield to maturity will solve the equation:

bond price = PV(future bond payments)

What are the future payments?

There are coupon payments every 6 months, and a face value payment at maturity.

What are the coupon payments?

The coupon payments are [face value x coupon rate]/2 = $10,000 x .06 x .5 = $300. Note that we divide by 2 because there are 2 coupon payments in a year. So the payment schedule is

6 months $3001 year $30018 months $3002 years $10,300

So the yield to maturity will solve the following equation:

Note that since payments are every 6 months for 2 years, there are a total of 2 x 2 = 4 payment periods. Also, the yield to maturity, i, is expressed on an annual basis, so i/2 represents the 6 month discount rate (note 2)

Like the fixed payment loan, this problem is solved with the aid of a table, financial calculator, or spreadsheet programs that do the trial-and-error calculations automatically. A financial calculator is not required for this course, so I provide loan or bond table when needed.

Consider the following bond table:

We are looking for a 2 year bond (shaded yellow), and a price of $9750. Looking at the table above we see that at 7.5% yield to maturity, the price is $9726.15. So the yield to maturity is slightly under 7.5% (7.37% to be more precise).

Click below for the "high tech" ways to solve this example:

Financial Calculator: TI BA II+ Excel spreadsheet

Looking at the bond table in example 3, there are 3 important points to be made about the relationship between bond prices, maturity, and the yield to maturity:

1. The yield to maturity equals the coupon rate ONLY when the bond price equals the face value of the bond.

2. When the bond price is less than the face value (the bond sells at a discount), the yield to maturity is greater than the coupon rate. When the bond price is greater than the face value (the bond sells at a premium), the yield to maturity is less than the coupon rate.

3. The yield to maturity is inversely related to the bond price. Bond prices and market interest rates move in opposite directions. Why? As interest rates rise, new bonds will pay higher coupon rates than existing bonds. The prices of existing bonds fall in the secondary market, so the yield to maturity rises. This negative relationship between interest rate and value is true for all debt securities, not just coupon bonds.

Consols

Consols promise interest payments forever, but never repay principal. Consols are fairly rare and are issued by governments, since they are the only entities that can realisticly promise interest payments forever. (The U.S. government does not issue consols, but the French government has.) The price of the consol is the present value of future payments, but the number of future payments are infinite. If i <1, then this infinite series converges to a finite amount (your book derives this on page 122 if you are curious):

Bond Yields

We see from examples above that calculating the bond price is based on knowing the yield. It is also true that we can calculate a yield based on the bond price. We use the term yield and interest rate interchangeably.

Yield to Maturity

The yield to maturity is the interest rate that makes the discounted value of the future payments from a debt instrument equal to its current value (market price) today. It is the yield bondholders receive if they hold a bond to its maturity.

Looking at the bond table in example 3, there are 3 important points to be made about the relationship between bond prices, maturity, and the yield to maturity:

1. The yield to maturity equals the coupon rate ONLY when the bond price equals the face value of the bond.

2. When the bond price is less than the face value (the bond sells at a discount), the yield to maturity is greater than the coupon rate. When the bond price is greater than the face value (the bond sells at a premium), the yield to maturity is less than the coupon rate.

3. The yield to maturity is inversely related to the bond price. Bond prices and market interest rates move in opposite directions. Why? As interest rates rise, new bonds will pay higher coupon rates than existing bonds. The prices of existing bonds fall in the

secondary market, so the yield to maturity rises. This negative relationship between interest rate and value is true for all debt securities, not just coupon bonds.

Current Yield

The yield to maturity is the truest measure of the interest rate, and very useful in comparing different debt securities. However there are other measure out there developed for their computational convenience. It this day of cheap computing, it is easy to forget that calculators were not available until 1975 (and then cost $200 for one that could just do arithmetic!). Bonds traded long before that, so traders used yield measures that approximated the yield to maturity but were easier to calculate.

The current yield is an approximation used for coupon bonds. It is simply the annual coupon payment divided by the price of the bond:

where C is the annual coupon payment and P is the bond price. This is obviously a lot simpler that the yield to maturity

The current yield is a better approximation

for longer maturity bonds and when the price of the bond is close to its face value.

example 4: Consider a 2-year Treasury note with a face value of $10,000, a coupon rate of 6%, and a price of $9750.

the current yield is

Recall that the true yield to maturity, from example 3, is 7.37%. So in this example, the approximation is lousy because it is only a 2-year bond and it is selling at 25% below its face value.

Holding Period Return

The yield to maturity assumes that the bond is held until maturity. If that is not true, then fluctuations in the bond price (which occur with interest rate fluctuations) will affect the return, or the gain to the investor from holding this security.

The return for holding a bond between periods t and t+1 is

where Pt is the initial price and Pt+1 is the price at the end of the holding period.

We can rewrite this formula as

The last term is the rate of capital gain, g, or the change in the bond price relative to the initial bond price. So a bond's return can be rewritten as

A bond's return is identical to the yield to maturity if the holding period is identical to the time left to maturity.

The Bond Market

Now let's take a look at how bond buyers and bond sellers determine the level of interest rates, and how changes in market conditions result in changing interest rates. Our discussion of asset demand above is important in deriving the supply and demand curves.

The Demand for Bonds

Bond demand is based on the behavior of those who buy bonds, or lenders/savers.

Consider a zero coupon bond with a face value of $1000. Suppose the bond has 1 year until maturity, and the expected holding period is one year. Then the bond's expected return is equal to its yield to maturity:

Using the formula above, we can calculate the expected return for various prices:

Bond Price i = exp. return700 42.86%750 33.33%800 25%850 17.65%900 11.11%950 5.26%

As the bond price rises, both the yield to maturity and the expected return fall. As the expected return falls, the quantity demanded of the bond will fall. So the bond demand curve looks like this:

At higher prices, the quantity demanded of bonds falls. Also, note that higher bond prices are associated with lower interest rates because bond prices and interest rates are negatively related.

The Supply of Bonds

To determine the level of interest rates, we also need the bond supply curve, which models the behavior of those who issue bonds, or borrowers. Higher bond prices mean lower interest rates, which encourage borrowing, holding other factors constant. So the bond supply curve slopes up with respect to bond prices:

In the bond market above, the equilibrium interest rate is 17.65%.

However, to understand why interest rates are always changing, we need to understand why equilibrium changes, or why supply and demand curves shift in the bond market.

What shifts the bond demand curve?

A change in wealth. As wealth increases, people will buy more bonds at each and every price, and the demand for bonds rises, or shifts right. So when an expanding economy increases both income and wealth, we expect bond demand to increase too.

A change in expected interest rates/returns. For bonds with more than a year to maturity, rising interest rates in the future will decrease the value of the bond (and hence the expected return). At each and every price, fewer bonds will be demanded. Bond demand will fall, or shift left when expected future interest rates fall. The size of the decrease will be larger for longer term bonds.

A change in expected inflation. If investors expect the inflation rate to rise, then they expect the real return on their bond to fall, as future payments are able to buy less. Higher inflation expectations decrease bond demand.

A change in the relative risk of bonds. At any given price or expected return, if bonds become riskier than other assets, people will switch to less risky assets. An increase in the relative risk of bonds with decrease bond demand.

A change in the relative liquidity of bonds. If it becomes harder to resell bonds in the bond market relative to other assets, people will switch to assets that are easier to resell. A decrease in the relative liquidity of bonds will decrease bond demand.

What shifts the bond supply curve?

A change in business conditions. Firms issue bonds to finance the purchase of capital equipment and the expansion of production. This makes sense only if this expansion is expected to be profitable. As economic conditions become more favorable, expected profitability rises and bond supply will increase or shift right. Also tax incentives for borrowing can also be considered a business condition.

A change in expected inflation. While rising inflation decreases the real return for those who buy bonds, it decreases the real cost of borrowing for those who issue bonds: For a given nominal interest rate (and bond price), higher inflation means a lower real interest rate. Thus, higher expected inflation increases bond supply.

A change in government borrowing. If the government runs budget deficits, the U.S. Treasury must issue additional bonds to finance the shortfall in tax revenue. At each and every bond price, the quantity supplied increases, so the bond supply curve shifts right. Conversely, federal budget surpluses could lead the U.S. Treasury to buy back and retire bonds with the excess revenue and decrease bond supply.

Two things to remember about the bond market:

1. The demand for bonds is the same as the supply of loanable funds. Those who buy bonds are providing loans to others and are receiving interest.

2. The supply of bonds is the same as the demand for loanable funds. Those who supply or issue bonds are borrowing money and paying interest.

Equilibrium Interest Rates

Any shift in the bond demand and/or bond supply curves implies a new equilibrium interest rate. Thus, when we observe fluctuating interest rates in the economy, the root cause is changes in the factors affecting bond supply and bond demand. Let's look a couple of applications.

Example 1: An increase in expected inflation (The Fisher Effect)

Suppose expected inflation is initially at about 3% with initial bond supply and demand curves of Bs and Bd (blue). The equilibrium interest rate is 5% (point 1):

Now suppose inflation expectations rise to 4%. Bond demand decreases (along with the expected real return) and bond supply increases (as the real cost of borrowing declines) to Bs' and Bd' (red). The new equilibrium interest rate is definitely higher (and the bond price lower):

The total impact on the quantity of bonds here is zero, but in general depends on the size of the shifts in the bond demand and supply curves. So the Fisher effect is this: when expected inflation rises, nominal interest rates will rise. This prediction of our model is validated by time series data on interest rates.

Example 2: An economic slowdown

Let's start again with initial bond supply and demand curves of Bs and Bd (blue). The equilibrium interest rate is 5% (point 1):

Now suppose we are in the first quarter of 2001, in the midst of an economic slowdown and concern about a recession. Again this condition will affect both the bond demand and bond supply curves. With the slowdown comes a decline in income and wealth the demand for bonds will decrease to Bd''. The slowdown also has negative implications for profits, so bond supply also declines to Bs'':

In general, where both bond supply and bond demand decrease, the total effect on the equilibrium interest rate is uncertain. Here the shift in bond supply is larger than the shift in bond demand, so the interest rate falls. This is consist with the data on interest rates and the business cycle: nominal interest rates tend to fall during recessions and rise during expansions. In other words, interest rates are procyclical.

The table below summarizes that impact of various factors and the bond market and the equilibrium level of interest rates:

The Effect of Selected Variables on the Bond Market and Equilibrium Interest Rates.

Variable Change in Variable Change in Bd Change in Bs Change in iWealth increase increase decreaseExpected Interest Rates increase decrease increaseExpected Inflation increase decrease increase ?Relative Risk increase decrease increaseRelative Liquidity increase increase decreaseBusiness Conditions increase increase increaseGovernment Borrowing increase increase increase

The Risks Associated with Holding Bonds

While bonds promise fixed cash flows over times, these financial instruments are not without risk. The risk varies depending on the issuer and current economic conditions, but all bonds carry some type of risk. There are three major risks:

Default Risk

This is the risk that the bond issuer will fail to make the promised payments in full and on time. One bond issuer, The United States government, is considered to have no default risk, so default risk is not applicable for U.S. Treasury securities. However all other issuers such as private corporations, state and local governments, and foreign governments carry some risk of default. The higher the default risk, the greater the bond yield. Why? Recall that investors are risk average and will demand a higher yield in order to hold an assets with greater risk.

Default risk can vary quite a bit among issuers, so there are rating systems used to assess this risk. We will look at this in greater detail in chapter 7.

Inflation Risk

Most bonds promise a fixed dollar payments (there are some bonds out there where payments are indexed to inflation). However, with any inflation, those fixed dollar payments will buy fewer goods and services in the future. Bond yields reflect both a real interest rate and an expected inflation rate. The risk is that future inflation is uncertain and could be much higher than expected, which drives down the real return for bondholders. All fixed rate bonds will carry inflation risk. Inflation risk is minimal in countries like the U.S. but it can be huge in developing countries.

Interest Rate Risk

Any bond price moves in the opposite direction of interest rates. Therefore a bond's price or value will fluctuate over the life of the bond as interest rates move up and down. This fluctuation in value again exposes the bondholder to risk, especially if the bondholder expects to sell the bond prior to its maturity. Let's reconsider the bond table from part I, example 3:

Look at each bond's price (the 2-year, 5-year, and 10-year bonds) as the yield to maturity rises from 6% to 8%. The prices fall for all of the bonds, but by different amounts. The price on the 2-year bond falls less than $400 or less than 4%. The price on the 10-year bond falls by more than $1300 or more than 13%. Maturity is a principle bond characteristic that affects price volatility: Prices (and thus returns) are more volatile for long-term bonds than short-term bonds. In other words, long-term bonds have greater interest-rate risk.

Why is this the case? Intuitively, with a long-term bond, you are "locked in" to a coupon rate for a longer period of time. So if newer bonds are issued with lower coupon rates, your long-term bond becomes much more valuable. If new bonds have higher coupon rates, your long-term bond becomes much less valuable. For a bond with less than 1 year left until maturity, the change in interest rates will not matter that much. The consequences of changing interest rates are much more serious for bonds with longer times left until maturity.

ALL BONDS HAVE SOME INTEREST-RATE RISK. So no bond, even Treasuries, are completely risk-free. U.S. Treasury Bills are the closest to a riskfree bond given their issuer and short time to maturity.

Sources of Bond Risk

Default Risk Inflation Risk Interest-Rate Risk

Default RiskRisk that a debtholder will not receive interest and principal when due. One way to gauge default risk is the Ratings issued by credit rating agencies such as Fitch Investors Service, Moody's, and Standard & Poor's. The higher the rating (AAA or Aaa is highest), the less risk of default. Some issues, such as Treasury bonds backed by the full faith and credit of the U.S. Government, are considered free of default risk.

ZEDEX Corp. issues one-year bond at 5% Price without risk = ($100 + $5)/1.05 = $100 Suppose there is 10% probability that ZEDEX Corp. goes bankrupt, get nothing Two possible payoffs: $105 and $0

Expected PV of ZEDEX bond payment = $94.5/1.05 = $90 If the promised payment is $105, YTM will be $105/90 – 1 = 0.1667 or 16.67% Default risk premium = 16.67% - 5% = 11.67%

Inflation RiskBonds promise to make fixed-dollar payments, and bondholders are concerned about thepurchasing power of those paymentsThe nominal interest rate will be equal to the real interest rate plus the expected inflation rate plus the compensation for inflation risk The greater the inflation risk, the larger will be the compensation for it Assuming real interest rate is 3% with the following information

Nominal rate = 3% real rate + 2% expected inflation + compensation for inflation risk

Interest-Rate RiskInterest-rate risk arises from the fact that investors don’t know the holding period yield of along-term bond. If you have a short investment horizon and buy a long-term bond you will have to sell it beforeit matures, and so you must worry about what happens if interest rates change Because the price of long-term bonds can change dramatically, this can be an important sourceof risk

Bond Ratings The risk of default (i.e., that a bond issuer will fail to make a bond’s promised payments)

is one of the most important risks a bondholder faces, and it varies among issuers. Credit rating agencies have come into existence to assess the default risk of different

issuers The bond ratings are an assessment of the creditworthiness of the corporate issuer. The definitions of creditworthiness used by the rating agencies are based on how likely

the issuer firm is to default and the protection creditors have in the event of a default. These ratings are concerned only with the possibility of the default. Since they do not

address the issue of interest rate risk, the price of a highly rated bond may be quite volatile.

Long Term Ratings by PACRAInvestment Grades: AAA: Highest credit quality. ‘AAA’ ratings denote the lowest expectation of credit risk. AA: Very high credit quality. ‘AA’ ratings denote a very low expectation of credit risk. A: High credit quality. ‘A’ ratings denote a low expectation of credit risk. BBB: Good credit quality. ‘BBB’ ratings indicate that there is currently a low expectation ofcredit risk.

Speculative Grades:BB: Speculative.‘BB’ ratings indicate that there is a possibility of credit risk developing, B: Highly speculative. ‘B’ ratings indicate that significant credit risk is present, but a limitedmargin of safety remains. CCC, CC, C: High default risk. Default is a real possibility.

Short Term Ratings by PACRA A1+: highest capacity for timely repayment A1: Strong capacity for timely repayment A2: satisfactory capacity for timely repayment may be susceptible to adverse economicconditions A3: an adequate capacity for timely repayment. More susceptible to adverse economicconditionB: timely repayment is susceptible to adverse changes in business, economic, or financial conditionsC: an inadequate capacity to ensure timely repaymentD: high risk of default or which are currently in default

Increased Risk reduces Bond Demand The resulting shift to the left causes a decline in equilibrium price and an increase in the bond

yield. A bond yield can be thought of as the sum of two parts: The yield on the Treasury bond (called “benchmark bonds” because they are close to being

riskfree) and A risk spread or default risk premium If the bond ratings properly reflect the probability of default, then lower the rating of the

issuer,the higher the default risk premium So we may conclude that when Treasury bond yields change, all other yields will change in

the same direction

Figures 7.2 and 7.3 in your textbook provide a look at different long-term and short-term rates between 1970 and 2003.

Note how U.S. Treasuries tend to have the lowest yields, while corporate Baa bonds have the highest yields. However, the size of the spreads is not constant over time. The spread between Baa bonds and U.S. government bonds is almost 200 basis points 1982, but less than 10 basis points in 1995. We look at two factors that explain the spread we see in figures 7.2 and 7.3: default risk and tax treatment

TAX EFFECTS & TERM STRUCTURE

The second important factor that affects the return on a bond is taxesBondholders must pay income tax on the interest income they receive from privately issuedbonds (taxable bonds), but government bonds are treated differentlyInterest payments on bonds issued by state and local governments, called “municipal” or “tax exempt” bonds are specifically exempt from taxation

A tax exemption affects a bond’s yield because it affects how much of the return the bondholdergets to keep

Tax-Exempt Bond Yield = (Taxable Bond Yield) x (1- Tax Rate).Term Structure of Interest Rates The relationship among bonds with the same risk characteristics but different maturities is called the term structure of interest rates.

A plot of the term structure, with the yield to maturity on the vertical axis and the time to maturity on the horizontal axis, is called the yield curve.

Term Structure “Facts” Interest Rates of different maturities tend to move together Yields on short-term bond are more volatile than yields on

long-term bonds Long-term yields tend to be higher than short-term yields.

The Expectations Theory

Assume that bond buyers do not have any preference for the maturity of a bond, or in other words bonds of different maturities are perfect substitutes. Given this key assumption, The expectations theory of the term structure states that the yield of a long-term bond will equal the average of the expected short-term interest rates over the same period.

How do we get from the assumption to the implication? First let's reconsider what it means for two goods to be perfect substitutes. If I hold Diet Coke and Diet Pepsi to be perfect substitutes then I really do not care which one I drink. So if Diet Coke costs $1/bottle and Diet Pepsi costs $1.25/bottle I will always pick Diet Coke, because I like it just as well. Thus if I have both Diet Coke and Diet Pepsi in my shopping cart at Wegman's, you can assume that they were the same price. Otherwise, I would only buy the cheaper soda, because they taste the same to me.

Now, consider an investment horizon of 5 years. Under the expectations theory we assume that investors are indifferent between (1) holding a 5-year bond the entire time or (2) holding 5 1-years bonds over each of the next 5 years. Here investors only care about the expected return. So if we observe investors buying both 1-year and 5-year bonds, then it must be the case that they expect the return to be the same. If investors expect one-year bond yields to be 5%, 6%, 7%, 8%, 9% over the next 5 years, then the 5-year bonds yield must solve the equation

Why? Because if the 5-year bond yield return is expected to be larger than 5 1-year bonds, then everyone will hold the 5-year bond. We observe investors holding both 5-year and 1-year bonds, so the expected returns must be equal, IF they are perfect substitutes. The equation above can be APPROXIMATED by

So then the long term bond yield (the 5-year bond) is an average of the expected short-term bond yields over the next 5 years.

Under the expectations theory, the yield curve tells us something about expected future short-term interest rates. If markets expect short term interest rates to rise, like the example above, then the current long-term rate (7%) is greater than the current short-term rate (5%), and the yield curve slopes up. So an upward sloping yield curve, under this theory, tells us that short-term rates are expected to rise.

How does the expectations theory stack up with reality? Let's reconsider the 3 facts about the yield curve, and see if the expectations theory is consistent with these facts.

1. Interest rates on bonds of different maturities generally move together. YES, under this theory we would predict that interest rates move together. If short term interest rates rise, then their average will rise too, pushing up long-term interest rates. If short-term interest rates fall, then their average will fall too, pushing down long-term interest rates.

2. Short-term bonds yields are more volatile than long-term bond yields, i.e. short-term yields move up and down more frequently and over a larger range than long term yields. YES, this is also consistent with the expectations theory. If long-term rates are an average of expected future short-term rates, then long term rates will be smoother. Any change in expected short term rates has a smaller impact on the average.

3. The yield curve usually slopes up. NO, the expectations theory does not predict this result.Under the expectations theory an upward sloping yield curve only occurs when short-term interest rates are expected to rise, or about 50% of the time.

Why the failure? Go back to the key assumption for this theory: bonds of different maturities are perfect substitutes. This is a very strict assumption that is not really realistic. We know from chapter 6 that long-term bonds exhibit greater price volatility which some investors will find unacceptable.

Well, as the great Meatloaf sang, "Two out of Three Ain't Bad." Let's consider alternative theories that build on the expectations theory.

The Liquidity Premium Theory

Recall that longer term bonds carry greater interest-rate risk and greater inflation risk. Given this, let's assume that bonds of different maturities are imperfect substitutes, with investors preferring short-term bonds. This means that investors would choose short-term bonds, all else being equal, but would be willing to hold long-term bonds if given an incentive to do so. Under the liquidity premium theory, long-term bonds yields are an average of expected short-term bond yields during the same period PLUS a liquidity (or term) premium.

To connect the assumption with the implication, think back to the whole Diet Coke/Diet Pepsi debate. Suppose I prefer Diet Coke when prices are the same, but I am willing to buy Diet Pepsi if it is a lot cheaper than Diet Coke. In this case Diet Coke and Diet Pepsi are imperfect substitutes, with my preferences leaning toward Diet Coke. I will only buy Diet Pepsi if I think it is a much better deal.

If investors do not like long-term bonds as well, then they have to be given an incentive, such as a higher expected return, in order to hold them. Consider our earlier numerical example where investors expect one-year bond yields to be 5%, 6%, 7%, 8%, 9% over the next 5 years. Now suppose that in addition, investors demand an extra 1% to hold a 5-year bond instead of 1-year bonds. Then the 5-year bond yield becomes

Under this theory, it is easy to see why the yield curve usually slopes up. If long-term bond yields include a liquidity premium, then they will usually be larger than short-term bond yields. So this theory explains fact #3. Also, since the long-term bond yield is still related to the average of short-term bond yields, this theory also explains facts #1 and 2. So now, by combining parts of two theories we come up with a third, and more realistic theory.

The downside of this theory is that it is more difficult to interpret the yield curve. The slope of the yield curve reflects two things (1) expectations about future short-term interest rates, and (2) the liquidity premium. If we do not know the size of the liquidity premium, we cannot always be sure about what the yield curve is saying about expected future short-term interest rates. An upward-

sloping yield curve could be caused by the expectation of rising interest rates or a liquidity premium, or both.

What Do the Default premium and the Yield Curve Tell Us?

Researchers have investigated whether interest rate spreads give us reliable information about

future interest rates

future inflation rates

future business cycles

The results are mixed, but fairly recently (1996) some economists at the Federal Reserve Bank of New York found that a declining spread between the 3 month Tbill and 10-year Tnote increases the probability of a recession within 6 to 12 months after the decline. An inverted yield curve (with a negative slope) predicts an economic slowdown fairly well.

Also, economists find the default premium between U.S. Tbills and commerical paper to be a reliable tool in forecasting business cycles.

The Yield Curve

To focus on maturity alone, we need to examine a set of bonds with identical risk, features, tax treatment, etc. but different maturities. In reality, only Treasury bonds satisfy these criteria. Municipal and private issuers do not issue enough different maturities to allow useful comparison. Treasury securities range in maturity from 3 months to 30 years.

A plot of Treasury bond maturities versus their yields is known as the yield curve. The shape of the yield tells us the relationship between short-term and long-term interest rates. Consider the sample yield curves below:

In curve (A), the yield curve is upward-sloping, so yields rise as maturity increases.

In curve (B), the yield curve is downward-sloping, or inverted, so yields fall as maturity increases.

In curve (C), the yield curve is flat, so yields are identical across all maturities.

In curve (D), the yield curve changes direction, so the short and long-term bonds have the highest yields, but intermediate-term bonds have lower yields.

The yield curve changes shape over time, depending on financial market conditions. However, in looking at historical data on Treasury yields, there are 3 important facts about the yield curve:

1. Interest rates on bonds of different maturities generally move together.

2. Short-term bonds yields are more volatile than long-term bond yields, i.e. short-term yields move up and down more frequently and over a larger range than long term yields.

3. The yield curve usually slopes up, i.e. long term yields tend to be higher than short-term yields.

In addition to describing the current relationship between short and long-term interest rates, the yield curve may also contain valuable information about investor expectations about future interest rates. To understand what a yield curve tells us we need to understand what causes yields to differ across maturities. We look at 2 alternative explanations, or theories of the term structure. We will "test" the usefulness of each theory by comparing the predictions of the theory to the empirical facts about the U.S. Treasury yield curve.

VALUING STOCK AND RISK

Note well:  stocks do not pay interest.  The returns to stockholders come in the form of dividends (periodic distributions of the company's profits) and (especially these days) capital gains (the profit you make from selling a stock for more than you paid for it).

Stock prices are widely watched and change by the minute. Prices are set through the interactions among the many traders on the various stock exchanges. Because the stock market has a huge number of traders, each one too small relative to the market to influence the price, we can say that the stock market is a competitive market, and stock prices are determined by supply and demand. Traders buy and sell securities based on their estimated valuations of them. But where do those estimated valuations come from?

The value of a stock ultimately depends on the expected future profits of the company.  Profitable companies can pay bigger dividends. 

--> The traditional approach to valuing stocks is as the expected present-day value of the company's future stream of dividends or profits (per share).  Some guesswork is involved here, as we don't know how much those dividends will be in the future or even when (or if) they'll be paid. 

If stocks and bonds carry equal risk, then the PDV of any stock is the present-day value of all future dividend payments associated with the stock. According to fundamental analysis of stock prices (a technique that Warren Buffett says he swears by), the proper price for a stock is its estimated PDV (just as the proper price of a bond is the PDV of all the payments it will be making). The PDV of a stock's entire future dividends is often called the stock's intrinsic value. -- Many of today's hottest stocks do not currently pay any dividends. If people expected them never to pay any dividends, not even in the distant future, then the PDV's, and hence the "proper" prices, of those stocks would be zero. The fact that stocks like Dell and Microsoft, which do not pay dividends, command high prices on the market suggests that people expect them to start paying dividends sometime in the future.  Then again, even if they pay no dividend or only a small dividend, a share of ownership in a profitable company is a good thing to have.

Using the standard PDV formulas to price stocks is fairly straightforward. The easiest case by far is when the company pays a dividend and is expected to pay that same dividend forever. (This may be a reasonable expectation for a very stable company, like a utility company.) In such cases, the appropriate PDV formula is the consol-bond formula, since a share of stock that pays the same yearly dividend forever is just like a bond that makes the same fixed yearly payment ($FP) forever.   (Recall:  In the consol bond formula -- number [3] on the PDV handout -- the PDV of getting that yearly fixed payment is $FP/i. The only thing different here is the notation -- instead of $FP, we use $D, for dividend.)-- For a given interest rate i, the PDV (and appropriate price) of a constant-dividend ($D) stock is

$D/i.

To repeat an earlier example: Suppose Minnesota Power stock pays a $2 dividend that is expected to continue forever, and the interest rate is 5%.--Q: What should the stock's price be?--A : $2/.05 = $40.

(We can rearrange that equation into another common financial statistic, the price-dividend ratio:--> (PDVstock )/(Dividend) = 1/i (i.e., price-dividend ratio is 1/i).-- In the Minnesota Power example, the price-dividend ratio is $40/$2 = $20, which is also equal to 1/i = 1/.05 = $20.)

Other cases are more complex, and different models have been developed to price stocks in those situations.

-- One case that's only a little bit more complex is a stock which pays dividends that are not constant but which grow at a constant annual rate (e.g., 1% per year).  Such a stock will be worth more than just the current dividend payment divided by i, because the total amount of payments is larger.  Fortunately, the sum of the PDV's of those payments converges to a geometric sum:

---- For a given interest rate i, a stock currently paying a dividend of $D, which is expected to grow at an annual rate of g, has an expected PDV (and appropriate price) of

$D*(1+g) / (i - g)

Which of the many interest rates in the economy should we use for i in this case?  This question is important because stocks are a lot riskier than most bonds.  Because people are risk-averse, they generally require a higher return if they are to hold stocks instead of bonds.  That higher return is known as the risk premium on stocks, or the equity premium.-- So i in these formulas should be either (a) the interest rate on a bond that's just as risky as stocks or (b) a more normal interest rate, like the Treasury bond rate, plus the risk premium for stocks.

Q: Why might the PDV/ intrinsic value approach not be such a good way to price stocks? A: Because nobody knows for sure what a company's future earnings and future dividends will be. The PDV of a share of a stock, or of any asset whose future returns are not known with precision, is just an estimate, and so the intrinsic value approach is only useful if you can accurately predict the company's future earnings. Most of us can't do that very well ("I don't have a crystal ball.") -- Additional caveats about the PDV approach to stock pricing: ---- Stocks and bonds do not carry equal risk.  Stocks are riskier, because the amount of the future dividend payments is not fixed (unlike the interest and principal payments on a bond) and because in the event of bankruptcy the firm must pay off its bondholders and other creditors before it can divide up its assets among its stockholders. ---- Even if you know a stock's price is way in excess of its PDV (and hence the stock is overpriced), there is still the possibility of selling the stock at a profit, if you can sell it before the stock-market bubble bursts.  That approach to the market is often called noise trading.  (It's potentially the way to get rich the fastest in the stock market, but it's also very risky, and many more people get burned by this strategy than get rich by it.  A "buy-and-hold" strategy is much safer.)

Although stocks don't pay interest, stock prices are strongly, and negatively, affected by changes in interest rates.  Two roughly equivalent reasons why:(1)  Stocks and bonds are substitutes. When people look to invest their money, they look at the expected returns of different assets, including stocks and bonds. If the interest rate (i) goes up, then more people will want to buy new bonds that pay those higher interest rates. So more people will buy bonds, and fewer people will buy stocks.  (Stated more properly, an increase in i means that the return on stocks worsens relative to the return on new bonds, so the demand for stocks will decrease, and stock prices will fall.)(2)  In the long term the appropriate price of a share of stock is the PDV of the company's future stream of earnings per share, and since a rise in i lowers the PDV of any and all future payments, then it lowers the PDV of all stocks.  (This reason may look totally different from [1], but it isn't,

since the market interest rate i in the denominator of the PDV formula represents the interest you could be earning.  For stocks and other investments, that interest rate is like your opportunity cost.)

Summing up:  How changes in interest rates affect stock prices

Stock prices, like old bond prices, are negatively related to the current interest rate.

If i goes up ->more people buy new bonds; demand for stocks falls ->

stock prices fall.

If i goes down ->fewer people buy new bonds; demand for stocks rises ->

stock prices rise.

Since stocks are typically sold at some point rather than held forever, there are valuation models that include the stock's expected sale price at some later date.

-- If the stock is to be sold at the end of the year, then its price now would be the PDV of dividends in the first year, plus the expected resale price of the stock at the end of the year.-- If the stock is to be sold n years from now, then its price now would be the PDV of dividends in the first n years, plus the PDV of the stock's expected resale price n years from now.

Whichever model one uses to estimate appropriate valuations of stocks, those estimates will tend to be volatile, because they will change whenever the interest rate (i, part of the denominator in every PDV term) changes or as new information that would affect future dividends or earnings becomes available. Small changes in interest rates or estimated profit growth can mean large changes in stock valuations, and hence prices. Even day to day, then, the stock market is often volatile.

The fundamental-analysis (or intrinsic-value) approach is not the only approach to stock valuation.-- Technical analysis involves trying to identify trends and patterns in the market and then take advantage of them.  (It doesn't seem to have a great track record.)-- The behavioral approach to investing focuses on investor psychology, especially as it may relate to irrational waves of optimism and pessimism that may sweep the market.  "Noise traders" who can recognize psychology-driven market fluctuations can make out quite well.  A good example seems to be John Maynard Keynes, the founding father of macroeconomics.

III.  THE EFFICIENT-MARKET THEORY OF THE STOCK MARKET

The efficient-market hypothesis (or theory) says the stock market as a whole does the best job possible in valuing and pricing stocks. The market acts rationally, says the theory, using all available, relevant information and leaving no profit opportunity unexploited. This would imply that strategic stock picking is pointless, because the market has already priced every stock appropriately, given the current information.

The efficient-market theory is an application of a theory that has been extremely influential in macroeconomics over the past thirty years, namely--

The theory of rational expectations: Expectations will be identical to optimal forecasts (the best guess of the future) using all available information.--Example: Your expectations of today's weather (which inform your choice of what to wear, etc.) are not rational if they're based on the guess that today's weather will be like yesterday's, or a hasty look outside. Rational expectations of the weather would involve listening to or reading a

top-quality forecast by a professional meteorologist.---- (If you didn't have time to listen to the weather on the radio this morning, it might have been a rational decision, if you had something better to do, but you will not have rational expectations of the weather. This goes to a key reason why people do not always have rational expectations - obtaining all the relevant, available information can be costly or inconvenient.)

In financial markets, people want to get rich, so they should follow all the relevant economic and financial series, read the company reports, and do whatever else is necessary to maximize one's (risk-adjusted) returns in the market. If enough traders in the stock market do this, then every stock's price will be rationally determined, and the prices of stronger stocks will be bid up and the prices of weaker stocks bid down, to the point where the expected return on every stock will be the same! At that point, a person looking for stocks to buy need not do any research of his own; he can just free ride on the wisdom of the other traders. In fact, he might as well make his picks by throwing darts at the newspaper stock listings...

News flash (a true story):A Swedish newspaper gave $1,250 each to five stock analysts and a chimpanzee named Ola, to test who could make the most money on the market in a one-month period. Ola the chimp, who made his choice of purchases by throwing darts at the names of companies listed on the Stockholm exchange, won the competition.

A fluke? Maybe, maybe not.-- For years, the Wall Street Journal did this every month, enlisting four Wall Street stock experts to pick one stock apiece, and then having someone throw darts four times at the paper's stock listings. After six months they'd compare the average returns on the four stocks the experts picked versus the four stocks the darts hit. Very often, the "dartboard portfolio" won; almost always it beat at least one or two of the pros' picks.

These kinds of studies are often conducted and reviewed by economists, too, somewhat more systematicallly.

The EFFICIENT-MARKET THEORY OF THE STOCK MARKET:  Stock prices reflect all available, relevant information.  When it comes to prices, the stock market is efficient in that "you get what you pay for" -- stock prices of the companies with the best prospects will be bid up to high levels, and stock prices of companies with weak prospects will be bid down to low levels.  Because the return on a stock is inversely related to what one pays for it, the returns on different companies will tend to be the same.  Corollaries:-- You can't outguess the market.-- Systematically "beating the market" (outperforming the market averages) is practically impossible.

According to the efficient-market theory, you'd be best advised to follow a PASSIVE INVESTMENT STRATEGY: Switch to index funds (mutual funds that simply track a stock-market average, rather than being actively managed), and hold them over a very long time period (a buy-and-hold, not buy-and-sell, strategy).

Q: Is the efficient-market theory of the stock market just a silly theory?A: NO! It's supported by hundreds of empirical studies.  (Caveat:  some other studies go against it.  More on them later.)-- FACT: The S&P 500 index outperformed over 2/3 of professionally managed portfolios for the decades of 1970s, 1980s, and 1990s. In nine of 13 years (1984-96), the S&P 500 index outperformed the majority of mutual funds. Over the 1990s, the S&P index has had a total return of 312 percent -- one-fourth greater than the average domestic stock fund.---- Notably, the indexes have outperformed the managed portfolios both when the market was doing poorly (the '70s) and when the market was doing great (the '80s and '90s.)

Q: Why do most mutual funds do so badly relative to the market? They're run by smart people, aren't they?A:(1) Capital gains taxes -- when a mutual fund sells stock at a profit, it gets taxed on those gains; if you buy stock and just hold it as its price appreciates, you don't pay taxes.(2) Transactions costs -- Buying and selling stocks means incurring brokerage or trading fees. Buying and holding stocks does not involve any transactions costs. (3) Over-managing, due to perverse incentives? -- pressures for short-term successes and to "look busy" in order to justify their fees. Also, since every managed fund wants to "beat the market," they often try to time the market -- i.e., be in when the market's soaring, be out when it's stagnant or hurting -- and it's much easier to lose money than to make money that way. Peter Lynch: "Far more money has been lost by investors preparing for corrections than has been lost in the corrections themselves."

What most of the mutual-fund houses have to say about index funds:(1) They're un-American. Trying to "beat the market" is the "American dream." (Huh?)(2) They point to the success of the funds that did beat the market.

[At about this point in the lecture I conducted the Eco 340 coin-tossing competition. It was inspired by a metaphor that efficient-market-theorist Burton Malkiel proposed for the following metaphor for the great mutual-fund success stories:]-- Imagine a coin-tossing contest with 1000 people. "The contest begins, and [they all] flip coins. Just as would be expected by chance, 500 of them flip heads, and these winners advance to the second stage of the contest and flip again. As might be expected, 250 flip heads. Operating under the laws of chance, there will be 125 winners in the third round, 62 in the 4th, 31 in the 5th, 16 in the 6th, and 8 in the 7th.-- By this time, crowds start to gather to witness the surprising ability of these expert coin tossers. The winners are overwhelmed with adulation. They are celebrated as geniuses in the art of coin tossing -- their biographies are written, and people urgently seek their advice. After all, there were 1,000 contestants, and only eight could consistently flip heads."----> POINT/ANALOGY: The big stock-market success stories are perfectly consistent with the laws of chance.Are today's mutual fund managers who beat the market several years in a row geniuses, or just lucky?  Given the thousands of mutual funds out there, luck surely explains many, if not all, of those success stories.

Moreover, even the most successful ones always issue the disclaimer, "Past performance is no guarantee of future performance." In fact, empirical tests of the efficient-market hypothesis typically find the top-ranked funds from one period generally earn only average returns in the next period. So market-beating funds have a tendency to fall to earth.

One objection:  Just because the repeated success of a (very) few individuals is consistent with the laws of chance doesn't mean it's explained by the laws of chance. Coincidence ain't causality. Talent might plausibly be the explanation, too; and it virtually has to be the explanation for such giants as Peter Lynch (Wall Street legend who ran Fidelity's Magellan Fund for the 20-plus years that it did beat the market and everybody else) and Warren Buffett, who still runs Berkshire Hathaway.-- On the other hand, Peter Lynch has retired (at age 47!) from active fund management, as have many of the other giants of the 1980s; and Berkshire Hathaway is a closed-end fund whose shares tend to sell for a big markup over their Net Asset Value (and they are priced so that a single share costs tens of thousands of dollars!).

Evidence in favor of the efficient market hypothesis:  A summing up:

Sub-par performance of investment analysts and mutual funds: Investment advisers' stock picks frequently trail the market as a whole, and frequently even trail "the dartboard picks." Most mutual funds do worse than the market averages. Even those that do the best typically earn mediocre or below-average returns in the next period. Mishkin's conclusion: Having performed well in the past does not indicate the an investment adviser or a mutual fund will perform well in the future.

Stock prices reflect relevant publicly available information. Changes in obvious fundamentals like interest rates and company earnings news do indeed cause stock prices to change as predicted. So stock prices do reflect at least some fundamentals. It's hard to say stock prices reflect all relevant available information, but it's hard to tell where the relevant information set ends.

o Q: Do stock prices always rise when there is good news?

o A: No. Only if it's a surprise. If the good news was expected, then it was already incorporated into the stock's price.

Random-walk behavior of stock prices: Stock prices follow a random walk if future changes in stock prices are unpredictable. (That sentence is basically the main implication of the efficient-market theory, which is often called the random-walk theory of the stock market.) Empirical studies suggest that stock prices do follow a random walk, for the most part: they find that stock price changes are not a function of past price changes or of other already-known factors. (New information will cause prices to change, but not old news, be it good or bad.) Likewise, technical analysis, which seeks to predict future stock price changes on the basis of past patterns, has notoriously underperformed the overall market.

Evidence against the efficient-market hypothesis

Although hundreds of empirical studies have been supportive of the efficient-market theory, most were largely conducted fairly early in the life of the theory (1970s, 1980s, early 1990s). More recent studies have been somewhat less favorable.  The recent studies do not prove that the stock market is usually inefficient, but they do reveal several anomalies in stock-price behavior that seem inconsistent with the efficient-market theory:

Small-firm effect: "Small cap" stocks - i.e., stocks issued by smaller companies - have earned higher risk-adjusted returns than other stocks. A truly efficient market would have bid up their prices in the early going so as to equalize their returns with those of other stocks. The small-firm effect is smaller now than it used to be, but it is still present.

January effect: There is a by-now-predictable pattern of stock prices rising sharply from December to January. Why don't more traders take advantage of this information by rushing in to buy stocks in December and sell them in January? If enough did, the January effect would disappear. It hasn't happened, though.

Market overreaction, excessive volatility: It appears that stock prices don't just react to news announcements like changes in company earnings, they overreact, to good news and bad news alike, by moving much more than the changes in fundamentals would warrant. If stock prices move much more than their fundamental values do, then stock prices display excessive volatility, and the stock market as a whole will tend to have excessive swings of its own. All this opens the door for shrewd investors to make a killing by taking advantage of the market's extreme swings; yet not enough of them have done so to eliminate those swings.

o The two recent stock-market crashes, Black Monday in 1987 and the tech crash of 2000, seem prime examples of excessive volatility. There were no evident changes in fundamentals (such as interest rates or company news) that would have been enough to cause such huge plunges in stock prices.  (Those crashes don't exactly demolish the efficient-market hypothesis, however, as long as the crashes could not have been predicted.)

Mean reversion: This one is iffy empirically, because the evidence is very mixed, but some studies have found that stocks with low returns in the past are more likely to do well in the future, while stocks with high returns in the past are more likely to do poorly in the future. The phenomenon is called mean reversion. If stock prices follow such a predictable pattern, then they do not follow a random walk.

New information is not always immediately incorporated into stock prices: The key word here is "immediate." The markets do process relevant new information like profit announcements, but whereas the efficient-market theory says they would process it within minutes of the announcement, in actuality we see stock prices react for many days to the same news.

Taking stock of the efficient-market hypothesis

Clearly this evidence is mixed and the studies are controversial, but the efficient-market theory still seems "a good starting point" for understanding stock prices. At heart, the theory isn't too different from the PDV-based approaches to valuing stocks at the beginning of this unit. But there are too many exceptions, most notably the market's excessive volatility, to make the efficient-market theory the last word in understanding stock prices. Perhaps the stock investors with rational expectations don't control enough shares to drive all stock prices to their appropriate levels? -- (Of note: For the bond market, the efficient-market theory looks very convincing.  There's much less uncertainty in the bond market than in the stock market.)

The impact of the efficient-market view is also mixed, but has been on the rise since at least the early 1990s. The tech boom and bust may have derailed it a bit, but index funds are still very popular.  Clearly the investing public has gradually become fond of index funds:  Vanguard's S&P-500 index fund became the country's second-largest mututal fund in the late 1990s.  The largest mutual fund company (Fidelity) introduced several index funds in the 1990s, in order to keep up with the competition, and numerous other mutual-fund houses introduced index funds of their own. 

Application: Practical guide to investing in the stock market-- How valuable are published reports by investment advisers? Not.-- Should you be skeptical of hot tips? Yes.-- In three words, what should a smart investor do?  Buy and hold.(All three of these answers follow straight from the efficient-market theory, which is, of course, controversial. But, empirically speaking, they all seem to work.)

One-Period Model

This simplest model of valuation would be to assume a single holding period, such as one year, for the stock. In this case you purchase the stock for an initial price, P0, and at the end of the year receive a dividend, Div1, and sell the stock for price P1. So the current value of the stock is the discounted value of the dividend and the resale price:

Here the appropriate discount rate, ke, is the required return on equity (the minimally acceptable return given the risk/uncertainty surrounding the stock value) and not the interest rate. (Your book uses the interest rate, but the concept of k is more accurate, because k includes a risk premium for holding stocks. This risk premium is necessary since stock owners are residual claimants.)

So, for example, if you demand a 10% equity return on XYZ stock, expect a dividend of $ 0.20 per share for the year and a share price of $50 one year from now, then your current value of the stock would be

In other words, you would not be willing to pay more than $45.64 for a share of XYZ stock today.

Note that even in this simple example, the valuation of stock is more uncertain that a Treasury bond. For the bond, the future cash flows are known and considered certain. But with the stock the future price and dividends are not known

Generalized Dividend Model

Now we can extend the one-period model to multiple periods. For n periods, the value of the stock would be

if the stock is held forever, then the sales price Pn is not an issue, and the model is rewritten as

Gordon Growth Model

Now let's make one more assumption: suppose dividends grow at a constant rate each year, g, and that g < ke. Then the stock value equation becomes

Using some rules about infinite series (see the footnote on page 188 or just trust me) this equation simplifies to

k, as the required equity return is really the sum of two components: the risk free return, rf, and the risk premium for holding stock, rp:

k = rf + rp

Yes, I know what you are thinking....

"So, Dr. Liz, what does this mathematical nightmare tell us about stock pricing?"

There are a couple of points to take from this exercise here:

1. Current stock prices depend on current dividends and their expected growth. An increase in either will lead to an increase in the value of the stock. So, for example, a poor economy reduces expected dividend growth and causes stock prices to fall.

2. The current stock price is also related to the required equity return. So if events cause investors to perceive stocks as riskier than before (like scandals involving financial statement fraud), then k will rise because investors want a higher return to compensate for higher risk. According to our model, an increase in k will cause stock prices to fall.

The models of stock valuation here would predict that the recession and slow recovery of our economy after 2001, along with the accounting scandals of firms like Enron and WorldCom, would cause stock prices to fall. And in 2001, 2002, that is exactly what happened.

Why stocks are risky? Stockholders receive profits only after the firm has paid everyone else, including bondholders It is as if the stockholders bought the firm by putting up some of their own wealth and borrowing the rest This borrowing creates leverage, and leverage creates risk Imagine a software business that needs only one computer costing $1,000 and purchase can

be financed by any combination of stocks (equity) and bonds (debt). Interest rate on bonds is 10%.

Company earns $160 in good years and $80 in bad years with equal probability

If the firm were only 10% equity financed, shareholders’ liability could come into play.o Issuing $900 worth of bonds means $90 for interest payments.o If the business turned out to be bad, the $80 revenue would not be enough to pay the interesto Without their limited liability, stockholders will be liable for $10 shortfall. But actually, they

will lose only $100 investment and not more and the firm goes bankrupt.o Stocks are risky because the shareholders are residual claimants. Since they are paid last,

they never know for sure how much their return will be.o Any variation in the firm’s revenue flows through to stockholders dollar for dollar, making their

returns highly volatile

The Stock Market’s Role in the Economy Shifts in investor psychology may distort prices; both euphoria and depression are

contagious When investors become unjustifiably exuberant about the market’s future prospects, prices

rise regardless of the fundamentals, and such mass enthusiasm creates bubbles.

Bubbles Bubbles are persistent and expanding gaps between actual stock prices and those

warranted by the fundamentals. These bubbles inevitably burst, creating crashes. They affect all of us because they distort the economic decisions companies and consumers make If bubbles result in real investment that is both excessive and inefficiently distributed,

crashes do the opposite; the shift to excessive pessimism causes a collapse in investment and economic growth

When bubbles grow large enough and result in crashes the stock market can destabilize the real economy

ROLE OF INTERMEDIARIES

The Role of Financial Intermediaries

So why is indirect financing so much more important? The reasons center around the power of information: how to get quality information at a reasonable cost. In this context, financial intermediaries perform 5 functions:

1. Pooling the resources of small savers

Many borrowers require large sums, while many savers offers small sums. Without intermediaries, the borrower for a $100,000 mortgage would have to find 100 people willing to lend her $1000. That is hardly efficient. Banks, for example, pool many small deposits and use this to make large loans. Insurance companies collect and invest many small premiums in order to pay fewer large claims. Mutual funds accept small investment amounts and pool them to buy large stock and bond portfolios. In each case, the intermediary must attract many savers, so the soundness of the institution must be widely believed. This is accomplished through federal insurance or credit ratings.

2. Providing safekeeping, accounting, and payments mechanisms for resources

Again, banks are an obvious example for the safekeeping of money in accounts, the records of payments, deposits and withdrawals and the use of debit/ATM cards and checks as payment mechanisms. Financial intermediaries can do all of this much more cheaply than you or I because

the take advantage of economies of scale. All of these services are standardized and automated on a large scale, so per unit transaction costs are minimized.

3. Providing liquidity

Recall that liquidity refers to how easily and cheaply an asset can be converted to a means of payment. Financial intermediaries make is easy to transform various assets into a means of payment through ATMs, checking accounts, debit cards, etc. In doing this, financial intermediaries must many short term outflows and investments will long term outflows and investments in order to meet their obligations while profiting from the spread between long and short term interest rates. Again, economies of scale allow intermediaries to do this at minimum cost.

4. Diversifying risk

We have seen in chapter 5 how diversification is a powerful tool in minimizing risk for a given leven of return. Financial intermediaries help investors diversify in ways they would be unable to do on their own. Mutual funds pool the funds of many investors to purchase and manage a stock portfolio so that investors achieve stock market diversification for as little at $1000. If an investor were to purchase stocks directly, such diversification would easily cost over $15,000. Insurance companies geographically diversify in ways that a Gulf Coast homeowner cannot. Banks spread depositor funds over many types of loans, so the default of any one loan does not put depositor funds in jeopardy.

5. Collecting and processing information

Financial intermediaries are experts at collecting and processing information in order to accurately gauge the risk of various investments and to price them accordingly. Indviduals do not likely have to tools or know-how to do the same, and certainly could not do so as cheaply as financial intermediaries (once again, economies of scale are important here). This need to collect/process information comes from a fundamental asymmetric information problem inherent in financial markets.

Financial Intermediaries and Asymmetric Information

Despite their importance, your textbook author refers to financial markets as "among the worst functioning of all markets." (268) This is due the fundamental fact the borrowers and debt/stock issuers know much more about their likelihood of success than potential lenders and investors. This asymmetric information causes one group with better information to use this advantage at the expense of the less-informed group. If not controlled, asymmetric infromation can cause markets to function very inefficiently or even break down completely.

Asymmetric Information

The lack of information on one side creates problems BEFORE the loan is made and AFTER the loan. To you or I, these problems are huge, but financial intermediaries use their size and expertise to minimize them.

Before a financial instrument is bought or sold, there is the problem of adverse selection. Basically, what happens is that the worst candidates (adverse) are more likely to be selected for the transaction. People who are bad credit risks are more likely to try and get a loan than those who are good credit risks. Thus, odds are that you might end up lending to someone with a bad credit risk. Knowing that, you just decide not to lend. Again, this problem occurs because of

asymmetric information: You do not have good information about a stranger's credit risk, although that stranger knows his/her own creditworthiness quite well. Banks, however, are experts at assessing credit risk and can distinguish the good from the bad. So you lend to the bank, and the bank lends to those who are good credit risks.

After a the loan is made, there is the problem of moral hazard. Once you lend someone money, you risk (the hazard) that he/she does something stupid to blow the money (immoral) and would be unable to pay you back. Your brother in-law claims to be investing in a restaurant franchise and will repay you with the profits, but once you lend him $10,000 he goes and blows it in Las Vegas. Knowing about this risk, you tell your brother-in-law to get lost, even though the franchise might be a good idea. Again, this is from asymmetric information: Your brother-in-law knows what he will do with the money but you can only guess. Banks are experts in monitoring and enforcing lending contracts in order to minimize the moral hazard problem.

Disclosure rules for public companies also mitigate the problems of asymmetric information. The SEC requires companies that sell securities to the public to publish quarterly financial statements and disclosure any relevant information in a timely manner. The requirement are not foolproof. As your book notes, the scandals with Enron and WorldCom, among others, demonstrate that financial statements may be manipulated in ways to deceive investors.

Note: adverse selection and moral hazard are important concepts that explain the structure and regulation of the financial sector as well as the major crises that have plagued the financial sector in the past 30 years, so take the time to understand these concepts.

Role of Financial Intermediaries in Reducing Information Costs

How do intermediaries reduce adverse selection and moral hazard? There are several ways.

Screening. Prior to a loan being given, a bank investigates a firm's or individual's credit history and financial status. Such information is fed into sophisticated computer programs that compute a "credit score" (known as a FICO score). The higher the score, the better the borrower. Also, banks specialize in lending to certain industries, especially local industries. This makes the screening process cheaper and more accurate, although the lack of diversification does increase the risk of the bank's asset portfolio

Monitoring. Once the loan is made, the bank must ensure that the borrower does not engage in risky activities that could lead to default. One way to prevent this is for banks to place "restrictive convenants" into the loan contract to prohibit certain activities, and then to check compliance and enforce the agreement when necessary.

Creating long-term customer relationships. Repeat customers will not require the same effort for screening and monitoring that new customers. Also, customers have an incentive to establish a good repayment record in order to get loans from the same bank in the future.

Collateral. Requiring a potential borrower to pledge assets to be turned over in case of default reduces credit risk in several ways. Obviously, it protects the bank from total financial loss in the event of a default. But it also screens out questionable borrowers (who will not have sufficient collateral) and reduces moral hazard problems since the borrower risks losing his/her property if a default occurs.

Credit rationing. Riskier borrowers will be expected to pay higher interest rates to compensate for this risk. However, ONLY the riskiest borrowers are willing to pay the highest rates. This is an extreme case of adverse selection. In this case, banks may be unwilling to assume the high risk levels and simply refuse to lend to these types of

borrowers. Alternatives, banks would lend out only small amounts, giving the borrower the incentive to establish a good payment record to obtain additional loans.

Disclosure. Disclosure rules for public companies also mitigate the problems of asymmetric information. The SEC requires companies that sell securities to the public to publish quarterly financial statements and disclosure any relevant information in a timely manner. The requirement are not foolproof. As your book notes, the scandals with Enron and WorldCom, among others, demonstrate that financial statements may be manipulated in ways to deceive investors