Section A .

(a) Using an example, explain a probability-based approach for calculating expected

returns and variance under uncertainty.

We can arrive at an expected return and variance of any asset on the basis of what we expect the return to be. This method would work, if we base our expectations on historical evidence. But

sometimes, when there are no historical evidences available or they are not relevant to base our expectation on, calculating the expected returns would be difficult.

At that time, when there is uncertainty, we try to find probabilities for various returns of that asset. We find these returns using multiple experiments or simulation techniques. The result of

these experiments would give us probabilities of various returns. We then use these probabilities to arrive at an expected return and variance.

Let us take an example of a stock.

Return (R) Probability (P)

0.07 0.1

0.08 0.2

0.09 0.25

0.10 0.25

0.11 0.2

Using the data here, we can find out the expected returns. We would multiple the returns with their expected probabilities, which we have gathered from experiments and then sum those to

arrive at an expected return. E(R) = 0.1(0.07) + 0.2 (0.08) + 0.25(0.09) + 0.25(0.10) + 0.2 (0.11)

= 0.0925 or 9.25%

The variance of return is: σ2 = 0.1(0.07-0.09)2 + 0.2(0.08-0.09)2 + 0.25(0.09-0.09)2+ 0.25 (0.10-0.09)2 + 0.2(0.11-0.02)2

= 0.000165 or 0.02%

(b)

Consider two assets with the following annual expected returns and standard deviations of

returns:

Asset E(R) σ

1 14% 22%

2 24% 28%

(i) For portfolios formed from these two assets, explain in detail how the portfolio

return and variance depends on correlation and asset weights.

The portfolio return depends upon the weights of asset in the portfolio and the expected returns of these portfolios.

E(R)p = w1.E(R)1 + w2.E(R)2

= .5(.14) + .5(.24) (Assuming equal weights) = 0.19

The standard deviation of return for the portfolio is not the same as the expected return of portfolio, which is based on weighted average. There is more to the standard deviation then the

weights alone and that is the relationship among the portfolio’s assets. The relationship of an asset return move in contrast to any other asset is known as the covariance. In order to determine the riskiness of portfolio returns, we require covariance among these two assets as well.

σ2 = w1

2 σ12 + w2

2 σ22 +2 w1.w2. Cov(a1,a2)

Where Cov(a1,a2) is the covariance between asset 1 and asset 2. This covariance is generally measured by correlation coefficient , which we calculate by dividing the covariance of returns

among two securities by the standard deviation of their returns.

12 = Cov(a1,a2)

σ1 σ2

The correlation coefficient is very convenient measure and a scaled one too. Its values lie in

between -1 and +1. Their notations are as follows:

= -1 : Perfectly negative correlation i.e. high (low) returns on asset 1 would lead to low (high) returns on asset 2.

= 0 : Zero correlation i.e. there is no systematic relationship of return among the assets.

= 1: Perfect positive correlation i.e. high (low) returns on asset 1 would unfailingly

lead to high (low) returns on asset 2.

Now the formula can also be written as, σ2 = w1

2 σ12 + w2

2 σ22 +2 w1.w2 σ1 σ2. 12

As the outcome of this formula defines the variance in portfolio retunes, we can see that a portfolio having perfectly negative correlation among asset would have least variance in

portfolio returns, when compared to the assets having zero or perfectly positive correlation coefficient and keeping the same weights and returns. This means a low correlation reduces the volatility of portfolio returns.

So now, we can say that the variance of portfolio depends upon three main factors:

Asset weight

Standard deviation of return among the asset

Correlation among the return of portfolio securities

(ii) Assuming now that the two assets are perfectly negatively correlated, calculate

the asset weights in a portfolio that has zero risk, and calculate the expected

return of this portfolio.

Here we would use the following formulae to calculate the portfolio weights:

σ2 = w12 σ1

2 + w22 σ2

2 +2 w1.w2 σ1 σ2. 12

or,

σ = [ w12 σ1

2 + w22 σ2

2 +2 w1.w2 σ1 σ2. (-1)]1/2 = w1 σ1 - w2 σ2 [using (a-b)2

= (a2+b2-2ab)]

w1 = σ2

σ1+ σ2

And w2 = 1- w1

So, w1 = 0.28 = 0.56 0.22+0.28

w2 = 1-0.56 = 0.44

Expected portfolio return would be:

E(R) = .44(.22) + .56(.28) = 0.0968 + 0.1568 = 0.2536 or 25.36%

(c) Explain why there are limits to diversification in practice.

Diversification refers to the process of spreading one’s investment to a variety of asset classes or different securities in a same asset class. As seen in the previous answer, diversification does

provide benefits by adding more securities in one’s investment portfolio and thus offsetting the negative price movement. So far, diversification has proven as a method to get more returns from one’s portfolio at the least risk. Now the question comes, why don’t everyone diversify and

earn supernormal returns.

The answer is because creating a fully diversified portfolio does not exist. In order to achieve a “diversified” portfolio, as per the theory one needs to hold every security that exist in this world. As a result, this is virtually impossible to hold every single existing security. Instead of that, we

generally consider investing in 25-30 stocks to achieve sufficient diversification. If an investor wants to invest in more than 25-30 securities, they generally invest in mutual funds, index funds

or closed-end funds. This saves them the extra cost as well, which they would incur in diversifying.

Another limitation is that the diversification helps to reduce only un-systematic risk, but we cannot reduce/eliminate the systematic risk associated with the portfolio. Systematic risk or

market risk is one which is common to all the securities. That risk is un-diversifiable risk and is not associated with the securities rather depend upon the market condition and economic condition.

2. Answer both parts.

(a) Using diagrams, explain the roles of ‘dominance’ and ‘efficient frontiers’ in the capital

asset pricing model (CAPM).

In 1952, Harry Markowitz coined a term known as ‘Modern Portfolio Theory’ in which he stated that an asset selection for a particular portfolio should not be based on the individual portfolio only, rather it should be done looking at the change in the asset’s price in relation to every other

asset in portfolio. Within the theory itself, Markowitz explains how to select a portfolio to earn best possible returns using diversification as a strategy. Few years later Jack Treynor, William

Sharpe, John Lintner and Jan Mossin independently worked to evolve the MPT and there came one Capital asset pricing model. An asset’s required rate of return can be assessed using the CAPM.

It is assumed in CAPM that any portfolio can be turned into efficient portfolio using the risk-

return profile. A portfolio is said to be “efficient”, if for a given level of risk it has the potential to generate the best possible expected level of return. So every risky security can be plotted on a graph having risk or standard deviation on x-axis and expected return on Y-axis. The left

boundary of this hyperbola region is then the “efficient frontier”, as it would generate the highest level of return for any given level of risk. The picture below this shows the efficient frontier.

On the efficient frontier there lies one optimal portfolio which has the lowest risk and highest

return. We need to do a mean-variance analysis to arrive at a set of portfolios which is done by identifying the expected return. This efficient frontier then helps in finding the portfolios which

are offering that level of return and take note of their risk levels. Efficient portfolios which are on particular risk level put provide superior returns from their similar risk peers are said to be the dominating portfolios. This dominant portfolio helps the investor to decide among the portfolios

on the basis of their risk-return relations. This is done by eliminating all the portfolios that are having same risk level but offer lower return than the dominant portfolio.

(b) Critically discuss to what extent the evidence on market ‘anomalies’ influences the

debate on the efficient markets hypothesis and behavioural finance.

The traditional framework says that the value of a security is always equal to the present value of future cash flows. This is nothing but the so called fundamental value of the security. The underlying hypothesis here is that the markets are efficient and all the securities in market are

priced at their fundamental values only. This signifies that there are no arbitrage opportunities available. When the price of any security deviates from its arbitrage value, an immediate

reaction is triggered from market to bring back the undervalued or overvalued security to its arbitrage-free price.

The anomaly in this EMH theory is that there have been evidences where the security prices tend to deviate from their fundamental values for extended periods. Sometimes, for longer periods,

these abnormalities exist in the market before disappearing. There has been no explanation by the economists for this behaviour of markets; rather behavioural finance has the explanation to

not only same but other abnormalities as well. The inability of various modern financial and economic theories to explain the presence of

various anomalies is explained by behavioural finance as logical and rational behaviour. Quick summary of anomalies that influence debate on EMH and behavioural finance are:

January effect: As per the January effect event the average monthly returns of small

firms is noticed to be highest in the month of January than in any other month. This is opposite to the EMH, which states that the prices of securities follow its fundamental valueless. However, as per behavioural finance, the explanation is that the investors sell

their loss making holdings in December to lock in tax losses. Come January, they re-invest in the securities and a upsurge in security prices is seen that leads the monthly

returns for January to be higher than other months of normal trading.

The winner’s curse: This phenomenon exists with the assets that are taken to bidding

process. Generally the winning bid is the one with much more than the asset’s intrinsic value. This opposes the EMH theory of assets being coming back to their fundamental

values after a period of disruption, but here it does not happen. According to behavioural finance, rational bidding does not happens because the aggressiveness of bid is directly correlated to the numbers of bidders participating in the bid. And unfortunately,

increasing the bid is the only alternative to win the bid. Here the value of asset being bid does not matter to the bidders. The EMH is opposite to the function of this event and thus

is not able to explain its reason.

Equity premium puzzle: This one anomaly has made experts in finance and economic

to think hard again on the fundamentals they are working upon. Studies reveal that over past 70 years, the stocks have shown an average 10% return. While the bonds real return

are only 3%, the stock return exceeds bond return by 6-7%. It forces us to think that the stocks are too risky to hold as compared to bonds since they are providing such greater

returns as compared to them. Conventional economies model calculates this equity premium to be much less than it actually is. Behavioural finance explains this by pointing the investment horizon of an investor as a reason for such high premium. It explains that

investors have “myopic” vision when it comes to loss aversion. They are very cautious about a little movement in price of the stock that they panic and start selling the stock

seeing a little loss. Here they ignore the long term impact of the stocks and hence it is believed that there must be enough premium for equities to compensate the investor’s for loss. Thus premium is the driving force for the people to invest in risky equities

securities.

3. Answer all parts.

(a)

The table presents the annual expected returns and standard deviations of returns for

three stocks and the market index. The risk free rate of return is 3% and the stock market

is in CAPM equilibrium.

Expected Return Standard Deviation

Fenby plc 6% 8%

North plc 13% 16%

Samson plc 21% 24%

Market index 11% 10%

(i) Calculate the beta values for each of these three stocks.

According to CAPM,

E(R) = Rfr + β (Rm - Rfr)

Fenby plc’s beta would be: North plc’s beta would be: Samson plc’s bet would be:

0.06 = 0.03 + β (0.11-0.03) 0.13 = 0.03 + β (0.11-0.03) 0.21 = 0.03 + β (0.11-0.03)

0.03 = β 0.10 = β 0.18 = β

0.08 0.08 0.08

β= 0.375 β= 1.25 β= 2.25

(ii) Calculate whether these three stocks plot on the capital market line. What conclusions

do you draw from this?

These three stocks would lie on CML if these stocks are properly valued. And we know they are

properly valued, if Sharpe ratio of stock is equal to the Sharpe ratio of market portfolio.

Sharpe ratio would be calculated by using formula: E(R) - Rfr)/ σ

Market Sharpe ratio = (0.11 - 0.03) / 0.1 = 0.8

Fenby plc’s Sharpe ratio North plc’s Sharpe ratio Samson plc’s Sharpe ratio

= (0.06 - 0.03) / 0.08 = (0.13-0.03)/0.16 = (0.21-0.03)/0.24

= 0.375 = 0.624 = 0.75

It is clear from the calculation above that the three stocks would not lie on the CML as they are either over valued or undervalued. So, there is an opportunity for the buyer to both buy the

undervalued stock and earn profits when its price rise or can short the overvalued stock to profit from decrease in price.

(iii) Using examples from parts (i) and (ii), explain the differences between the capital

market line and the security market line.

The capital market line is used for a particular portfolio to represent its rate of return depending upon the risk free rate of return and various levels of risk. On the other hand, security market

line is not used for a particular portfolio rather a market and gives a graphical representation of the risk and return of market any given time.

Other difference is the measurement of risk factor. While the CML uses standard deviation as the risk factor the SML uses beta to measure the risk contribution by a particular security to the

market. So basically CML represents efficient portfolios whereas SML would represent both efficient and non-efficient portfolios.

At the time of graphical representation, CML defines the y-axis as the expected return of portfolio. On the contrary, SML takes its y-axis to be the return of securities and x-axis to beta.

CML represents standard deviation on its x-axis. It is often considered CML to be a superior when it comes to measuring of risk. The SML is derived from CML the sole difference in

derivation being the measure of risk, which is beta in SML and standard deviation is CML. While the CML could be used to point out the risk/return relationship of efficient portfolio, the SML could be used for same purpose for individual assets as a measure of sensitivity to

fluctuation in markets.

(b)

Aran plc has a beta value of 1.5 and its shares may be purchased for £120. This particular

asset has an expected return of 40% over one year. One-year risk-free bills may be

purchased at £5 and offer a 4% return. The market portfolio has an expected return of

16% over one year, and shares in a fund which tracks the market portfolio sell at £120.

(i) Aran plc is mispriced. Using a simple diagram, explain this situation.

Aran plc’s expected return should be calculated using formula, E(R) = Rfr + β (Rm - Rfr)

E(R) = 0.04 + 1.5 (0.16 - 0.04)

E(R) = 0.22 or 22%

This means that the stock is undervalued as the expected return is more than fundamental

returns. So that means the stock is underpriced, that is why the stock is expected to give 40% return ,whereas looking at the CAPM model, the stock’s return should be 22%.

(ii) Devise a strategy to exploit the mispricing, and illustrate the cash flows arising from

this strategy.

In order to exploit the current situation, one must buy the stock at current value and sell the stock

when it reaches to its optimum value. Buying at the current price at £120, means that the stock is going to appreciate in value to provide 40% return, which is £168 at the end of the year.

Initial cash outflow: £120 Ultimate cash inflow: £168

Profits: £48

(iii) Identify the beta value of the strategy and explain the meaning of arbitrage.

Beta value of strategy is: Stock return/ Market return i.e. 0.40/0.16 = 2.5

Arbitrage refers to a simultaneous buying and selling of an asset in order to profit from difference is price in different markets. It is a trade that takes place when an asset has different

prices in different markets. This happens only for a very short amount of time, post which the market forces of demand and supply forces the asset back to its same price. It is the existence of

market inefficiencies that lead to the existence of arbitrage. With the advancement in technology, it is difficult for a trader to exploit the arbitrage opportunities. For this, the traders apply certain systems to capture the price differences which sustains for a span of few seconds

before vanishing and they try to profit from it.

Section B

(In our discussion, by options we mean European options)

4.

Using detailed examples, explain how forwards, futures and options provide different types

of opportunities for managing the risk of positions in underlying assets .

Forwards, futures and options are all derivative instruments which depend upon its underlying

asset for deriving their values. The majority of usage of derivatives is done for doing hedging. Hedging refers to the technique of reducing the risk to an extent that it becomes bearable. We would discuss the different types of risk management by these one by one.

Forwards : Forwards are contracts which are traded OTC that is there is no exchange involved in

the trade. These are tailor made instruments created to suit the needs of involved parties. Forwards is most widely used instrument to manage exchange rate risks. It helps parties lock down the future exchange rate for the transaction they would take place in future. For example:

‘A’ having its business in England has entered into a contact with another party from US for getting services for 3 months and in turn would have to pay $50,000. ‘A’ fears that the USD in

relation to GBP would appreciate and as a result he would have to pay more in GBP to get $50,000 for payment. So he enters into a forward contract which enables them to lock exchange rate at 1.67 USD/GBP. So at the end of three months, whatever the rate of USD/GBP maybe, he

would get USD at 0.60 USD/GBP and would make payment with that. Here the other party may be interested to get their hands on GBP after three months at an exchange rate of 0.60

GBP/USD, as they might have to make some payment in GBP and fear that the GBP/USD exchange rate would appreciate and they could end up paying more in USD. So the forward contract here comes off as a benefit to both the parties involved and they were able to manage

risk using that.

Futures: As opposed to forwards, Futures are exchange traded contracts, and hence are standardized. They have much less counterparty default risk as the exchange acts at counterparty to all the contracts. Futures are widely used as a hedging tool in commodities segment. For

example: A farmer anticipates to have a good wheat this time and he wants to lock down its future price so that he does not gets affected by price fluctuation. On the other hand, a trader is

of the view that the wheat prices might get too high because of demand coming from corporates and wants to buy the wheat at a pre-decided price after 6 months. These two parties get in futures contract with the exchange and were able to lock in their proceeds for 6 months in

advance. BY entering into futures contract they have limited their exposure to price movement risk.

Options: Options can be both exchange traded as well as over-the-counter traded instruments. Options can act as an insurance policy to parties involved by limiting the downside risk and

allowing the party to adore the full-upside.

There are two type of option: Call option and put option. Call option gives owner the right but not the obligation to but pre-specified quantity of goods or

securities at pre-specified prices. Put option gives the right to the owner to sell the goods or securities of pre-specified at pre-specified prices. Once the option buyer decides to exercise the

option, the option writer has the obligation to honour the option, because buyer paid a premium to earn this exercise right.

One of the most widely use of options is to safeguard oneself from volatility in stock markets. For example: ‘A’ has a big stake in Google Inc, however he is of the view that new regulation

may squeeze up the company profits this year and hence stock prices would go south. This new

legislation is yet to be voted and passed. So, to protect him from the downside, the investor purchase 3 month put option for $550 for say, $50 premium. Thus, he has insured himself from

price falling beyond $550, and even if that happens, he could sell it at $550 only and lock down further loss (apart from $50 premium).

5. Answer both parts.

(a) For option contracts, explain the meanings of ‘time value’, ‘intrinsic value’ and ‘price

determinants’.

The value of any option is decided using two inputs i.e. option’s intrinsic value and option’s time value. Option’s intrinsic value is calculated using the underlying price and strike price.

Intrinsic value (call) = Underlying price – Strike price

Intrinsic value (put) = Strike price – Underlying price

Specifically for the call option, intrinsic value is the difference of underlying price and strike price whereas for put option it’s the difference of strike price minus underlying price. By

definition the only options that have intrinsic values are in-the-money options. For example: If a stock is priced at $30 and has a $25 call option with 60 days of time period. It was selling on premium of $6.5. The intrinsic value of call option would be = Underlying price –

Strike price i.e. $30- $25 = $5. The time value of an option refers to any premium that is in excess to the intrinsic value of

option premium.

Time value = Premium – Intrinsic value

Generally, the time value of option depends upon the time to expiration of option contract.

Greater the time to contract expiration, greater the time value of option would be. This is because the investors considered it appropriate to pay extra for having a extra time with them.

Since, it is believed that more the time is available the more chances are that the option would expire as profitable. With the passage of time and when the option expiry comes closer, the time value of premium reduces and ultimately becomes zero at expiration. This reduction in time

value is known as ‘Time decay’. Continuing on the above example only, we can calculate the time value of option by subtracting the intrinsic value from premium

Time value = $6.5 - $5 = $1.5 Price determinants are the factors on which the value of option is dependent upon. These are:

Stock price, strike price, variance of underlying assets, and time to expiration, interest rates and dividend paid. Following table shows the impact of price determinants on option values. Please

note that their inverses are also true.

Factor Call Value Put Value

Increase in Stock Price Increases Decreases

Increase in Strike Price Decreases Increases

Increase in variance of underlying asset Increases Increases

Increase in time to expiration Increases Increases

Increase in interest rates Increases Decreases

Increase in dividends paid Decreases Increases

(b) Analyse binomial option valuation by comparing the approaches using (i) implied

probabilities and (ii) no-arbitrage conditions.

The binomial option pricing model is used to find the values of options using a generalizable numerical method. This model was proposed in1979 by Cox, Ross and Rubinstein. This method is used to calculate value of options over a period of time rather than a particular point of time.

It is mostly used for valuing American options as they can be exercised anytime.

Assume that we have a share of stock whose current price is $100/share. During the next month, the price of the stock is either going to go up to $110 (up state) or go down to $90 (down state). No other outcomes are possible over the next month for this stock's price. Now assume that a

call option exists on this stock. The call option has a strike price of $100 and matures at the end of the month. The value of this call option at the end of the month will be $10 if the stock price

is $110 and 0 if the stock price is $90. The payoff at maturity (one month from now) for this call option is:

Beginning Value End of Month Value $10 given a stock price of $100

Call Price today $ 0 given a stock price of $ 90

(i) Implied probabilities: This here is a simple example of binomial model. For the purpose of

pricing option, binomial model uses implied probability approach. In this the historical volatility of stock is used as a benchmark to redefine the probability. Like in the example above, we used 50% probability of call price going up and going down. But using the implied probability

approach, we take a different set of probabilities to reach to an option price. However, generally, people do not use this strategy at a larger extent as they consider probabilities as irrelevant and

counter intuitive. Instead of this, the no-arbitrage condition provides a much more relevant value to options.

(ii) No-arbitrage conditions: The pricing of options is also done by binomial takes no-arbitrage strategy. An alternative to the risk less hedge approach to valuing options using the binomial

model is the risk neutral approach. The basic argument in the risk neutral approach is that since the valuation of options is based on arbitrage and is therefore independent of risk preferences; one should be able to value options assuming any set of risk preferences and get the same

answer. As such, the easiest model is the risk neutral model. The general approach to option pricing is first to assume that prices do not provide arbitrage opportunities. Then, the derivation

of the option prices (or pricing bounds) is obtained by replicating the payoffs provided by the option using the underlying asset (stock) and risk-free borrowing/lending.

Consider a call option on a stock with exercise price X. And assume that the stock pays no dividends.)

At time 0 (today): Intrinsic Value = Max[S-X, 0],

The intrinsic value sets a lower bound for the call value: C > Max[S-X, 0]

In fact, considering the payoff at time T, Max[ST-X, 0] we can make a stronger statement:

C > Max[S-PV(X), 0] ≥ Max[S-X, 0]

Where PV(X) is the present value of X (computed using a borrowing rate). If the above price restriction is violated we can arbitrage. But the market forces of demand and supply does not

allow this to happen as a result a no-arbitrage price is always prevalent and the value of option is decided using that particular model only.

6.

(a) Explain the covered interest rate parity condition and demonstrate its relevance to the

pricing of currency forwards.

Covered interest rate parity (CIP) refers to a nominal interest rate of any country against any other economy’s nominal interest rate along with a forward premium rate between these two economies.

RUSD = REUR + f

So, CIP states that if there is any interest rate gain on USD cash deposit over the EUR cash deposit, the depreciation of USD against EUR would completely wipe out these gains. The same

is represented by Forward premium ‘f’’. Mathematically forward premium ’f’ is calculated as: (F/E)-1

Here, F is the nominal forward exchange rate and E is the nominal spot exchange rate of the two currencies we are dealing with. Overall, covered interest rate parity provides a no arbitrage

condition to the participants. There are three main variables on which the forward exchange rate is dependent upon:

Spot exchange rate of two currencies

Interest rates of domestic currency

Interest rates in foreign currency

CIP represents a situation in which not only the investor’s exposure to foreign exchange risk is covered but also it makes sure that there are equal returns to the domestic investor, whether

They invest in domestic country, or

Convert currency at spot exchange rates, or

They invest in the foreign currency with the interest rate prevailing there and fixing a

forward exchange rate to covert back the money in domestic currency.

This is because of the interest rate equilibrium created by forward exchange rate; the investor seems indifferent to invest in domestic or foreign currency at the known rates. This is why the CIP provides a no-arbitrage condition. The following equation is used to calculate the forward

exchange rate using spot rate, foreign and domestic rates.

Forward exchange rate = Spot exchange rate ((1+REUR )/ (1+RUSD))

The pricing of currency forwards is done using the same equation. Using the example of the U.S. Dollar and the EUR with a spot exchange rate of USD/EUR= 1.2213 and one-year interest rates

of 1.25% and 0.80% respectively for the U.S. and Euro, we can calculate the one year forward rate as follows:

EUR/USD = Spot ((1+REUR )/ (1+RUSD)) = 1.2213*((1+0.0080)/ (1+0.0125))

= 1.21587

Forward points: Forward rate – spot rate = 1.21587 – 1.2213 = -0.0055

These are known as 0.55 pips by traders. The interest rate differential between two currencies is reflected by these forward points. The forward rates calculated using this equation can be either

positive or negative, which depends upon the interest rates prevailing. Going forward, the higher yielding currency will be discounted and lower yielding currency is compounded.

Section C

1.

An investment advisor has selected only three stocks as his current recommendations to

clients. The tables present the expected returns, standard deviations and correlation

coefficients for the three stocks.

Expected returns Standard deviation of returns

Biggar plc 11% 19%

Halfpenny plc 20% 26%

Thirsty plc 14% 21%

Correlation coefficients between returns

Biggar and Halfpenny 0.34

Biggar and Thirsty 0.82

Halfpenny and Thirsty 0.08

The investment advisor has also recommended that the decision about which stocks to buy

should involve selecting the optimal equally weighted portfolio containing two of these

three stocks (i.e. 50-50 weights).

(a) Calculate estimates of the risk and return for the following three equally weighted

portfolios: (i) Biggar and Halfpenny; (ii) Biggar and Thirsty; (iii) Halfpenny and Thirsty.

Risk of a portfolio can be calculated following equation:

σ2 = w12 σ1

2 + w22 σ2

2 +2 w1.w2 σ1 σ2. 12

(i) Biggar and Halfpenny: (0.5^2)(0.19^2) + (0.5^2)(0.26^2) + (2*0.5*0.5*0.19*0.26*0.34) = 3.43%

(ii) Biggar and Thirsty: (0.5^2)(0.19^2) + (0.5^2)(0.21^2) + (2*0.5*0.5*0.19*0.21*0.82) = 3.64%

(iii) Halfpenny and Thirsty: (0.5^2)(0.26^2) + (0.5^2)(0.21^2) + (2*0.5*0.5*0.26*0.21*0.08) =

3.01% Return on portfolio can be calculated using following equation:

E(R)p = w1.E(R)1 + w2.E(R)2

(i) Biggar and Halfpenny = (0.5*0.11) + (0.5*0.20) = 15.50% (ii) Biggar and Thirsty = (0.5*0.11) + (0.5*0.14) = 12.50% (iii) Halfpenny and Thirsty = (0.5*0.20) + (0.5*0.14) = 17.00%

(b) Explain which one of these three portfolios you believe to be the most attractive.

The portfolio containing Halfpenny and Thirsty is the most attractive portfolio as it offers the

maximum return (17%) at minimum risk (3.01%) as compared to other portfolios. Modern portfolio theory explains that a portfolio should be chosen based on the risk/return analysis. If

the portfolio has a greater return for same level of risk or if it same return for less level of risk as compared to the other peer portfolio.

(c) Discuss your views on the investment advisor’s recommendations.

Investment advisor’s recommendation for the three stocks is not very strategic as we can see that

none of the stock is able to provide returns as compared to the risk embedded with them. Looking at the risk levels, we can assume that the investor is not averse to risk and is willing to take the risk to earn supernormal returns. So the investment advisor must recommend such stock

which have return equivalent to their risk and negatively correlated as well, to maintain the portfolio balance.

(d) Explain the principles of diversification and discuss the limits to diversification.

Diversification refers to the process of spreading one’s investment to a variety of asset classes or different securities in a same asset class. As seen in the previous answer, diversification does

provide benefits by adding more securities in one’s investment portfolio and thus offsetting the negative price movement. So far, diversification has proven as a method to get more returns from one’s portfolio at the least risk. Now the question comes, why don’t everyone diversify and

earn supernormal returns.

The answer is because creating a fully diversified portfolio does not exist. In order to achieve a “diversified” portfolio, as per the theory one needs to hold every security that exist in this world. As a result, this is virtually impossible to hold every single existing security. Instead of that, we

generally consider investing in 25-30 stocks to achieve sufficient diversification. If an investor wants to invest in more than 25-30 securities, they generally invest in mutual funds, index funds

or closed-end funds. This saves them the extra cost as well, which they would incur in diversifying.

Another limitation is that the diversification helps to reduce only un-systematic risk, but we cannot reduce/eliminate the systematic risk associated with the portfolio. Systematic risk or

market risk is one which is common to all the securities. That risk is un-diversifiable risk and is

not associated with the securities rather depend upon the market condition and economic condition.

2.

(a) The following information is available for Greene plc.

Date Share Price Annual Dividend

1st January 2006 225 pence -

31st December 2006 205 pence 5 pence

31st December 2007 216 pence 7 pence

31st December 2008 232 pence 9 pence

Calculate the annual rates of return (both arithmetic and logarithmic) for each year.

Assume that dividends are reinvested.

Return on 31st December 2006

Arithmetic return: Ending value + Dividend / Starting value Logarithmic return: (a*b*c)1/3 – 1 where a,b,c are 1-arithmetic returns

Return on 31st December 2007

Return on 31st December 2008

(b) The following information is available on the percentage rates of return on various

assets under three alternative states of the world (with probabilities given).

State (and Probability)

Asset Recession (0.4) Static (0.5) Growth (0.1)

IFM plc 1 % 5 % 12 %

OAG plc -5 % 9 % 23 %

Market -4 % 11 % 16 %

Arithmetic return = ((205 + 5) – 225) / 225 = -6.67%

Logarithmic return = 225 (1 + x) = 205 + 5 x = -6.67%

Arithmetic return = ((216 + 7) - 205 )/ 205

= 8.78%

Logarithmic return = ((1-.0667)(1+.0878))^1/2 -1

= 0.76%

Arithmetic return = ((232 + 9) – 216) / 216 = 11.57%

Logarithmic return = ((1-.0667)(1+.0878) (1+.1157))^1/3 -1 = 4.24%

Risk free asset 4 % 4 % 4 %

(i) For each asset, calculate its expected return, standard deviation and covariance with the

market return.

Expected return: E(R)p = P1.E(R)1 + P2.E(R)2 + P3.E(R)3

Expected return can be calculated by the product of probability with the asset return.

IFM plc = (0.4*0.01) + (0.5*0.05) + (0.1*0.12) = 4.10% OAG plc = (0.4*- 0.05) + (0.5*0.09) + (0.1*0.23) = 4.80%

Market return = (0.4*- 0.04) + (0.5*0.11) + (0.1*0.16) = 5.50%

Standard deviation: σ2 = w12 σ1

2 + w22 σ2

2 +2 w1.w2 σ1 σ2. 12

IFM plc’s Standard deviation with market return, σ2 = (0.4*((0.01- 0.04) ^2)) + (0.5*((0.05-0.11)

^2)) + (0.1*((0.12-0.16) ^2)) = 0.23% σ = 0.0023^ (1/2) = 0.0482 or 4.82%

OAG plc’s Standard deviation with market return, σ2 = (0.4*((-0.05 - 0.04) ^2)) + (0.5*((0.09-

0.11) ^2)) + (0.1*((0.23-0.16) ^2)) = 0.39% σ = 0.0039^ (1/2) = 0.0627 or 6.27%

Market variance, σ2 = (0.4*((-0.04 - 0.055) ^2)) + (0.5*((0.11-0.055) ^2)) + (0.1*((0.16-0.055)

^2)) = 0.62% σ = 0.0062^ (1/2) = 0.07874 or 7.84%

Covariance: ((R1-E(R1)+(Rm -(E(Rm))/n-1

IFM plc=((0.01-0.0410)+(0.05-0.0410)+(0.12-0.0410)+(-0.04-0.055)+(0.11-0.055)+(0.16-

0.055))/2 = 0.0610

OAG plc= ((-0.05-0.048)+ (0.09-0.048)+ (0.23-0.048)+(-0.04-0.055)+(0.11-0.055)+(0.16-0.055))/2

= 0.0955

(ii) Calculate whether stocks IFM plc and OAG plc lie on the capital market line (CML)

and explain what you conclude from this.

Sharpe ratio = (E(r) – rf )/ σ

For IFM plc = (0.041 – 0.04)/ 0.0482 = 0.02

For OAG plc = (0.048 – 0.04)/ 0.0627 = 0.13

Market Sharpe ratio = (E(r) – rf )/ σM = (0.055 – 0.04)/ 0.0784 = 0.19

This explains that the Sharpe ratio of none of the stock is equal to the market Sharpe ratio of

19%, this means these stocks do not lie on the CML. The Sharpe ratio of market portfolio forms the slope of CML. We can say that the portfolios are not the fully efficient portfolios and do not

provide sufficient return for the given level of return. There may be other portfolios at the same risk level offering ore returns or offering similar returns but with lesser risk.

(iii) Calculate the beta values for IFM plc and OAG plc.

IFM plc’s beta = Covariance s, m/variance s = 0.0610/0.0482 = 1.26 OAG plc’s beta = 0.0955/0.0627 = 1.52

(iv) Are the expected returns for IFM plc and OAG plc consistent with the security market

line (SML) and, if not, what changes would you expect to occur to restore equilibrium?

In order to check the consistency of returns with the SML, we need to calculate the Treynor’s

ratio. The Treynor’s ratio of the market portfolio is the same across the SML and all the portfolios that lie on it would always have same Treynor’s ratio.

Trenor’s ratio = (E(r) – rf )/ β

Market’s Treynor ratio = (0.055 – 0.04)/ 1 = 0.015

(Beta for market portfolio is slope of SML and is always =1) IFM plc’s Treynor ratio = (0.041 – 0.04)/ 1.26 = 0.000794

OAG plc’s Treynor ratio = (0.048 – 0.04)/ 1.52 = 0.005263

We can see that none of the both has a Treynor ratio equal to Treynor ratio of market portfolio. In order for the equilibrium to achieve, we expect that the over-buying and over-selling of undervalued and overvalued stocks would allow the stocks to reach their fundamental values

where they would be earning returns similar to fundamental returns. When the securities are prices correctly they would be plotted on SML.

3.

(a) Explain the principles of the ‘capital market line’ of the capital asset pricing model

(CAPM) and discuss the ‘market price of risk’ in this context.

CAPM basically explains the impact of an asset with non-diversifiable risk on a well-diversified portfolio. This non-diversifiable risk of asset is generally represented by Beta or β. The model takes into account the contribution of risk free rate of return, expected return of market and the

beta. CAPM helps to determine expected returns at various levels of risk (beta). Basically the capital market line is used for a particular portfolio to represent its rate of return depending upon

the risk free rate of return and various levels of risk.

The figure on left shows

the depiction of CML and the various levels. The

point ‘m’ is the market portfolio, imitating which all rational investors must

weight their portfolios. This means that the

rational investor must decide the asset weight in their portfolio as per the

weights in market portfolio. Since the CML combines both risky as well as risk free assets, the risk-return profiles of all the points along CML are superior to efficient frontier. The only

exception being the market portfolio. In fact the market portfolio is the point of tangency of CML to efficient frontier. From the prospective of CML, the market portfolio is composed entirely of risk free assets and it does not hold any of the risk-free securities. For a group of

portfolios to lay on CML, it is necessary that their Sharpe ratio must be equal to the Sharpe ratio of portfolio. If the Sharpe ratio is different than a stock picking rule of thumb is the assets having

Sharpe ratio lying below the CML should be sold and assets having Sharpe ratio above the CML must be bought.

Market price of risk refers to the risk premium that one gets for bearing a risk. It is calculated by subtracting the risk free rate from market rate of return. The impact on a return of stock is

magnified by market risk of premium multiplying it by beta. This risk premium should be enough to compensate the investor for the amount of risk they take on. In order to measure, if the market price of risk is sufficient to compensate the investors for their gain or not, we compare

the Sharpe ratio with the Sharpe ratio of other portfolios that have same risk. If the Sharpe ratio for individual portfolios with same level of risk is higher than other, it means that better returns

are there at a similar level of risk. We can also calculate the additional return earned for one unit of excess return and see if it is feasible for the investor to invest.

(b) Analyse the similarities and differences among the CAPM, the arbitrage pricing theory

and the Fama and French model.

All three of the theories described above i.e. CAPM, APM and FFM are used to determine that how the markets value risky assets. All these models help the decision makers by providing them a required rate of return for risky assets. Following the main similarities among these three:

No taxes or transaction cost

Information is freely available to all the investors

The market consists of many buyers and sellers and none of whom has a power to

influence security prices.

Risk free assets are prevalent, on which the unlimited borrowing and lending can be

done.

There are no arbitrage opportunities available as the markets are in competitive

equilibrium.

All the models state that in market equilibrium how the risky assets are placed.

All of them provide the decision makers with the required rate of return that should be there on risky securities.

While CAPM use beta as a measure of risk, APM uses multiple risk factors and FFM uses 3 factors for measurement of risk. FFM uses the variables such that return on stock index, excess

return of portfolio of small stock over portfolio of large stocks and excess return on a portfolio of high book-to-market stocks over a portfolio of low book-to-market stocks.

CAPM is based on the investors’ portfolio demand and equilibrium and APT uses factor model of return and arbitrage. While CAPM uses single period, both APT and FFM can be used in both

single period and multi period cases. CAPM and FFM have pre-defined the factors which affect the risk and return whereas APT does not implicitly states the factors on which the risk-return is

based. CAPM uses the securities’ systematic risk and market price of risk to determine the risk premium, whereas the APT makes use of securities’ sensitivity to each other and risk premium associated to each other. CAPM advocates buying of stock based on their risk appetite ad

comparing it with market portfolio. APT also supports the same whereas the FFM believes in value investing rather than risk assessment. It says that the stocks with low prices are to be

bought instead of comparing it with risk-reward system. CAPM and APT uses microeconomic models such as risk free rate, exchange rate, inflation rate in its consideration of appropriate price for a security, whereas FFM uses firm specific characters such as firm’s size, book value to

equity ratio.

Section D

4.

(a) Using financial market examples, explain the differences among speculation, hedging

and arbitrage

Speculation refers to a practise of getting into financial transaction which is risky and hoping to

make profits out of price movements. Speculation is considered for creating an efficient market. Those who participate in speculation are not concerned about the fundamental value of security

rather are concerned about the rice movements, be it for any reason. For example: A speculator would invest in stock looking at a level from where it can earn profits with price movement, looking at the condition, he may choose to buy or short the stock.

Hedging is a risk management technique, which involves taking an opposite position in a trade

which is intended to offset the potential gain/loss in the may occur due to movement in stock being opposite to the intension. In simple words, a person or a company uses the hedge to save themselves form a big loss occurring out of price movement. A person would want to hedge a

particular cash inflow, which he is going to get after three months. So that person would buy the FX futures and lock down the exchange rate for future and saved him for potential downside

Arbitrage refers to a simultaneous buying and selling of an asset in order to profit from difference is price in different markets. It is a trade that takes place when an asset has different

prices in different markets. This happens only for a very short amount of time, post which the market forces of demand and supply forces the asset back to its same price. It is the existence of

market inefficiencies that lead to the existence of arbitrage. With the advancement in technology, it is difficult for a trader to exploit the arbitrage opportunities. For this, the traders apply certain systems to capture the price differences which sustains for a span of few seconds

before vanishing and they try to profit from it. For example a person would get into arbitrage opportunity as a stock is selling at higher price on some other exchange, so he could buy the

stock from one and simultaneously sell it on other exchange booking risk-less profit.

One of the major differences is that while speculation is pure risk taking to earn profits, hedging

is done to avoid profits or a part of risk management; arbitrage is done to exploit the price differentials. The kind of precision and timing required in arbitrage is not required in hedging

and speculation. If we look from an effort wise basis, the arbitrage requires least amount of effort and is more of technology driven, whereas the hedging is more of a calculation driven and the speculation is all about price movements and gut instinct without much of calculations.

(b) Explain the main propositions of the efficient markets hypothesis and analyse the

evidence on financial market ‘anomalies’.

As per the EMH, the current stock prices fully reflect the available current information about the

value of a security and it is not possible to earn supernormal profits apart from what the markets are earning. One of the most exciting issues that are discussed in EMH is the reason of price

change in securities and means of taking those changes. The traditional framework says that the value of a security is always equal to the present value of

future cash flows. This is nothing but the so called fundamental value of the security. The underlying hypothesis here is that the markets are efficient and all the securities in market are

priced at their fundamental values only. This signifies that there are no arbitrage opportunities available. When the price of any security deviates from its arbitrage value, an immediate reaction is triggered from market to bring back the undervalued or overvalued security to its

arbitrage-free price.

The anomaly in this EMH theory is that there have been evidences where the security prices tend to deviate from their fundamental values for extended periods. Sometimes, for longer periods, these abnormalities exist in the market before disappearing. There has been no explanation by

the economists for this behaviour of markets; rather behavioural finance has the explanation to not only same but other abnormalities as well.

Over-reaction and under-reaction: As per EMH investors react quickly to new

information, take actions and leads to such a price which reflects the new information. There may be chances that an investor is over reactive or under reactive to particular information depending upon the degree of impact it has on the investor’s stocks. In a

research that has been carried for around 30 years now, it has been proved that the stocks of a company reflect its earnings announcement for over a year1. As per EMH, the prices should have been fully reflecting the information pretty quickly and not as long as one

year.

January effect: As per the January effect event the average monthly returns of small firms is noticed to be highest in the month of January than in any other month. This is

opposite to the EMH, which states that the prices of securities follow its fundamental valueless. However, the EMH contradicting explanation is that the investors sell their loss making holdings in December to lock in tax losses. Come January, they re-invest in

the securities and a upsurge in security prices is seen that leads the monthly returns for January to be higher than other months of normal trading.

The winner’s curse: This phenomenon exists with the assets that are taken to bidding

process. Generally the winning bid is the one with much more than the asset’s intrinsic value. This opposes the EMH theory of assets being coming back to their fundamental

values after a period of disruption, but here it does not happen. In contrast to EMH, rational bidding does not happens because the aggressiveness of bid is directly correlated

to the numbers of bidders participating in the bid. And unfortunately, increasing the bid is the only alternative to win the bid. Here the value of asset being bid does not matter to

the bidders. The EMH is opposite to the function of this event and thus is not able to explain its reason.

Equity premium puzzle: This one anomaly has made experts in finance and economic to think hard again on the fundamentals they are working upon. Studies reveal that over

past 70 years, the stocks have shown an average 10% return. While the bonds real return are only 3%, the stock return exceeds bond return by 6-7%. It forces us to think that the

stocks are too risky to hold as compared to bonds since they are providing such greater returns as compared to them. Conventional economies model calculates this equity premium to be much less than it actually is. Behavioural finance explains this by pointing

the investment horizon of an investor as a reason for such high premium. It explains that investors have “myopic” vision when it comes to loss aversion. They are very cautious

about a little movement in price of the stock that they panic and start selling the stock seeing a little loss. Here they ignore the long term impact of the stocks and hence it is believed that there must be enough premium for equities to compensate the investor’s for

loss. Thus premium is the driving force for the people to invest in risky equities securities.

5.

(a) Analyse the pricing of forward contracts and demonstrate the principles of hedging

using forward contracts.

A forward contract is one where the two parties agreed to buy or sell an agreed goods or services at an agreed price on an agreed future date. On that future date, the parties exchange the goods or

services with the price agreed upon. Theoretically, forward price is calculated by formula; F = S0erT

Here, S0 is the spot price of asset. r is the risk free interest rate, T is time to maturity. As previously discussed as well, Forward prices exist in no arbitrage conditions, which means that it

makes the availability of are no-risk free profits. For example: An asset has a current spot price $550 and the interest rate is 1.25%. Time to maturity is 6months.

Price of future contract would be. F = 550.e6*(0.0125/12) = $550(1.00627) = $553

We can see from the above example that the price of future contract is depended upon following factors:

Spot price

Risk free interest rate

Time to maturity.

Initially the value of future contract is zero and it changes with the change in spot prices. An example of no arbitrage condition can be seen with an assumption that F > S0erT

Buy the asset at spot price today.

Enter into a contract to provide the asset at time T at price F

On delivery date, sell the asset at F

Utilize the proceeds from F to pay the loan, which has increased to S0erT

Earn profits equivalent to F- S0erT With the assumption that S0erT > F, we would do the exact inverse of the above mentioned steps

to hedge and gain. Following example can be used to explain in detail the hedging procedure.

‘A’ having its business in England has entered into a contact with another party from US for getting services for 3 months and in turn would have to pay $50,000. ‘A’ fears that the USD in relation to GBP would appreciate and as a result he would have to pay more in GBP to get

$50,000 for payment. So he enters into a forward contract which enables them to lock exchange rate at 1.67 USD/GBP. So at the end of three months, whatever the rate of USD/GBP maybe, he

would get USD at 0.60 USD/GBP and would make payment with that. Here the other party may be interested to get their hands on GBP after three months at an exchange rate of 0.60 GBP/USD, as they might have to make some payment in GBP and fear that the GBP/USD

exchange rate would appreciate and they could end up paying more in USD. So the forward contract here comes off as a benefit to both the parties involved and they were able to manage

risk using that. Sometimes forward contracts are required to buy or deliver physical goods and in that case there

is an addition in formula for calculating futures price. We then add up a cost of storage (carry) to incorporate the cost of buying the assets today and storing it for delivery per the profile of future

buyer or seller. A simple example here would explain the concept more clearly. Suppose an investor needs to purchase 100 tonnes of sugar three months from now. He can

either purchase it today or pay the storage cost for three months or he can enter into forward contract for the same. The forward price here would be calculated based on the cost of storage

and rate of interest. Suppose he borrows a sum of $10,000 from bank today at 6% per annum. He buys the 100 tonnes of sugar and put it in a warehouse, which would charge him $10 per tonne of sugar kept there for 1 year.

Bank to paid at the end of three months = 10,000*(1+(0.06/4) = $10,150

Payment to warehouse = 1000*1/4 = $250 Total cost = $10,150 + $250 = $10,400

In actual the investor paid for per tonne sugar would be: $10,400/100 = $104 This has to be the price of sugar forward three months to now in order to maintain no-arbitrage

equilibrium.

(b) Explain the similarities and differences among forwards, futures and options.

Forwards : Forwards are contracts which are traded OTC that is there is no exchange involved in

the trade. These are tailor made instruments created to suit the needs of involved parties. Forwards is most widely used instrument to manage exchange rate risks. It helps parties lock down the future exchange rate for the transaction they would take place in future.

Futures: As opposed to forwards, Futures are exchange traded contracts, and hence are

standardized. They have much less counterparty default risk as the exchange acts at counterparty to all the contracts. Futures are widely used as a hedging tool in commodities segment.

Options: Options can be both exchange traded as well as over-the-counter traded instruments. Options can act as an insurance policy to parties involved by limiting the downside risk and

allowing the party to respect the full-upside.

Similarities of forward, futures, option are:

All three can be used as risk management tools for hedging.

There value falls when the expiration date approaches.

There is daily settlement for both futures and options.

All three required to an action to be taken in future, whether or not it is taken depends upon the holder’s willingness and ability.

Key differences in these three are:

One of the biggest fundamental differences in options as compared to forwards or futures

is that the option holder has no obligation to exercise the contract, whereas it becomes legally binding for future or forward market participant.

Futures differ from forward in a way that futures are traded on exchanges and are in standardised form whereas forwards are tailor are contracts to suit the needs of parties

and there is no exchange regulating the forwards contract.

While buying an option, one has to pay money in the form of premium, whereas in case

of futures there is no such upfront payment that is made, rather it is marked to market every day.

6.

(a) Explain the main propositions of ‘behavioural finance’.

Conventional finance theory says that participants of financial markets are wealth maximises i.e. they are making rational decisions, which would lead to maximization of their wealth. However,

there are circumstances that lead the emotions and psychology to overpower the rationality and hence causing people to behave in irrational and unpredictable ways. Behavioural finance is a

relatively new field of study. It combines the conventional economics and finance with behavioural and cognitive psychological theory. With this combination, it is able to provide answers to the irrational behaviour people in financial markets. Following are some of the key

propositions explained in behavioural finance for the irrational behaviour of people:

Anchoring: As and when a new house is built an anchor is built. On which the whole structure is based. Similarly the people have a conventional wisdom which dictates their

decision making power. For example: Diamond anchor states that a diamond ring should cost around 2 months of a person’s salary. It is highly unlikely that every person could afford the same and as a result they end u taking debt to achieve the standard. So, the

rationality should be that the ring is one which is affordable and not be benchmarked by one’s salary, but the anchoring forces people to behave irrationally.

Mental accounting: It refers to people separating their money in separate accounts based on the subjective importance to them. Many people do mental accounting without even

realizing how illogical it can be. People tend to save money for new house or new car but are not able to pay credit card bills, which are attracting 20% annually. If y\they would pay

off the expensive debt first and then save, would leave them a lot less trouble and lot more money.

Confirmation and hindsight bias: People have a preconceived notion or opinion about

everything they come across. They tend to selective filtration of information that comes across them to support their preconceived notions. Suppose an investor learns about a ‘hot’ stock from an unverified source. He will do the research to prove the information to be

correct and then invest in the same. As a result he ends up having losses. Hindsight bias comes into play when a person has an opinion about something based on past experience.

This opinion would not allow the person to work opposite to it and hence forcing the person to continue the same opinion.

Herd behaviour: It is the propensity of persons to imitate the action of larger group. A variety of reasons lead to this behaviour. First one is the social pressure of conventionality.

Since, people are social animals; they tend to follow what the society follows to appear as a part of it. The second reason is thinking that a large group of people cannot be wrong at a same time.

Gambler’s fallacy: This proposition is based on people’s thinking about certain random

events that happen. These events force an individual to believe the probability of happening or an event is less likely. Such thinking is incorrect because the individual base the

probability of events on its past occurrence rather than rational probability. Suppose a series of coin toss leads to occurrence of head for all5 times forces an individual to think that 6 th time also the head will occur. They forget that the probability of head is same as probability

of tail i.e. 50%

(b) Explain the main features and mechanics of the foreign exchange market.

A foreign exchange market is one where the currencies of different countries are bought and sold

against one another. It is interchangeably called as foreign currency market but in actual it is a foreign exchange market as the commodity that is traded on the market is more appropriately called foreign exchange rather than a foreign currency. This market is one of the largest and

most perfect markets. The volume of trade that takes place there are largest as compared to any other market. Currently it’s about $1 trillion.

Foreign exchange market is one of the perfect markets that can exist. It possesses all the requirements that are required for perfect markets.

A large number of buyers and sellers

Homogenous products Free flow of information Absence of barriers to entry

Since there is lot more access to information, insider trading becomes much less important. The

foreign exchange markets are importance in their own way. They help in determining a crucial macroeconomic factor i.e. the exchange rate of two currencies which in turn strongly affects the performance of economies and their businesses. It is important to understand that foreign

exchange is required for carrying out any international economic transaction.

Unlike the organized exchanges like the stock market or the futures market, foreign exchange market is primarily an OTC market, wherein the participants rarely meet and know each other.

Even the actual currency is seen rarely. The participants in these markets are the traders, mainly foreign exchange traders, who participate on their own behalf or on the behalf of clients or

companies requiring foreign exchange. All type of participants is there namely speculators, arbitragers and hedgers. The economic concept of price takers and price makers blends very well

with the foreign exchange market. The price/market makers are large commercial banks as they are the ones who need foreign exchanges and they provide fixed rates on which they are always ready to buy/sell the currencies. They have a two sided clientele. They involve in interbank

transaction in the wholesale segment and on the retail front they deal with customers. Various large corporations such as investment banks and other financial institutions do not take help of

commercial banks for their foreign exchange needs and involve in the market on their own. The mechanics of a foreign exchange transaction is a fairly simple like any other trade. It

follows sequential steps:

Price discovery: The trader decides upon the rate at which the transaction could be concluded. There are various factors involved in this decision; these can be client

directed or self decisive. After the price levels are decided, trader gives the order or execution of trade via either telephone or via email.

Settlement: Settlement refers to conclusion of transaction. The currencies are exchanged

on the pre-decided rates. In order to keep a check on activities of traders, the settlement is done by what we know as back office.

Position keeping: The resulting position is then monitored by dealer and he calculates the profit and loss on the position. Based on this monitoring, the trader may decide to

close the position. The foreign exchange market apart from providing a marketplace for exchanging the currencies

also helps in determination of spot exchange rate of currencies. Another feature of foreign exchange market is that it uses a bid and ask feature. The difference in bid-ask is known as

dealing spread. The retail transactions have much high spreads as compared to the interbank transactions.

(c) A UK stock portfolio held by the ‘MarketTrack’ fund currently has a perfectly positive

correlation with the UK FTSE100 stock market index. The portfolio manager is concerned

about UK stock market volatility over the next six months and intends to lock-in a value

for the portfolio in June 2010 by using the FTSE100 index futures contract. The current

value of the portfolio is £4.408 million, the current level of the FTSE100 index is 5,510 and

the current quotation for FTSE100 index futures is 5,618. The FTSE100 index futures

contract specification is £10 per index point. Explain how the hedging will be implemented,

and use numerical illustrations to confirm that the hedge will successfully lock-in a

portfolio value for June 2010.

Let N* be the optimal number of futures contract which are required for hedging a position. N* = P/A

Here, P is the portfolio’s current value and A is the current value of stock underlying one future contract.

= 4,408,000/(10*5510)

= 80 contracts

The person enters into 80 contracts to sell at 5618. Suppose on the expiration date, the value of FTSE100 index is 5618, the contract value would be marked to market and person has to pay the

other party a sum of $86,400 [(5618-5510)*10*80] for 80 contracts.

The loss of $86,400 would be offset by the increase in value of portfolio by the same amount $86,400 [(4,408,000/5510)*5618].

References

1. Bernard V. and Thomas J.,' Evidence that stock prices do not fully reflect the

implications of current earnings for future earnings". Journal of Accounting and

Economics 13, 305, 1990.