LONDON METROPOLITAN UNIVERSITY

DEPARTMENT OF ECONOMICS

EC2009 ECONOMICS OF FINANCIAL MARKETS

UNIT HANDBOOK

Level 2

Semester I

2006-2007

BA (Hons) Economics/Financial/Business/Global Economics

ES213 ECONOMICS OF FINANCIAL MARKETS

In this unit you will study the nature of financial assets, the idea of risk and return and the idea of a market in which risk and uncertainty play a central role. You will also learn about financial assets whose values depend on the values of other assets in complex ways, together with their use for hedging against risk and for the direct trading of risk. Please note that this unit has a strong conceptual/quantitative aspect.

Objectives 1. To introduce students to financial markets, risk and returns. 2. To study modern portfolio theory and the nature of diversification. 3. To study the role asset pricing models such as the CAPM. 4. To introduce the basic features and uses (hedging) of options and futures.

Learning Outcomes By the end of this unit students should:

1. Be able to compute the risk of a two security portfolio.2. Be able to understand beta coefficients (β) as a measure of systematic risk. 3. Have an understanding of the use of derivatives for simple hedging. 4. Have a critical appreciation of the assumptions underlying modern finance theory.

The Teaching Team.For the first half of the unit lectures and tutorials will be given by Gerry Kennally (module leader). Sherry Chan will take over for the second half of the unit.

To contact:Gerry Kennally Room Moorgate MG529

Extension 1690email g.kennally@londonmet.ac.uk

Sherry Chan Room Moorgate Extensionemail

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ES213 ECONOMICS OF FINANCIAL MARKETS

Level 2 Semester I 2003-04

Syllabus

Recommended Texts

*Fabozzi F and F Modligiani (1996) Capital Markets 2/ed Prentice-Hall [FM].

[*recommended text for those with non-mathematical backgrounds]

Fabozzi F, F Modligiani & MG Ferri (1998) Foundations of Financial Markets and Institutions 2/e Prentice-Hall [FMF].

**Alexander OF, WF Sharpe & IV Bailey (1999) Investments 6/e Prentice-Hall [ASB].

[**recommended text for those with some mathematical background. This is the one to use if you can. If not use Fabozzi&Modigliani and go on to this.]

These and other learning resources can be found in the Moorgate library. Additional reading may be given in the lectures.

Lecture Topics

1. Financial Markets and Assets

Debt versus equity; properties of financial assets; classification of markets, risk and returns.

FM 1* PMF 10 ASB 1*

2. Modern Portfolio Theory (2 weeks)The individual's optimisation problem in the face of risk.

(a) Risk and return for stocks and portfolios (correlations/covariances).(b) Markowitz diversification and the efficient frontier.(c) Tobin's extension (adding a risk free asset).

FM *8 FMF 10 ASB *7 *8 *9

3. Asset Pricing: CAPM and APT (2 weeks) The action of the market.Market and unique risk.CML; the risk/return relationship for efficient assets.SML; the risk/return relationship for all assets beta coefficients (β ): mispriced stocks. Factor pricing models: factor versus nonfactor risk.

FM *9 FMF 13 ASB 10* 11

. 4. Introduction to Derivatives

Derivatives; long and short positions; exchange-traded versus OTC; forwards, futures, options

FM *1

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5. Futures Markets (2 weeks)

Futures and forward contracts, forward price for an investment asset, valuing forward contracts,

stock index futures, currency futures (Euro-Fx Futures).

FM *10 FMF 26 ASB 25*

6. Stock Option Markets (2 weeks)

Call and put equity options; long and short positions; intrinsic and time value; at- in-, out of-

money options; stock options on LIFFE; FTSE index options.

FM * 11 FMF 27 ASB 24*

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Assessment

This is comprised of two components:

1. Unseen test: First Friday in December 2006 (30% ).

2. Unseen examination February 2007 (70% ).

(Exact date to be announced)

Note that, while this course and assessment has a strong quantitative (statistical) element,

students will be expected to display conceptual and critical skills also.

Tutorial 1.

1. You buy efm.com shares at £10, receive a dividend of £0.50 and sell at £11. What is your rate

of return?

2. What is the difference between return and rate of return? In what sense does an investor's rate

of return represent an increase in wealth?

3. Criticise the following statement: “ Bank X has made profits of £5bn this year. Profits of this

magnitude are unjustifiable under any circumstances.”

4. Have equities become riskier during the past year? How would you demonstrate that they have

become riskier or less risky?

5. Why were dot.com shares so risky in the first years of the millenium? Are they now more or less

risky?

6. Given the following probability table for the rate of return Ri

Ri(%) pi

4 1/3

8 1/3

12 1/3

a) Calculate the expected rate of return .

b) Hence calculate the variance and standard deviation of R.

c) Construct a new probability table for R with p1=p3=1/4 and p2=1/2.

d) Repeat a) and b) above for the new rate of return.

(See my handout)

7. Given securities A, B , C and D have the expected rate of return and standard deviations as

given in the table below:

A 10 12

B 10 15

C 9 12

D 11 15

Decide which securities dominate which.

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Tutorial 2.

1. Given below are 12 portfolios with their expected returns and standard deviations. You are also given the amount of satisfaction they give to X

Portolio No.

Expected rate of return(%)

Standard Deviation (Volatility)(%)

Amount of Satisfaction to X (utils)

1 5 0 102 6 10 103 9 20 104 14 30 105 10 0 206 11 10 207 14 20 208 19 30 209 15 0 3010 16 10 3011 19 20 3012 24 30 30

Graph X's identifiable indifference curves.

2. We usually assume typical investors prefer portfolios lying to the "northwest" of other portfolios. Explain the significance of this assumption i.e. give its behavioural description.

3. What is it about the typical investor that is represented by making indifference curves upward sloping?

3. Explain why more steeply sloped indifference curves imply greater risk aversion.

4. What is it about the typical investor that is represented by making indifference curves convex?

7. What common empirical observations suggest that individuals are not risk averse in all situations?

8. Who do you expect to be more risk averse, the young or the old? Why?

9. Consider the diagram showing indifference curves for two individuals, Mike Emilyan and Sheila Va Gambole. Determine whether Mike or Sheila:a) is more risk averse;b) prefers investment A to Bc) prefers investment C to D.Give reasons for your answers.Diagram is drawn on hard copy version.

E(R)

A

B

CD

SvG

ME

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Tutorial 3.

1. We have estimated the following probability distribution for stock A:

State of the World Probability Return(%) RDeep Recession .1 -10Mild Recession .25 0Trend Growth .4 10Increased Growth .2 20Boom .05 30

i) Calculate the expected rate of return for A (E(R)).ii) Calculate the variance and standard deviation of the return on A (Var(R) and SD(R)).iii) In what units would you measure the expected rate of return, variance and standard deviation?iv) In view of your answer to iii), why do we use SD rather than Var as a measure of volatility?Notice we could have worked out E(R), Var(R) and SD(R) without knowing the nature of the states of the world if we only knew the probabilities of the various possible rates of return.

2. We have estimated the following probability distributions for rates of return on two stocks, X Ltd and Y plc:

RX(%) RY(%) Probability15 -10 .1510 5 .25 10 .30 20 .35

Using these estimates, find:a) the expected rates of return of X and Y;b) the variances of X and Y;c) the covariance between X and Y;d) the correlation coefficient between X and Y.e) use this information to calculate the volatility of a portfolio of 25% of X and 75% of Y.

3. At the beginning of 2003 Ghimmi da Xash owned the following four securities in the following amounts (numbers of shares) and with the following current and end-of-year prices.Security No of Shares Current Price(£) Expected end of

year price(£)A 100 50 60B 200 35 40C 50 25 50D 100 100 110

What was the expected return on Ghimmi's portfolio in 2003?

4. Given the following covariance matrix on securities A, B and C, find the correlation matrix. Why is the correlation coefficient a better measure of the relationship between securities than are the covariances?

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5. Suppose Wendy Uptoncombs invests in the three securities of question 4 in the proportions:XA=.5, XB=.3, XC=.2. Find the volatility of the portfolio.

6. A portfolio’s expected return is equal to the weighted average of the expected returns of the component securities. Why is the portfolio’s risk (standard deviation) not equal to the weighted average of the standard deviations of its component securities?

7. Under what conditions will the standard deviation of a portfolio be equal to the weighted average of the standard deviations of its component securities? Show this mathematically for a two-security portfolio. (Bear in mind that . Use the formula for the variance of the portfolio and see what different possible values of produce.).

8. Why would you expect to find individual securities in the "eastern" part of the risk/return diagram and more portfolios the further "northwest" you go? Why is this a problem for the small investor and how do fixed capital trusts attempt to overcome it? How did this go wrong in 2002?

9. Why do most investors prefer to hold a diversified portfolio of securities rather than putting all their wealth into one asset?

10. Why would you expect most US common stocks to have positive covariances? Give examples of what you would expect to be high and low covariance stocks.

11. How does correlation relate to diversification?

12. What relationship do you expect between the prices of shares in large hotel groups and shares in airlines? How does the price of oil come into this? What financial reason does Paris Hilton have to worry about the politics of the Middle East and South America?

13. In risk return space illustrate:a) individual assets;b) the Markowitz feasible set;c) the Markowitz efficient set.d) Explain why the Markowitz feasible and efficient sets are the shape they are.

14. What information does an investor need to identify his or her optimal portfolio? Make a list.

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Tutorial 4.

1. Describe the key assumptions underlying the CAPM.

2. Rate each assumption on a scale of –5 (totally unbelievable) to +5 (obviously true). In each case, say why you have rated the assumption in the way you have.Now look again at the assumptions you think are incorrect and say whether they are approximately true and how much difference they make to the working of the markets.

3. As with Q12 of the last tutorial sheet, show the feasible set and the efficient set of the CAPM world.

4. What information would the individual investor need in order to find his or her optimal portfolio in a CAPM world?

5. Explain the separation theorem.

6. Does the individual investor's attitudes to risk affect the risky part of his portfolio in the CAPM world? How does the attitude to risk affect the overall portfolio?

7. In the equilibrium world of the CAPM is it possible for a security not to be part of the market portfolio? Explain.

8. How does the answer to Q7 lead to Roll's critique of the CAPM.

9. If we take Roll's critique as justified, under what conditions would research based on the CAPM not be misleading? Are these conditions likely to hold?

10. Explain the price adjustment process that equilibrates the supply and demand for assets.

11. Suppose an investor is holding the market portfolio in period 1. Something happens to cause prices to change. Does the investor need to buy and sell securities in order to go on holding the market portfolio?

12. Given an expected return of 12% for the market portfolio, a risk-free rate of return of 6% and a market portfolio standard deviation of 20%, draw the Capital Market Line.

13. Explain the significance of the Capital Market Line. What portfolios lie on it?

14. Assume that two securities constitute the market portfolio. They have the following expected returns, standard deviations and proportions:Security Expected

Return(%) Standard Deviation(%)

Proportion

A 10 20 0.4B 15 28 0.6 Based on this information and given a correlation of 0.3 between the two securities and a risk-free rate of return of 5%, specify the equation for the Capital Market Line.

15. Explain the difference between the Security Market Line and the Capital Market Line.

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16. The market portfolio is assumed to be composed of four securities. Their covariances with the market and their proportions are shown below:Security Covariance with Market ProportionA 242 0.2B 360 0.3C 155 0.2D 210 0.3Given these data, calculate the market portfolio's standard deviation.

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Tutorial 5.

1. Explain the significance of the slope of the Security Market Line. How might its slope change over time?

2. What securities and portfolios lie on the Security Market Line?

3. Suppose a security lay off the Security Market Line. How would the market react to bring it back on? Consider both securities that lie above and those that lie below the line.

4. In the CAPM does the price of a security depend on:a) its expected rate of return;b) its volatility;c) its covariance with the market?Explain why.

5. The risk of a well diversified portfolio to an investor is measured by the standard deviation of the portfolio's return. Why shouldn't the risk of an individual security be calculated in the same way?

6. Arnez Tegformyoldage owns a portfolio composed of three securities. The betas of those securities and their proportions in Arnez' portfolio are shown below. What is the beta of Arnez' portfolio?

Security Beta ProportionA 0.9 0.3B 1.3 0.1C 1.05 0.6

7. Assume that the expected return on the market portfolio is 15% and its standard deviation is 21%. The risk-free rate of return is 7%. What is the standard deviation of a well-diversified portfolio with an expected return of 16.6%

8. Given that the expected return on the market portfolio is 10%, the risk-free rate of return is 6%, the beta of stock A is 0.85 and the beta of stock B is 1.2:a) Draw the Security Market Line.b) Derive the equation of the Security Market Line.c) Find the equilibrium expected returns of stocks A and B.d) Plot the two risky securities on the Security Market Line.

9. Given the following information on securities A and B, the market portfolio, and the risk-free rate of return:

EXPECTED RETURN(%)

CORRELATION WITH MARKET PORTFOLIO

STANDARD DEVIATION(%)

Security A 15.5 0.9 20Security B 9.2 0.8 9Market portfolio 12.0 1.0 12Risk-free rate of return

5.0 0.0 0

a) Draw the Security Market Line.b) What are the betas of the two securities?c) Plot the two securities on the Security Market Line.

10. The CAPM allows the standard deviation of a security to be segmented into market and unique risk. Explain the difference between the two.

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Tutorial 6-7: Futures Markets.

1. List the advantages of trading in futures contracts rather than forward contracts.

2. List the disadvantages.

3. Explain the leveraging aspect of futures contracts.

4. In the physical market asset X is priced at £80. Asset X pays £4 every 6 months and the

next payment is due exactly 6 months from now. The current 6 month interest rate at which

funds can be borrowed or lent is 6% p. a.

i) What is the theoretical futures price for a contract with a settlement in 6 months?

ii) What action would you take if the futures price were £83?

iii) What action would you take if the futures price were £76?

5. Why does the actual futures price often deviate from the theoretical futures price?

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6. Tutorial 8-9: Option Markets.

1. What is the difference between a put and a call option?

2. What is the difference between a long and a short position?

3. What is the difference between a European and an American option?

4. What options can be traded on LIFFE?

5. Explain how this statement can be true: " A long call position offers potentially unlimited gains

if the underlying asset's price rises, but a fixed maximum loss if the underlying asset's price

drops to 0."

6. Suppose a call option on a stock has a strike price of £70 and a cost of £2; and suppose you buy

the call. Identify the profit to your investment at the calls expiration for each of the following

values of the underlying stock: £25, £70, £100, £400.

7. Suppose you had sold the call option of Q6. What would your profit be at expiration for each of

these stock prices?

8. Why does an option writer need to post margin?

9. Buying a put is just like short-selling the underlying asset. You gain the same thing from either

position if the underlying asset's price falls. If the price goes up you have the same loss.

Agree or disagree?

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7. Tutorial 10: Option Markets Continued.

1. At the end of December 1998 for ABC the following option prices were on offer, where X

is the strike price and the underlying share price (S) of ABC is 430.

Calls

A

B

C

X Mar June Sept

420 11 22 30

460 2 9 16

a) Indicate which ABC call series are in-the-money and out-of-the-money.

b) Evaluate and show time value and intrinsic value of all the calls.

c) Evaluate and show the expected profits profile resulting from a short call position using the

ABC June 420 calls. Under what circumstances would you take such a position.

2. The price of the ABC March 160 call option quoted on LIFFE is 9p. If the underlying

share price(S) of ABC is 156:

a) Is this call in-the-money or out-of-the-money?

b) Evaluate and show the expected profit profiles resulting from a short and a long call

position.

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Quantifying Profitability and Risk.

How do we quantify profitability (returns) and risk for single stocks.

Assume all returns are normally distributed.

a) Expected Returns.

Define expected returns for a single security:

E(R)= piRi pi: weights (probabilities)

Expected returns are a weighted average of possible returns.

b) Standard Deviation.

Risk is measured by standard deviation (square root of variance) of returns.

SD=

Measures the average distance from the mean.

SD is in the same units as returns(e.g. % p.a).

Variance would convey the same information, but would not be in the right units & therefore

not so easy to interpret.

Dominance Principle.

Assume investors:

prefer more wealth to less (non-satiation)

are risk averse.

Efficient portfolios dominate other portfolios.

A dominates B if:

EITHER

The expected return on A is greater than that on B and the risk is no greater

ie E(RA)>E(RB) while SD(A) SD(B)

OR

The expected return on A is no less than that on B and the risk is smaller

ie E(RA) E(RB) while SD(A)<SD(B).

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Portfolio Returns and Risk.

Portfolios have possible rates of return just as individual securities do.

Therefore they have expected rates of return and standard deviations just as individual securities

do.

Portfolio returns are easy to relate to the returns of the component securities, but risk is more

complex. Why?

Portfolio returns are just weighted averages of the security returns with the weights equal to the

shares of the securities in the portfolio.

Portfolio risk involves:

weighted variances

weighted covariances.

The latter allow for interactions or relationships between returns on different stocks.

Correlation is a normalised measure of (linear) relationship.

Corr(A, B)=Cov(A,B)/σAσB

Diversification tends to reduce overall portfolio risk.

Markowitz Model.

An approach to diversification for portfolios composed of risky equities.

Markowitz diversification involves constructing portfolios with low pairwise correlations

between the component securities.

The set of all such portfolios forms the feasible set of risk/return combinations.

The ones with the highest return for a given level of risk (or the lowest risk for a given level of

return) form the efficient set or frontier. They are the Northwest frontier of the feasible set of

risk/return combinations.

Efficient Frontier.

How to construct.

Dominant portfolios only.

Disaggregation of total risk: market and specific (only this can be diversified).

Tobin Extension.

The Tobin extension to Markowitz adds a risk-free asset.

Assumptions.

Linear efficient frontier.

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Asset Pricing Models.

Derived from the Tobin model: CML for efficient portfolios.

The CAPM(SML) is a model for correctly pricing risk.

E(Ri)=r+βi(E(RM)-r)

APT uses more factors, but there is no agreement as to what they should be.

Index or Factor Models.

These are regression models for beta estimation.

They differ from CAPM which is an equilibrium pricing model.

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