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Investment Analysis and Portfolio Management

ERASMUS Assignment 2006-2007Semester 1

1. (a) An investor buys 1000 shares at 60 each. The initial margin requirementis 50% and the maintenance margin is 30%. If the stock falls to 50, will theinvestor receive a margin call?

(b) 500 shares are purchased on margin at the beginning of the year for 30

per share. The initial margin requirement was 55%. Interest of 13% was paidon the margin loan and no margin call was ever faced. A dividend of 1 per share is received.

i. If the stock were sold for 40 per share at the end of the year, what isthe return for the year?

ii. Calculate the return if the purchase had been made using cashinstead of on the margin.

(c) Through a margin account, 200 shares are short sold for 50 per share.The initial margin requirement is 45%.

i. If the price of the stock rises to 58 per share, what is the actualmargin in the account?

ii. If the price of the stock falls to 42 per share, what is the actualmargin in the account?

(d) Is it true that the potential loss on a short sale is infinite? What is themaximum return?

2. The following table provides estimates of the mean returns, standard deviationsand correlations of three assets

A B C

Mean 20 15 10Standard Deviation 40 25 20

2.0= AB 3.0= AC 4.0= BC

The risk-free rate of return is 5.

What are the mean and variance of the following portfolios:

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a. An equally weighted portfolio of A and B

b. A portfolio consisting of 1/4 B and 3/4 C c. An equally weighted portfolio of A , B and C

Plot the portfolio frontiers (without short selling) when A is combined with B , when A is combined with C , and when B is combined with C . Using these frontiers sketch(you can calculate if you wish) the portfolio set when portfolios can contain all threeassets.

3. The correlation between assets A and B is - 0.1. The expected return of A is 8%and its standard deviation 10%. For B , the expected return is 12% and the standarddeviation 20%.

a. Find the proportions of A and B that define the minimum variance portfolio.

b. What is the value of the minimum standard deviation?

c. What is the expected return on the minimum variance portfolio?

Now assume a riskfree asset is also available with a return of 5%.

d. What is the composition of the tangency portfolio of risky assets?

e. What is the market price of risk?

4. Describe the Capital Asset Pricing Model, paying particular attention to itsassumptions. What are its implications for portfolio choice and portfolio evaluation?

5. (i) Define the single index model. How does it differ from the CAPM?

(ii) You have estimated a beta of 0.85 for H&M Inc. What factors would you take intoaccount in adjusting this value?

Assume that returns are generated by a model where the market is the single factor.The details of the model for three stocks are:

Stock Alpha Betaie Portfolio weight

A 2.2 1.1 7 0.2 B 0.6 0.8 2.3 0.5C 3.0 1.0 1 0.3

The expected return on the market is 12% with a standard deviation of 18%.

(iii) What is the portfolio's expected rate of return?

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(iv) What is the standard deviation of the return on the portfolio?

(v) Discuss the limitations of the market model as a guide to portfolio choice.

Work to be returned by 9 January 2007 to:

G.D. MylesDepartment of EconomicsUniversity of Exeter Exeter EX4 4PUUK.