# Exam Paper

Topics: Capital asset pricing model, Modern portfolio theory, Put option Pages: 5 (965 words) Published: January 12, 2013
Section A

Answer FOUR questions from Section A

Each question carries 15 marks.

1.You are given the following data:

E(RA) = 0.04var(RA) = 0.0025cov(RA, RB) = 0.001
E(RB) = 0.08var(RB) = 0.0049

(a)For an equally weighted portfolio (with portfolio weights xA=0.5 and xB=0.5) comprising securities A and B, calculate the following:

(i)The expected return on the portfolio, E(RP), (ii)The standard deviation of the return on the portfolio, ((RP). (5 marks)

(b)Calculate the portfolio weights that are associated with the minimum variance portfolio. (5 marks)
(c)What are E(RP), var(RP) and ((RP) for the minimum variance portfolio? (5 marks)

2.(a)With reference to the Capital Asset Pricing Model (CAPM) with a risk-free asset, explain what is meant by the following:

(i)Capital market line,
(ii)Security market line,
(iii)Characteristic line.
(9 marks)

(b)Suppose the relevant equilibrium model is the CAPM with unlimited borrowing and lending at the risk-free rate.

Given RF = 0.04 and E(RM) = 0.10, complete the blanks in the following table:

StockE(Ri)(i

1-0.4
20.088-
(6 marks)

3.(a)With reference to the Capital Asset Pricing Model (CAPM), explain what is meant by the following statement:

“The total variance in the return on any security can be partitioned into two components, representing systematic risk and unsystematic risk”.

(6 marks)
(b)Refer to the following data:

Stock i((Ri, RM)var(Ri)

A0.30.04
B0.150.09

E(RM) = 0.1var(RM) = 0.02RF = 0.05

Note: ((Ri, RM) denotes the correlation coefficient between Ri and RM; i.e. ((Ri, RM) =[pic]

Calculate beta ((i) and expected return [E(Ri)]:
(i)for stock A,
(ii)for stock B,
(iii)for an equally weighted portfolio comprising stocks A and B. (9 marks)

4.(a)Calculate the present value of a treasury bond with a nominal value of £100, a coupon of 5% and a term to maturity of 4 years. The current yield to maturity is 8%.
(5 marks)

(b)Calculate the Macaulay duration of the treasury bond described in (b).
(5 marks)

(c)Explain briefly how Macaulay Duration is used by bond portfolio managers.
(5 marks)

5.The current £/\$ exchange rate is £1=\$1.9580. The UK one-year risk-free rate of return is [pic]=0.06, and the US one-year risk-free rate of return is [pic]=0.04. The one-year currency forward price is £1=\$1.9245.

Assuming zero transactions costs, you are asked to devise a trading strategy that yields a guaranteed profit after one year. Your answer should include calculations showing how much profit your strategy delivers. (15 marks)

6.(a)Explain briefly the following terms:

(i)Call option
(ii)European option
(iii)American option
(6 marks)

(b)The current price per unit of a certain share is £120. A European put option, which gives the holder the option to sell the share in one year’s time, has an exercise price of £130. There is a probability of 0.5 that in one year’s time the share price will have risen to £150, and there is a probability of 0.5 that in one year’s time the share price will have fallen to £100.

(i)If an investor decides to buy three shares, how many put options should he also buy in order to construct a riskless portfolio? (ii)Assuming the risk-free rate of return is 5%, calculate the current price of the put option. (9 marks)

Section B

Answer TWO questions from Section B

Each question...