Investment Analysis and Portfolio Management
ERASMUS Assignment 2008-2009
Semester 1
- i. Define the yield and duration of a bond. [2 marks]
ii. Three pure discount bonds, all with face values of $1000, and maturities of 1, 2 and 3 years are priced at $940, $920 and $910 respectively. Calculate their yields.
[7 marks]
iii. Use the result from (ii) to calculate the forward rates and discount factors. What would be the equilibrium price of a coupon bond with a maturity of 3 years, a face value of $1000 and a coupon of $50? [7 marks]
iv. What is the term structure? How does liquidity preference explain its common properties? [9 marks]
- i. How is a historic beta calculated and why might you want to adjust the value? [4 marks]
ii. How can betas be employed in investment analysis? [6 marks]
iii. Assume there are two stocks, A and B, with and , and idiosyncratic variation . If the variance of the market is , calculate the variance of a portfolio consisting of 40% of stock A and 60% of stock B. [6 marks]
iv. Plot the portfolio frontier if A and B are the only two risky assets available and short-selling is not possible. [9 marks]
3. For a risk-averse investor with mean-variance preferences:
i. Show how preferences are affected by an increase in risk aversion. [4 marks]
ii. Describe the construction of the efficient portfolio frontier with and without a risk-free asset. [8 marks]
iii. Assuming a risk-free asset is available, show how the proportion of it in the investor's optimal portfolio is affected by an increase in risk aversion. [5 marks]
iv. What are the limitations of this model of portfolio choice? [8 marks]
4. Describe the Capital Asset Pricing Model, paying particular attention to its assumptions and implications for portfolio choice. Evaluate its strengths and weaknesses relative to Arbitrage Pricing Theory. [25 marks]
5. (i) Describe call and put options, making sure that you distinguish between American and European. Show how a risk-free portfolio can be constructed using these options.
[12 marks]
(ii) Describe how the binomial model can be used to price a call option. [8 marks]
(iii) Compute the equilibrium price of a European put option with 1 year until the exercise date when the exercise price is £3.20, the current stock price £3.00, and the stock price at the exercise date may be £3.30 or £3.15. Assume that the annual risk free rate of return is 7%. [13 marks]
(v) Repeat (iii) splitting the time until maturity into (a) two sub-periods; (b) three sub-periods.
Work to be returned by 14 January 2008 to:
G.D. Myles
Department of Economics
University of Exeter
Exeter
EX4 4PU
UK.