1(i) Using the following information about US and UK market returns and beginning of period $/£ exchange rates:
Period US Return UK Return $/£ Exchange Rate
1 8% 6% $2.00
2 14 2 1.80
3 2 −4 1.80
4 11 8 1.70
5 14 17 1.60
6 5 6 1.60
7 − − 1.90
(a) Compute the average return in each market from the standpoint of a US investor and from the perspective of a UK investor. [5 marks]
(b) What is the covariance of the domestic market and exchange rate returns from the standpoint of each investor? [10 marks]
(c) What is the standard deviation of return for each market from the standpoint of each investor?[5 marks]
(ii) Write notes on the following returns techniques available for assessing portfolio performance and explain how they are used. [15 marks]
(a) Sharpe’s measure
(b) Treynor’s measure
(c) Jensen’s alpha measure
(d) Why is Jensen’s alpha generally preferred over the other alternative measures of Sharpe and Treynor for assessing portfolio performance? Explain in detail. [15 marks]
2 (i) How is value-at-risk (VAR) used to measure portfolio performance? Is this concept useful in the approach to portfolio risk assessment? [10 marks]
(ii) The risk management team of Planet Capital believe that the firm’s €100,000,000 stock portfolio will have a 10 per cent return standard deviation during the coming week and that its portfolio’s return is normally distributed.
(a) What is the probability of Planet Capital losing €10,000,000 or more? [5 marks]
(b) What is the euro loss expected with a 5 per cent probability? [5 marks]
(c) What is the euro loss expected with a 1 per cent probability? [5 marks]
3. Explain why it is important to have an understanding not only of the market forces driving observed nominal interest rates but also the characterisation of the random nature of interest rates. [15 marks]
(Hint explain the stochastic process as defined in interest rate models)
4. (a) The following spot interest rates for maturities of one, two, three and four years are currently observable in the market:
r1 = 4.3% ,
r2 = 4.9% ,
r3 = 5.6% ,
r4 = 6.4%
Compute the forward rates for f1,1, f1,2, and f1,3, where f1,n refers to a forward rate for the period beginning in one year and extending for n years. [5 marks]
(b) Based on the spot rates in 4(a), and assuming a constant real interest rate of 2 per cent, what are the expected inflation rates for the next four years? [5 marks]
