a) Consider a consumption commodity. Explain briefly why there is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative.

b) A fund manager has a portfolio worth 30 million. The manager is concerned about the

future performance of the market and plans to use six-month futures contracts on the

FTSE100 index to hedge the risk. The correlation coefficient between the returns of the

portfolio and the FTSE 100 index is 0.7, the standard deviation of the portfolio returns is

0.5, whereas the standard deviation of the index returns is 0.3. The current level of the

index is 770, and one contract represents 250 times the index. The continuously

compounded interest rate is 4% per year. Assuming a dividend yield of 0%, what position

should the fund manager take to minimise the risk of her portfolio? Provide the answers for two cases: with marking-to-market being ignored as well as with marking-to-market taken into account.

c) Calculate the effects of the hedging strategy of part (b) on the managers' returns, if the

level of the index in six months is 740 or 890. Furthermore, calculate the effects of a strategy that increases the beta of the portfolio to 2. Consider only the positions where the marking to market is ignored.

d) Consider a forward contract to purchase a bond whose current price is 95 and will providea coupon of 4 in 4 months. The forward contract matures in 10 months, the forward price is 96 and the risk free rate is 3% (continuously compounded) for all maturities. Evaluate whether there is an arbitrage opportunity and if so, design a strategy that takes advantage of it.

e) A swap contract between X and Y matures in 7.5 months. It has a swap rate of 6% p.a.

(quarterly compounded) on a principal of 10 million. X has agreed to pay 3-month Libor

and to receive 6% p.a. fixed (quarterly compounded), quarterly. Calculate the value of the

swap for company Y. The 3-months Libor rate observed 1.5 months ago was 3.4%

(quarterly compounded) and today the (continuously compounded) 1.5-month Libor, 4.5-

month Libor and 7.5-month Libor are 4%, 5% and 6%, respectively.