a)Supposewe are on April 21. A company has an equity portfolio worth 120 million with a beta of 1.15. The company would like to use the July equity index futures contract toincreasethe beta of its portfolio to1.65 during the period April 21 to June 21. The index futures price is currently 1,250 and each contract is on250 times the index.

i.What position should the company take?(7marks)

ii.Suppose that the company changes its mind and decides toreducethe beta of its portfolio from 1.15 to0.75. What position in futures contracts should it take?(8marks)

b)A non-dividend paying stock is currently traded for 40. A European call option written on the above stock expiring in 9months,costs 4 and has a strike price of 42. Interest rates for all maturities are 7%per annum with continuous compounding. The price of a European put option with the same maturity and strike price is 6. Explain the arbitrage opportunities and calculate the potential profit.(15 marks)

c)A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash flow problems.(10 marks)

d)Briefly discuss the following statement: "The presence ofspeculatorsin futures marketsisharmful". Link your discussion totherelevant theory.(10 marks)