a (a) The price of a forward contract on a share is given by F = Soe" where So is the current share price, r is the risk-free rate of interest, and T is the length of the contract. A one-year forward contract on a non-dividend paying share is entered into when the share price is 40 and r = 10%. (i) What is the forward price and the initial value of the forward contract? [2] (ii) Six months later, the price of the share is 45 and the risk free rate is still r = 10%. What are the forward price and the value of the forward contract? [2] (b) An asset currently has a price of 10. Suppose that six-months future prices of : (i) 11 (ii) 10.10 are available. If the risk free rate is r = 6%, show that a risk-free profit can be made in both cases. [6] (c) Three friends Tom, Jerry, and Kate are members of an investment club. They each have a total of 10,000 to invest in three companies A, B, and C. On 1st Nov 2016, the following prices were available () B A 55 110 Share Call Put Strike price, K 0.91 2.48 58 2.17 4.33 115 13 0.89 0.09 12.5 They made the following investments (not considering any dividends and commissions) Tom bought 80 A shares, 200 B calls and saved the rest of the money in the bank Jerry bought 50 B shares, 400 C puts and saved the rest of the money in the bank Kate bought 50 A shares, 100 B calls and spent the rest on C shares. The options expired after six months and the bank interest rate was 5% compounded continuously (assume that fractional numbers of shares may be purchased). If, at the end of six months, A shares were worth 59, B shares 108 and C shares 12, find the value of each of the three friends portfolios and, hence the returns they made on their original investment of 10,000. [10]