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Three friends Amy, Susan and Catherine are members of an investment club. They each have...

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Three friends Amy, Susan and Catherine 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 August 2019, the following prices were available (prices in ). Company A B Share price 40 20 30 Call option price 0.80 1.20 4.20 Put option price 7.61 4.61 1.51 Strike price, K 48 24 28 The friends made the following individual investments (no dealing charges of dividends were paid). Amy bought 30 A shares, 400 C puts and saved the rest of the money in the bank. Susan bought 50 A shares, 400 B calls, 100 C puts and put the rest of the money in the bank. Catherine bought 100 A puts, 50 B shares 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 this time, A shares were worth 42, B shares 12 and C shares 22, find the value of each of the friends portfolios and, hence, the returns they made on their original investment of 10,000. (9 marks)

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