Answers to Selected Problems Problem 1 11 The farmer can short 3 contracts that have 3 months to maturity If the price of cattle falls the gain on the futures contract will offset the loss on the sale of the cattle If the price of cattle rises the gain on the sale of the cattle will be offset by the loss on the futures contract Using futures contracts to hedge has the advantage that it can at no cost reduce risk to almost zero Its disadvantage is that the farmer no longer gains from favorable movements in cattle prices Problem 1 12 The mining company can estimate its production on a month by month basis It can then short futures contracts to lock in the price received for the gold For example if a total of 3 000 ounces are expected to be produced in September 2014 and October 2014 the price received for this production can be hedged by shorting a total of 30 October 2014 contracts Problem 1 13 The holder of the option will gain if the price of the stock is above 52 50 in March This ignores the time value of money The option will be exercised if the price of the stock is above 50 00 in March The profit as a function of the stock price is shown below Problem 1 14 The seller of the option will lose if the price of the stock is below 56 00 in June This ignores the time value of money The option will be exercised if the price of the stock is below 60 00 in June The profit as a function of the stock price is shown below 1 505101520203040506070ProfitStock Price 100102030405060020406080100120ProfitStock Price Problem 1 20 a The trader sells 100 million yen for 0 0080 per yen when the exchange rate is 0 0074 per yen The gain is millions of dollars or 60 000 b The trader sells 100 million yen for 0 0080 per yen when the exchange rate is 0 0091 per yen The loss is millions of dollars or 110 000 Problem 1 21 a The trader sells for 50 cents per pound something that is worth 48 20 cents per pound Gain b The trader sells for 50 cents per pound something that is worth 51 30 cents per pound Loss 0 5000 0 4820 50 000 900 0 5130 0 5000 50 000 650 Problem 2 11 There is a margin call if more than 1 500 is lost on one contract This happens if the futures price of frozen orange juice falls by more than 10 cents to below 150 cents per lb 2 000 can be withdrawn from the margin account if there is a gain on one contract of 1 000 This will happen if the futures price rises by 6 67 cents to 166 67 cents per lb Problem 2 15 The clearing house member is required to provide 20 2 000 40 000 as initial margin for the new contracts There is a gain of 50 200 50 000 There is also a loss of 51 000 50 200 20 16 000 on the new contracts The member must therefore add 20 000 on the existing contracts 100 40 000 20 000 16 000 36 000 to the margin account Problem 2 16 Suppose and are the forward exchange rates for the contracts entered into July 1 2013 and September 1 2013 respectively Suppose further that All exchange rates are measured as yen per dollar The payoff from the first contract is is the spot rate on January 1 2014 million yen and the payoff from the second contract is million yen The total payoff is therefore million yen Problem 2 23 The total profit is 40 000 0 9120 0 8830 1 160 If you are a hedger this is all taxed in 2014 If you are a speculator 40 000 0 9120 0 8880 960 is taxed in 2013 and 40 000 0 8880 0 8830 200 is taxed in 2014 2 10000006 10000011 1F2FS1 SF 2 FS 1221 SFFSFF Problem 3 12 Suppose that in Example 3 4 the company decides to use a hedge ratio of 0 8 How does the decision affect the way in which the hedge is implemented and the result If the hedge ratio is 0 8 the company takes a long position in 16 December oil futures contracts on June 8 when the futures price is 8 It closes out its position on November 10 The spot price and futures price at this time are 95 and 92 The gain on the futures position is The effective cost of the oil is therefore 92 88 16 000 64 000 20 000 95 64 000 1 836 000 or 91 80 per barrel This compares with 91 00 per barrel when the company is fully hedged Problem 3 16 The optimal hedge ratio is The beef producer requires a long position in producer should therefore take a long position in 3 December contracts closing out the position on November 15 Problem 3 18 A short position in lbs of cattle The beef contracts is required It will be profitable if the stock outperforms the market in the sense that its return is greater than that predicted by the capital asset pricing model Problem 4 10 The equivalent rate of interest with quarterly compounding is where or The amount of interest paid each quarter is therefore or 304 55 3 12070614 20000006120000 50000301326501500 R401214Re 0034 1 01218Re 0121810000304554 Problem 4 11 The bond pays 2 in 6 12 18 and 24 months and 102 in 30 months The cash price is Problem 4 14 The forward rates with continuous compounding are as follows to Year 2 4 0 Year 3 5 1 Year 4 5 7 Year 5 5 7 Problem 5 9 A one year long forward contract on a non dividend paying stock is entered into when the stock price is 40 and the risk free rate of interest is 10 per annum with continuous compounding a What are the forward price and the initial value of the forward contract b Six months later the price of the stock is 45 and the risk free interest rate is still 10 What are the forward price and the value of the forward contract a The forward price is given by equation 5 1 as or 44 21 The initial value of the forward contract is zero b The delivery price in the contract is 44 21 The value of the contract f after six months is given by equation 5 5 as i e it is 2 95 The forward price is or 47 31 Problem 5 10 The risk free rate of interest is 7 per annum with continuous compounding and the dividend yield on a stock index is 3 2 per annum The current value of the index is 150 What is the six month futures price Using equation 5 3 the six month futures price is or 152 88 4 004050042100044150046200482522221029804eeeee 0F0110404421Fe K0105454421fe 295 0105454731e 0070032 0515015288e Problem 5 14 The …