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1 UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem Set – 1 (Supplemental Questions) _______________________________________________________________________________ 1. Explain the similarities and differences between forwards and futures contract on the same asset. You may want to consider (but not limited to) the following points for the differences: a) How trade is conducted b) Liquidity c) Counter-party risk d) Flexibility 2. A trader enters into a short futures contract to sell 5,000 bushels of wheat for 200 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? 3. The fictional country of Heaven has announced a floating exchange rate policy against a basket of other currencies, including the dollar ($), euro ( uni0404 ) and yen (¥) with weights of one-half for the dollar and one- quarter each for the euro and yen (so that 1H = 0.5$ + 0.25 uni0404 + 0.25¥). Suppose that there are spot and futures markets for the Heaven currency against the other big three. A US company has just signed a contract to sell equipments to this country, to be paid on the first of January 2012. Show how this company could hedge this contract. 4. A Swiss company purchased a product from a US firm. The delivery date is in March (40 days from now), and the purchase price of the machine tools is SFR 5million. The US firm is concerned about exchange rate movements between now and the delivery date and considers hedging its exposure. The futures price for March is $0.7021 USD/SFR. One futures contract is for SFR 125,000. a) Construct the optimal hedge using the futures contract described above. How many contracts does the US firm have to buy/sell in order to hedge the exchange rate risk? b) Demonstrate that this hedge is perfect by looking at scenarios where the SFR is $0.65, $0.70 and $0.75. 5. You have a $100 million portfolio of U.S. stocks and you want to hedge your portfolio using 1-year futures on the U.S. market stock index (S&P 500). Today, the S&P 500 index is 1100 points with a zero dividend yield, and the annual interest rate is 6.1837% [ 6%, C.C.]. In this case, one futures contract has a value of $250 × 1100 = $275,000. a) What should be the 1-year S&P 500 futures price in order to preclude arbitrage opportunities? [Lecture-4] b) Which position should you take in the 1-year S&P 500 futures if the beta of the portfolio relative to the S&P 500 is 1.4. c) Assume that the beta of your portfolio is 1.4 and that you apply the hedging strategy proposed in (b). Compute the value of the hedged portfolio in one year if the S&P 500 is 1000, 1100, or 1200. In the three cases, compare the return of the hedged portfolio to the risk-free interest rate. Briefly explain your result. 6. A company needs to buy 1 million gallons of heating oil in June 2012. The current futures price for this expiration date is $0.8190 per gallon, while the current spot price is $0.9602. Each futures contract is for 42,000 gallons of oil.
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2 a) Suppose that the correlation between changes in futures and spot prices over the life of the hedge is 0.98 and that both have equal variances. How many futures contracts should the company trade to set up a hedge? Should it use a long or a short hedge?
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