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# Chap017 - Chapter 17 Futures Markets and Risk Management...

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Chapter 17 - Futures Markets and Risk Management CHAPTER 17 FUTURES MARKETS AND RISK MANAGEMENT 1. Selling a contract is a short position. If the price rises, you lose money. Loss = (850 – 800) x 250 = \$12,500 2. Futures price = 800 x (1 + .01 - .02) = 792 3. The theoretical futures price = 900 x (1 + .04) = 936. At 941, the gold futures contract is overpriced. To benefit from the mispricing, we borrow 900 today and use it to buy 900 worth of gold. At the same time, we short one gold contract at a price of 941. One year from today we sell the gold at the contract price of 941 and use the proceeds to repay the loan, plus interest, of 936. Thus, the arbitrage profit is 941 – 936 = \$5. 4. Margin = 115,098 x .15 = 17,264.70. Total \$ loss = 115,098 – 108,000 = 7,098. Total % loss = 7,098 / 17,264.70 = 41.11 % loss 5. a. The required margin is 779.40 x 250 x .10 = \$19,450 b. Total gain = (790 – 779.40) x 250 = \$2,650 Percentage return = 2650 / 19450 = .1362 or 13.62% c. Total loss = (771.61 – 779.40) x 250 = -\$1,947.50 Percentage loss = -1947.50 / 19450 = -.10 or 10% loss 6. The ability to buy on margin is one advantage of futures. Another is the ease with which one can alter holdings of the asset. This is especially important if one is dealing in commodities, for which the futures market is far more liquid than the spot market so that transaction costs are lower in the futures market. 7. Short selling results in an immediate cash inflow, whereas the short futures position does not: Action Initial Cash Flow Cash Flow at Time T Short sale +P 0 –P T Short futures 0 F 0 – P T 17-1

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Chapter 17 - Futures Markets and Risk Management 8. F 0 = S 0 (1 + r f – d) = 800 × (1 + 0.03 – 0.02) = 808 9. According to the parity relationship, the proper price for December futures is: F Dec = F June × (l + r f ) l/2 = \$946.30 × (1.04) 1/2 = \$965.04 The listed futures price for December is too low relative to the June price. You should long the December contract and short the June contract. 10. a. . Action Initial Cash Flow Cash Flow at Time T Buy stock –S 0 S T + D Short futures 0 F 0 – S T Borrow S 0 –S 0 (1 + r) Total 0 F 0 + D – S 0 (1 + r) b. The net initial investment is zero, whereas the final cash flow is not zero. Therefore, in order to avoid arbitrage opportunities the equilibrium futures price will be the final cash flow equated to zero. Accordingly: F 0 = S 0 (1 + r) – D c. Noting that D = (d × S 0 ), we substitute and rearrange to find that: F 0 = S 0 (1 + r – d) 11. a. F 0 = S 0 (1 + r f ) = \$150 × 1.03 = \$154.50 b. F 0 = S 0 (1 + r f ) 3 = \$150 × (1.03) 3 = \$163.91 c. F 0 = S 0 (1 + r f ) 3 = \$150 × (1.05) 3 = \$173.64 12. a. Spot price 800 Income yield (%) 2.00% Futures prices versus maturity Interest rate (%) 3.00% Today's date 1/1/2010 Spot price 800.00 Maturity date 1 2/14/2010 Futures 1 800.96 Maturity date 2 5/21/2010 Futures 2 803.06 Maturity date 3 11/18/2010 Futures 3 807.03 Time to maturity 1 44 Time to maturity 2 140 Time to maturity 3 321 17-2
Chapter 17 - Futures Markets and Risk Management 17-3

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Chapter 17 - Futures Markets and Risk Management b. Spot price 800 Income yield (%) 2.00% Futures prices versus maturity Interest rate (%) 1.00% Today's date 1/1/2010 Spot price 800.00 Maturity date 1 2/14/2010 Futures 1 799.03 Maturity date 2 5/21/2010 Futures 2 796.92 Maturity date 3 11/18/2010 Futures 3 792.96 Time to maturity 1 44 Time to maturity 2 140 Time to maturity 3 321 13.
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