edu-2009-fall-exam-fm-sol - SAMPLE SOLUTIONS FOR...

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1 SAMPLE SOLUTIONS FOR DERIVATIVES MARKETS Question #1 Answer is D If the call is at-the-money, the put option with the same cost will have a higher strike price. A purchased collar requires that the put have a lower strike price. (Page 76 ) Question #2 Answer is C 66.59 – 18.64 = 500 – K exp(–0.06) for K = 480 (Page 69) Question #3 Answer is D The accumulated cost of the hedge is (84.30-74.80)exp(.06) = 10.09. Let x be the market price. If x < 0.12 the put is in the money and the payoff is 10,000(0.12 – x ) = 1,200 – 10,000 x . The sale of the jalapenos has a payoff of 10,000 x – 1,000 for a profit of 1,200 – 10,000 x + 10,000 x – 1,000 – 10.09 = 190. From 0.12 to 0.14 neither option has a payoff and the profit is 10,000 x – 1,000 – 10.09 = 10,000 x – 1,010. If x >0.14 the call is in the money and the payoff is –10,000( x – 0.14) = 1,400 – 10,000 x . The profit is 1,400 – 10,000 x + 10,000 x – 1,000 – 10.09 = 390. The range is 190 to 390. (Pages 33-41) Question #4 Answer is B The present value of the forward prices is 10,000(3.89)/1.06 + 15,000(4.11)/1.065 2 + 20,000(4.16)/1.07 3 = 158,968. Any sequence of payments with that present value is acceptable. All but B have that value. (Page 248) Question #5 Answer is E
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2 If the index exceeds 1,025, you will receive x – 1,025. After buying the index for x you will have spent 1,025. If the index is below 1,025, you will pay 1,025 – x and after buying the index for x you will have spent 1,025. One way to get the cost is to note that the forward price is 1,000(1.05) = 1,050. You want to pay 25 less and so must spend 25/1.05 = 23.81 today. (Page 112) Question #6 Answer is E In general, an investor should be compensated for time and risk. A forward contract has no investment, so the extra 5 represents the risk premium. Those who buy the stock expect to earn both the risk premium and the time value of their purchase and thus the expected stock value is greater than 100 + 5 = 105. (Page 140) Question #7 Answer is C All four of answers A-D are methods of acquiring the stock. The prepaid forward has the payment at time 0 and the delivery at time T . (Pages 128-129) Question #8 Answer is B Only straddles use at-the-money options and buying is correct for this speculation. (Page 78) Question #9 Answer is D This is based on Exercise 3.18 on Page 89 . To see that D does not produce the desired outcome, begin with the case where the stock price is S and is below 90. The payoff is S + 0 + (110 – S ) – 2(100 – S ) = 2 S – 90 which is not constant and so cannot produce the given diagram. On the other hand, for example, answer E has a payoff of S + (90 – S ) + 0 – 2(0) = 90. The cost is 100 + 0.24 + 2.17 – 2(6.80) = 88.81. With interest it is 93.36. The profit is 90 – 93.36 = –3.36 which matches the diagram.
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3 Question #10 Answer is D [rationale-a] True, since forward contracts have no initial premium [rationale-b] True, both payoffs and profits of long forwards are opposite to short
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.

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edu-2009-fall-exam-fm-sol - SAMPLE SOLUTIONS FOR...

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