Chapter10 - Investment Science Chapter 10 Solutions to...

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Investment Science Chapter 10 Solutions to Suggested Problems Dr. James A. Tzitzouris < [email protected] > 10.1 We are given that S = $412 , M = 3 (quarters), and r = 9% (compounded quarterly). The storage cost is $2 per ounce per year, so c k = $0.50 for each quarter k = 0 , 1 , and 2 (at the beginning of the quarter). We use the formula: along with the following intermediate results: to arrive at 10.2 There is a typo in the text. The exponent “M” should be “-M” in the formula. Suppose at time zero you: 1. borrow S(0) 2. buy 1 unit of the asset for S(0) 3. take a short position of (1-q) M units at a forward price of F per unit 4. at the beginning of each period, sell q units of the asset to pay the cost of carry Note that the total cash outlay for these actions is zero. F = S d 0,3 k = 0 M 1 c k d k , M d 0,3  = 1 1 0.09 4 3 = 0.9354 d 1,3  = 1 1 0.09 4 2 = 0.9565 d 2,3  = 1 1 0.09 4 1 = 0.9780 F = $ 440.45 $ 0.5345 $ 0.5227 $ 0.5112 = $ 442.02
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10.2 (continued) At the time of delivery, you have (1-q)M units of the asset remaining. Then you do the following: 1. make delivery and receive F(1-q)M as payment 2. repay your loan with S(0)/d(0,M) Your total profit is F(1-q)M – S(0)/d(0,M) . If this amount is anything but zero (negative or positive), then you have made a profit (or received a loss) without making any investment (i.e., without taking any risk). Thus, consistent with our assumption that arbitrage opportunities do not exist, the profit must be zero. Here, we have glossed over the case where the profit is negative. Technically speaking, a negative profit is possible
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Chapter10 - Investment Science Chapter 10 Solutions to...

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