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# 1s - THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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1 T HE U NIVERSITY OF H ONG K ONG F ACULTY OF B USINESS AND E CONOMICS FINA0301 CDE - D ERIVATIVES First Semester, 2009-2010 Tutorial 1 Problem Set Solution – Chapter 1 & 2 checkbld Practice Questions Question 1 A short sale of XYZ entails borrowing shares of XYZ and then selling them, receiving cash. Therefore, initially, we will receive the proceeds from the sale of the asset, less the proportional commission charge: 300 (\$30.19) 300 (\$30.19) 0.005 \$9,057 0.995 \$9,011.72 × - × × = × = When we close out the position, we will again incur the commission charge, which is added to the purchasing cost: 300 (\$29.87) 300 (\$29.87) 0.005 \$8,961 1.005 \$9,005.81 × + × × = × = Finally, we subtract the cost of covering the short position from our initial proceeds to receive total profits: \$9,011.72 \$9,005.81 \$5.91. - = We can see that the commission charge that we have to pay twice significantly reduces the profits we can make. Question 2 (a) The investor buys 180-day call option, and takes a short position in a 180-day forward contract. If S T is the terminal spot rate, the profit from the call option is: max ( S T 1.57, 0) – FV(0.02) The profit from the short-forward contract is: 1.6018 - S T

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FINA0301 – Tutorial 1 Solution Mr. Clive Man Chung HO 2 The profit from the strategy is therefore: max (0, S T – 1.57) – 0.0205 + 1.6018 - S T max (0, S T – 1.57) + 1.5813 - S T 1.5813 - S T when S T 1.57 0.0113 when S T > 1.57 This shows that the profit is always positive. (b) The investor buys 90-day put option, and takes a long position in a 90-day forward contract. If S T is the terminal spot rate, the profit from the put option is: max (0, 1.64 - S T ) – FV(0.02) The profit from the long-forward contract is: S T 1.6056 The profit from the strategy is therefore: max (0, 1.64 - S T ) – 0.02025 + S T – 1.6056 max (0, 1.64 - S T ) + S T – 1.62585 S T 1.62585 when S T 1.64 0.01415 when S T < 1.64 The profit is therefore always positive. Question 3 (Refer to Tutorial 1 Notes p.2-3 for Cash and Carry and Reverse Cash and Carry Arbitrage without Dividend) Question 4 (a) The payoff to a long forward at expiration is equal to: Payoff to long forward = Spot price at expiration – forward price
FINA0301 – Tutorial 1 Solution Mr. Clive Man Chung HO 3

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1s - THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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