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Sample Questions on Derivatives (1)

# Sample Questions on Derivatives (1) - FIN 353 Exercise...

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FIN 353: Exercise Problems on Derivative Assets 1. Sample problem on Futures Hedging: On July 1, an investor holds 50,000 shares of a certain stock. The market price is \$30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of \$50 times the index. a. What strategy should the investor follow? b. If in one month, the S&P index changes to 1,450, while the price of the stock goes down to \$28, what is the net hedging result? Solution: (a): A short hedge is needed by selling 20 S&P 500 futures. 20 contracts are needed since (\$30x50,000)/(\$50x1,500). (b) Spot Futures July 1: Hold 50,000 shares at \$30/share July 1: Sell 20 S&P 500 Futures at 1,500 Total value = \$1,500,000 Total value = 20x\$50x 1,500 = \$1,500,000 August 1: Share price at \$28/share August 1:Buy back 20 futures contracts Total Value = \$1,400,000 at 1,450 Total value = \$20 x \$50 x 1,450 = \$1,450,000 Loss = \$100,000 Gain = \$50,000 This is an imperfect hedge because the stock price is moving faster and wider than the S&P 500 index, that means the stock beta is greater than 1. You need to buy more contracts for a perfect hedge. For this case, 40 contracts will be needed. 2. From Saunders and Cornett, Ch. 10, Solution to #14: a. Total profit = (\$150 - \$136) - \$5 = \$9 per share. b. If the price of the underlying stock is \$130 (less than the exercise price), you will not exercise the option. Thus, your profit is -\$5 per share (the cost of the option).

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3. From Saunders and Cornett, Ch. 10, Solution to #15: a. If the price of the underlying stock is \$40 (greater than the exercise price), you will not exercise the option. Thus, your profit is -\$.50 per share (the cost of the option). b. Total profit = (\$38 - \$34) - \$.50 = \$3.50 per share. 4. From Saunders and Cornett, Ch. 10, Solution to #18: The Black-Scholes model examines five factors that affect the price of an option: 1) the spot price
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