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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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