OR649_2_hm1_sol - OR649/SYST659 Fall 2011 Assignment#1 soln...

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OR649/SYST659: Fall 2011 Assignment #1 soln Problem 1.2. Explain carefully the difference between hedging, speculation, and arbitrage. A trader is hedging when she has an exposure to the price of an asset and takes a position in a derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is betting on the future movements in the price of the asset. Arbitrage involves taking a position in two or more different markets to lock in a profit. Problem 1.10. Suppose you own 5,000 shares that are worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next four months? You could buy 50 put option contracts (each on 100 shares) with a strike price of $25 and an expiration date in four months. If at the end of four months the stock price proves to be less than $25, you can exercise the options and sell the shares for $25 each. Problem 1.21. “Options and futures are zero-sum games.” What do you think is meant by this statement? The statement means that the gain (loss) to the party with the short position is equal to the loss (gain) to the party with the long position. In aggregate, the net gain to all parties is zero. Problem 1.27 In March, a US investor instructs a broker to sell one July put option contract on a stock. The stock price is $42 and the strike price is $40. The option price is $3. Explain what the investor has agreed to. Under what circumstances will the trade prove to be profitable? What are the risks? The investor has agreed to buy 100 shares of the stock for $40 in July (or earlier) if the party on the other side of the transaction chooses to sell. The trade will prove profitable if the option is not exercised or if the stock price is above $37 at the time of exercise. The risk to the investor is that the stock price plunges to a low level. For example, if the stock price drops to $1 by July (unlikely but possible), the investor loses $3,600. This is because the put options are exercised and $40 is paid for 100 shares when the value per share is $1. This leads to a loss of $3,900 which is only a little offset by the premium of $300 received for the options. Problem 1.32. On July 15, 2010, an investor owns 100 Google shares. As indicated in Table 1.3, the share price is about $497 and a December put option with a strike price $460 costs $27.30. The investor is comparing two alternatives to limit downside risk. The first
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involves buying one December put option contract with a strike price of $460. The
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