ch_16_sol - CHAPTER 16: OPTIONS MARKETS 1. 2. 3. C is...

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CHAPTER 16: OPTIONS MARKETS 1. C is false. This is the description of the payoff to a put, not a call. 2. C is the only correct statement. 3. Each contract is for 100 shares: $7.25 × 100 = $725 4. Cost Payoff Profit Call option, X = 75 8 1/8 5 - 3 3/8 Put option, X = 75 3 0 –3 Call option, X = 80 5 1/8 0 –5 1/8 Put option, X = 80 4 3/4 0 –4 3/4 Call option, X = 85 3 3/8 0 - 3 3/8 Put option, X = 85 7 3/4 5 - 2 3/4 5. In terms of dollar returns: Stock price: 80 100 110 120 All stocks (100 shares) 8,000 10,000 11,000 12,000 All options (1000 shares) 0 0 10,000 20,000 Bills + options 9,360 9,360 10,360 11,360 In terms of rate of return, based on a $10,000 investment: All stocks –20% 0% 10% 20% All options –100% –100% 0% 100% Bills + options –6.4% –6.4% 3.6% 13.6% 16-1
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All options All stocks Bills plus options S T 100 –100 0 – 6.4 Rate of return (%) 100 110 6. a. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the straddle would be $10 + $7 = $17. b. Since the straddle cost $17, this is the amount by which the stock would have to move in either direction for the profit on either the call or put to cover the investment cost (not including time value of money considerations). 7. a. Sell a straddle, i.e., sell a call and a put to realize premium income of $4 + $7 = $11. b. If the stock ends up at $50, both the options will be worthless and your profit will be $11. This is your maximum possible profit since at any other stock price, you will need to pay off on either the call or the put. The stock price can move by $11 (your initial revenue from writing the two at-the-money options) in either direction before your profits become negative. c. Buy the call, sell (write) the put, lend the present value of $50. The payoff is: Position Initial Outlay Final Payoff S T < X S T > X –––––– –––––– Call (long) C = 5 0 S T – 50 Put (short) – P = – 7 –(50–S T ) 0 Lending 50/(1 + r) 1/4 50 50 ––––––– ––––––––––––––––– ––––– ––––––– TOTAL 5 – 7 + S T S T The initial outlay equals the present value of $50 - $2. In either scenario, you end up with the same payoff as you would if you bought the stock itself. 16-2
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8. a. By writing covered call options, Jones takes in premium income of $30,000. If the price of the stock in January is less than or equal to $45, he will have his stock plus the premium income. But the most he can have is $450,000 + $30,000 because the stock will be called away from him if its price exceeds $45. (We areignoring interest earned on the premium income from writing the option over this short time period.) The payoff structure is: Stock price Portfolio value less than $45 10,000 times stock price + $30,000 more than $45 $450,000 + $30,000 = $480,000 This strategy offers some extra premium income but leaves substantial downside risk. At an extreme, if the stock price fell to zero, Jones would be left with only
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ch_16_sol - CHAPTER 16: OPTIONS MARKETS 1. 2. 3. C is...

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