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Brealey. Myers. Allen Chapter 20 Solution

# Brealey. Myers. Allen Chapter 20 Solution - CHAPTER 20...

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162 CHAPTER 20 Understanding Options Answers to Practice Questions 1. a. The put places a floor on value of investment, i.e., less risky than buying stock. The risk reduction comes at the cost of the option premium. b. Benefit from upside, but also lose on the downside. c. A naked option position is riskier than the underlying asset. Investor gains from increase in stock price, but loses entire investment if stock price is less than exercise price at expiration. d. Investor exchanges uncertain upside changes in stock price for the known up-front income from the option premium. e. Safe investment if the debt is risk free. f. From put-call parity, this is equivalent (for European options) to ‘buy bond.’ Therefore, this is a safe investment. g. Another naked, high-risk position with known up-front income but exposure to down movements in stock price. 2. While it is true that both the buyer of a call and the seller of a put hope the price will rise, the two positions are not identical. The buyer of a call will find her profit changing from zero and increasing as the stock price rises [see text Figure 20.1(a)], while the seller of a put will find his loss decreasing and then remaining at zero as the stock price rises [see text Figure 20.2(b)]. 3. Let P 3 = the value of the three month put, C 3 = the value of the three month call, S = the market value of a share of stock, and EX = the exercise price of the options. Then, from put-call parity: C 3 + [EX/(1 + r) 0.25 ] = P 3 + S Since both options have an exercise price of \$60 and both are worth \$10, then: EX/(1 + r) 0.25 = S From put-call parity for the six-month options, we have: C 6 + [EX/(1 + r) 0.50 ] = P 6 + S Since S = EX/(1 + r) 0.25 and EX/(1 + r) 0.50 is less than EX/(1 + r) 0.25 , then the value of the six-month call is greater than the value of the six-month put.

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163 4. You would buy the American call for £4, exercise the call immediately in order to purchase a share of Drake and Eider stock for £5, and then sell the share of Drake and Eider stock for £10. The net gain is: £10 – (£4 + £5) = £1. If the call is a European call, you should buy the call, deposit in the bank an amount equal to the present value of the exercise price, and sell the stock short. This produces a current cash flow equal to: £10 – £4 – (£5/1.05) = £1.24 At the maturity of the call, the action depends on whether the stock price is greater than or less than the exercise price. If the stock price is greater than £5, then you would exercise the call (using the cash from the bank deposit) and buy back the stock. If the stock price is less than £5, then you would let the call expire and buy back the stock. The cash flow at maturity is the greater of zero (if the stock price is greater than £5) or [£5 – stock price] (if the stock price is less than £5). Therefore, the cash flows are positive now and zero or positive one year from now. 5.
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Brealey. Myers. Allen Chapter 20 Solution - CHAPTER 20...

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