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B choice b calls have hedge ratios less than 10 so

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b. Choice B: Calls have hedge ratios less than 1.0, so the shares have higher profit potential. For an equal number of shares controlled, the dollar exposure of the shares is greater than that of the calls, and the profit potential is therefore greater. 21-6
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27. a. The value of the call option is expected to decrease if the volatility of the underlying stock price decreases. The less volatile the underlying stock price, the less the chance of extreme price movements and the lower the probability that the option expires in the money. This makes the participation feature on the upside less valuable. The value of the call option is expected to increase if the time to expiration of the option increases. The longer the time to expiration, the greater the chance that the option will expire in the money resulting in an increase in the time premium component of the option’s value. b. i. When European options are out of the money, investors are essentially saying that they are willing to pay a premium for the right, but not the obligation, to buy or sell the underlying asset. The out-of-the-money option has no intrinsic value, but, since options require little capital (just the premium paid) to obtain a relatively large potential payoff, investors are willing to pay that premium even if the option may expire worthless. The Black-Scholes model does not reflect investors’ demand for any premium above the time value of the option. Hence, if investors are willing to pay a premium for an out-of-the-money option above its time value, the Black-Scholes model does not value that excess premium. ii. With American options, investors have the right, but not the obligation, to exercise the option prior to expiration, even if they exercise for non-economic reasons. This increased flexibility associated with American options has some value but is not considered in the Black-Scholes model because the model only values options to their expiration date (European options). 28. S = 100; current value of portfolio X = 100; floor promised to clients (0% return) σ = 0.25; volatility r = 0.05; risk-free rate T = 4 years; horizon of program a. Using the Black-Scholes formula, we find that: d 1 = 0.65, N(d 1 ) = 0.7422, d 2 = 0.15, N(d 2 ) = 0.5596 Put value = $10.27 Therefore, total funds to be managed equals $110.27 million: $100 million portfolio value plus the $10.27 million fee for the insurance program. The put delta is: N(d 1 ) – 1 = 0.7422 – 1 = –0.2578 Therefore, sell off 25.78% of the equity portfolio, placing the remaining funds in T-bills. The amount of the portfolio in equity is therefore $74.22 million, while the amount in T-bills is: $110.27 million – $74.22 million = $36.05 million 21-7
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b. At the new portfolio value, the put delta becomes: –0.2779 This means that you must reduce the delta of the portfolio by: 0.2779 – 0.2578 = 0.0201 You should sell an additional 2.01% of the equity position and use the proceeds to buy T-bills. Since the stock price is now at only 97% of its original value, you need to sell: $97 million × 0.0201 = $1.950 million of stock 29. a. American options should cost more (have a higher premium). American
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b Choice B Calls have hedge ratios less than 10 so the...

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