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# 21 16 c the call sells at an implied volatility 1100

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c. The call sells at an implied volatility (11.00%) that is less than recent historical volatility (12.00%); the put sells at an implied volatility (14.00%) that is greater than historical volatility. The call seems relatively cheap; the put seems expensive. 40. True. The call option has an elasticity greater than 1.0. Therefore, the call’s percentage rate of return is greater than that of the underlying stock. Hence the GM call responds more than proportionately when the GM stock price changes in response to broad market movements. Therefore, the beta of the GM call is greater than the beta of GM stock. 41. True. The elasticity of a call option is higher the more out of the money is the option. (Even though the delta of the call is lower, the value of the call is also lower. The proportional response of the call price to the stock price increases. You can confirm this with numerical examples.) Therefore, the rate of return of the call with the higher exercise price responds more sensitively to changes in the market index, and therefore it has the higher beta. 42. As the stock price increases, conversion becomes increasingly more assured. The hedge ratio approaches 1.0. The price of the convertible bond will move one-for- one with changes in the price of the underlying stock. 43. Salomon believes that the market assessment of volatility is too high. Therefore, Salomon should sell options because the analysis suggests the options are overpriced with respect to true volatility. The delta of the call is 0.6, while that of the put is 0.6 – 1 = –0.4. Therefore, Salomon should sell puts and calls in the ratio of 0.6 to 0.4. For example, if Salomon sells 2 calls and 3 puts, the position will be delta neutral: Delta = (2 × 0.6) + [3 × (–0.4)] = 0 44. Using the true volatility (32%) and time to maturity T = 0.25 years, the hedge ratio for Exxon is N(d 1 ) = 0.5567. Because you believe the calls are under-priced (selling at an implied volatility that is too low), you will buy calls and short 0.5567 shares for each call you buy. 45. The calls are cheap (implied σ = 0.30) and the puts are expensive (implied σ = 0.34). Therefore, buy calls and sell puts. Using the “true” volatility of σ = 0.32, the call delta is 0.5567 and the put delta is: 0.5567 – 1.0 = –0.4433 Therefore, for each call purchased, buy: 0.5567/0.4433 = 1.256 puts 21-17
46. a. To calculate the hedge ratio, suppose that the market index increases by 1%. Then the stock portfolio would be expected to increase by: 1% × 1.5 = 1.5% or 0.015 × \$1,250,000 = \$18,750 Given the option delta of 0.8, the option portfolio would increase by: \$18,750 × 0.8 = \$15,000 Salomon’s liability from writing these options would increase by the same amount. The market index portfolio would increase in value by 1%. Therefore, Salomon Brothers should purchase \$1,500,000 of the market
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21 16 c The call sells at an implied volatility 1100 that...

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