# Question: You are currently managing a stock portfolio worth 55 million

You are currently managing a stock portfolio worth $55 million and you are concerned that over the next four months equity values will be flat and may even fall. Consequently, you are considering two different strategies for hedging against possible stock declines:

(1) buying a protective put, and (2) selling a covered call (i.e., selling a call option based on the same underlying stock position you hold). An over-the-counter derivatives dealer has expressed interest in your business and has quoted the following bid and offer prices (in millions) for at-the-money call and put options that expire in four months and match the characteristics of your portfolio:

a. For each of the following expiration date values for the unhedged equity position, calculate the terminal values (net of initial expense) for a protective put strategy.

35, 40, 45, 50, 55, 60, 65, 70, 75

b. Draw a graph of the protective put net profit structure in Part a, and demonstrate how this position could have been constructed by using call options and T-bills, assuming a risk-free rate of 7 percent.

c. For each of these same expiration date stock values, calculate the terminal net profit values for a covered call strategy.

d. Draw a graph of the covered call net profit structure in Part c, and demonstrate how this position could have been constructed by using put options and T-bills, again assuming a risk-free rate of 7percent.

(1) buying a protective put, and (2) selling a covered call (i.e., selling a call option based on the same underlying stock position you hold). An over-the-counter derivatives dealer has expressed interest in your business and has quoted the following bid and offer prices (in millions) for at-the-money call and put options that expire in four months and match the characteristics of your portfolio:

a. For each of the following expiration date values for the unhedged equity position, calculate the terminal values (net of initial expense) for a protective put strategy.

35, 40, 45, 50, 55, 60, 65, 70, 75

b. Draw a graph of the protective put net profit structure in Part a, and demonstrate how this position could have been constructed by using call options and T-bills, assuming a risk-free rate of 7 percent.

c. For each of these same expiration date stock values, calculate the terminal net profit values for a covered call strategy.

d. Draw a graph of the covered call net profit structure in Part c, and demonstrate how this position could have been constructed by using put options and T-bills, again assuming a risk-free rate of 7percent.

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