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Chapter 5: Q15-10I (page 513)

An investor purchases a stock for \(38 and a put for \).50 with a strike price of \(35. The investor sells a call for \).50 with a strike price of $40. What is the maximum profit and loss for this position? Draw the profit and loss diagram for this strategy as a function of the stock price at expiration.

Short Answer

Expert verified

Maximum profit = $2

Maximum loss = - $3.

Step by step solution

01

Given Information

Initial outlay = $38

So purchase price of stock and payoff of position would be between $35 and $40

Maximum profit = $40 - $38 = $2

Maximum loss = $35 - $38 = - $3.

02

Drawing of profit-loss diagram

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Most popular questions from this chapter

Imagine you are a provider of portfolio insurance. You are establishing a four-yearprogram. The portfolio you manage is currently worth $100 million, and you promise toprovide a minimum return of 0%. The equity portfolio has a standard deviation of 25%per year, and T-bills pay 5% per year. Assume for simplicity that the portfolio pays nodividends (or that all dividends are reinvested).

a. What fraction of the portfolio should be placed in bills? What fraction in equity?

b. What should the manager do if the stock portfolio falls by 3% on the first day of trading?

Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes in interest rates than the rate of return of the underlying bond?

Michael Weber, CFA, is analyzing several aspects of option valuation, including the determinants of the value of an option, the characteristics of various models used to value options, and the potential for divergence of calculated option values from observed market prices.

a. What is the expected effect on the value of a call option on common stock if (i) the volatility of the underlying stock price decreases; (ii) the time to expiration of the option increases.

b. Using the Black-Scholes option-pricing model, Weber calculates the price of a three-month call option and notices the option’s calculated value is different from its market price. With respect to Weber’s use of the Black-Scholes option-pricing model, (i) discuss why the calculated value of an out-of-the-money European option may differ from its market price; (ii) discuss why the calculated value of an American option may differ from its market price.

You purchase a Treasury-bond futures contract with an initial margin requirement of 15% and a futures price of \(115,098. The contract is traded on a \)100,000 underlying par value bond. If the futures price falls to $108,000, what will be the percentage loss on your position?

The multiplier for a futures contract on a certain stock market index is \(250. The maturity of the contract is one year, the current level of the index is 1,000, and the risk-free interest rate is .2% per month. The dividend yield on the index is .1% per month.

Suppose that after one month, the stock index is at 1,020.

a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.

b. Find the holding-period return if the initial margin on the contract is \)10,000.
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