Zinc Company is currently trading for $30 per share. The stock pays no dividends. You are interested in valuing a one-year at-the-money European put option on Zinc stock. Assume that the volatility of Zinc stock is 40% per year and its beta is 0.95. The risk-free interest rate is 6%. (a) What is the intrinsic value of the put option? What is the time value of the put option? Interpret these two values. (b) You would like to replicate this put option using a portfolio of stocks and bonds. What portfolio would you hold? (c) What is the leverage ratio of the put option? What is the beta of the put option? Based on your answers, discuss why investors may want to include put options in their portfolios. (d) If you hold an American put option, would it ever be optimal to exercise it early? If so, under what circumstance?
Zinc Company is currently trading for $30 per share. The stock pays no dividends. You are interested in valuing a one-year at-the-money European put option on Zinc stock. Assume that the volatility of Zinc stock is 40% per year and its beta is 0.95. The risk-free interest rate is 6%. (a) What is the intrinsic value of the put option? What is the time value of the put option? Interpret these two values. (b) You would like to replicate this put option using a portfolio of stocks and bonds. What portfolio would you hold? (c) What is the leverage ratio of the put option? What is the beta of the put option? Based on your answers, discuss why investors may want to include put options in their portfolios. (d) If you hold an American put option, would it ever be optimal to exercise it early? If so, under what circumstance?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:Zinc Company is currently trading for $30 per share. The stock pays no dividends. You
are interested in valuing a one-year at-the-money European put option on Zinc stock.
Assume that the volatility of Zinc stock is 40% per year and its beta is 0.95. The risk-free
interest rate is 6%.
(a) What is the intrinsic value of the put option? What is the time value of the put option?
Interpret these two values.
(b) You would like to replicate this put option using a portfolio of stocks and bonds. What
portfolio would you hold?
(c) What is the leverage ratio of the put option? What is the beta of the put option? Based
on your answers, discuss why investors may want to include put options in their
portfolios.
(d) If you hold an American put option, would it ever be optimal to exercise it early? If so,
under what circumstance?
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