You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $107 at year-end. XYZ currently sells for $107. Over the next year the stock price will increase by 9% or decrease by 9%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co.
a. Suppose the desired put option were traded. How much would it cost to purchase?
b. What would have been the cost of the protective put portfolio?
c. What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 107? Show that the payoff to this portfolio and the cost of establishing the portfolio matches that of the desired protective put.
Portfolio
S = 97.37
S = 116.63
Buy 0.5 shares
Invest in T-bills
Total
| You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $107 at year-end. XYZ currently sells for $107. Over the next year the stock price will increase by 9% or decrease by 9%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co. |
| a. Suppose the desired put option were traded. How much would it cost to purchase? b. What would have been the cost of the protective put portfolio?
|
Related questions
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.
a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)
| Expected return | % per year |
| Standard deviation | % per year |
b. Suppose your risky portfolio includes the following investments in the given proportions:
| Stock A | 22% |
| Stock B | 31% |
| Stock C | 47% |
What are the investment proportions of your clientâs overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
| Security | Investment Proportions | |
| T-Bills | % | |
| Stock A | % | |
| Stock B | % | |
| Stock C | % | |
c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)
| Reward-to-Volatility Ratio | |
| Risky portfolio | |
| Clientâs overall portfolio | |
