Chapter 5: Q31I (page 555)
These three put options all are written on the same stock. One has a delta of -.9, one a delta of -.5, and one a delta of -.1. Assign deltas to the three puts by filling in the table below.
Put | X | Delta |
A | 10 | |
B | 20 | |
C | 30 |
-.1, -.5 and -.9
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You buy a share of stock, write a one-year call option with X = \(10, and buy a one-year put option with X = \)10. Your net outlay to establish the entire portfolio is $9.50. What must be the risk-free interest rate? The stock pays no dividends.
Rich McDonald, CFA, is evaluating his investment alternatives in Ytel Incorporated by analyzing a Ytel convertible bond and Ytel common equity. Characteristics of the two securities are given in the following exhibit:
a. Calculate, based on the exhibit, the
i. Current market conversion price for the Ytel convertible bond.
ii. Expected one-year rate of return for the Ytel convertible bond.
iii. Expected one-year rate of return for the Ytel common equity.
One year has passed and Ytel’s common equity price has increased to $51 per share. Also, over the year, the yield to maturity on Ytel’s nonconvertible bonds of the same maturity increased, while credit spreads remained unchanged.
b. Name the two components of the convertible bond’s value. Indicate whether the value of each component should decrease, stay the same, or increase in response to the:
i. Increase in Ytel’s common equity price.
ii. Increase in bond yield.
Suppose the S&P 500 Index portfolio pays a dividend yield of 2% annually. The index currently is 1,200. The T-bill rate is 3%, and the S&P futures price for delivery in one year is $1,233. Construct an arbitrage strategy to exploit the mispricing and show that your profits one year hence will equal the mispricing in the futures market.
Maria VanHusen, CFA, suggests that forward contracts on fixed-income securities can beused to protect the value of the Star Hospital Pension Plan’s bond portfolio against thepossibility of rising interest rates. VanHusen prepares the following example to illustratehow such protection would work:
a. Should the investor buy or sell the forward contract to protect the value of the bondagainst rising interest rates during the holding period?
b. Calculate the value of the forward contract for the investor at the maturity of theforward contract if VanHusen’s bond price forecast turns out to be accurate.
c. Calculate the change in value of the combined portfolio (the underlying bond and theappropriate forward contract position) six months after contract initiation.
You would like to be holding a protective put position on the stock of XYZ Co. to lockin a guaranteed minimum value of \(100 at year-end. XYZ currently sells for \)100. Overthe next year, the stock price will either increase by 10% or decrease by 10%. The T-billrate 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 thepayoff that would be provided by a protective put with X = $100? Show that thepayoff to this portfolio and the cost of establishing the portfolio matches that ofthe desired protective put.
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