Chapter 5: Q3B (page 512)
The following price quotations are for exchange-listed options on Primo Corporation common stock.
Company | Strike | Expiration | Call | Put |
Primo 61.12 | 55 | February | 7.25 | .48 |
With transaction costs ignored, how much would a buyer have to pay for one call option contract?
$725
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In each of the following cases, discuss how you, as a portfolio manager, could use financial futures to protect a portfolio.
a. You own a large position in a relatively illiquid bond that you want to sell.
b. You have a large gain on one of your long Treasuries and want to sell it, but you would like to defer the gain until the next accounting period, which begins in four weeks.
c. You will receive a large contribution next month that you hope to invest in long-term corporate bonds on a yield basis as favorable as is now available.
The following diagram shows the value of a put option at expiration:
Ignoring transaction costs, which of the following statements about the value of the put option at expiration is true?
a. The expiration value of the short position in the put is \(4 if the stock price is \)76.
b. The expiration value of the long position in the put is -\(4 if the stock price is \)76.
c. The long put has a positive expiration value when the stock price is below \(80.
d. The value of the short position in the put is zero for stock prices equaling or exceeding \)76.
The one-year futures price on a particular stock-index portfolio is 1,218, the stock index currently is 1,200, the one-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a \(1,200 investment in the index portfolio is \)15.
a. By how much is the contract mispriced?
b. Formulate a zero-net-investment arbitrage portfolio, and show that you can lock in riskless profits equal to the futures mispricing.
c. Now assume (as is true for small investors) that if you short-sell the stocks in the market index, the proceeds of the short sale are kept with the broker and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming you don’t already own the shares in the index)? Explain.
d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relationship? That is, given a stock index of 1,200, how high and how low can the futures price be without giving rise to arbitrage opportunities?
Reconsider the determination of the hedge ratio in the two-state model (Section 16.2), where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for each of the following exercise prices: \(120, \)110, \(100, \)90? What do you conclude about the hedge ratio as the option becomes progressively more in the money?
An investor buys a call at a price of \(4.50 with an exercise price of \)40. At what stock price will the investor break even on the purchase of the call?
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