Chapter 5: Q20I (page 515)
In what ways is owning a corporate bond similar to writing a put option? A calloption?
Owning the corporate bond is similar to writing a put option because bondholder have right to recover the loan amount if firms value goes down. Call feature of bond makes bond like owning the call option.
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The S&P 500 Index is currently at 1,200. You manage a \(6 million indexed equityportfolio. The S&P 500 futures contract has a multiplier of \)250.
a. If you are temporarily bearish on the stock market, how many contracts should yousell to fully eliminate your exposure over the next six months?
b. If T-bills pay 2% per six months and the semi-annual dividend yield is 1%, what is theparity value of the futures price? Show that if the contract is fairly priced, the totalrisk-free proceeds on the hedged strategy in part (a) provide a return equal to theT-bill rate.
c. How would your hedging strategy change if, instead of holding an indexed portfolio,you hold a portfolio of only one stock with a beta of .6? How many contracts wouldyou now choose to sell? Would your hedged position be riskless? What would be thebeta of the hedged position?
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 |
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.
You are attempting to formulate an investment strategy. On the one hand, you think there is great upward potential in the stock market and would like to participate in the upward move if it materializes. However, you are not able to afford substantial stock market losses and so cannot run the risk of a stock market collapse, which you recognize is also possible. Your investment adviser suggests a protective put position:
Buy shares in a market-index stock fund and put options on those shares with three months until expiration and exercise price of \(1,040. The stock index is currently at \)1,200. However, your uncle suggests you instead buy a three-month call option on the index fund with exercise price \(1,120 and buy three-month T-bills with face value \)1,120.
a. On the same graph, draw the payoffs to each of these strategies as a function of the stock fund value in three months. (Hint: Think of the options as being on one “share” of the stock index fund, with the current price of each share of the index equal to \(1,200.)
b. Which portfolio must require a greater initial outlay to establish?
( Hint: Does either portfolio provide a final payoff that is always at least as great as the payoff of the other portfolio?)
c. Suppose the market prices of the securities are as follows:
Stock Fund | \)1200 |
T -bill (Face value \(1,120 | \)1080 |
Call (Exercise price \(1,120 | \)160 |
Put (Exercise price \(1040 | \)8 |
Make a table of profits realized for each portfolio for the following values of the stock price in three months: S T = \(0, \)1,040, \(1,120, \)1,200, and $1,280. Graph the profits to each portfolio as a function of S T on a single graph.
d. Which strategy is riskier? Which should have a higher beta?
A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Jerry Harris sells one July silver futures contract at a price of \(28 per ounce, posting a \)6,000 initial margin. If the required maintenance margin is $2,500, what is the first price per ounce at which Harris would receive a maintenance margin call?.
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