A call option on Jupiter Motors stock with an exercise price of $75 and one-year expiration is selling at $3. A put option on Jupiter stock with an exercise price of $75 and one-year expiration is selling at $2.50. If the risk-free rate is 8% and Jupiter pays no dividends, what should the stock price be?
Call option Selling = C = $3.00
Exercise price =X = $75
Rate = r = 8%
Put option Selling = P = $2.50
Stock price = C + X / (1+r) ^t – P
=$3 + $75/ (1+8%)^1 - $2.50
You establish a straddle on Walmart using September call and put options with a strike price of $50. The call premium is $4.25 and the put premium is $5.
a. What is the most you can lose on this position?
b. What will be your profit or loss if Walmart is selling for $58 in September?
c. At what stock prices will you break even on the straddle?
The Excel Applications box in the chapter (available at www.mhhe.com/bkm ; link to Chapter 17 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates.
a. Suppose that today is January 1, 2012. Assume the interest rate is 1% per year and a stock index currently at 1,200 pays a dividend yield of 2%. Find the futures price for contract maturity dates of February 14, 2012, May 21, 2012, and November 18, 2012.
b. What happens to the term structure of futures prices if the dividend yield is lower than the risk-free rate? For example, what if the interest rate is 3%?
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:
T -bill (Face value $1,120
Call (Exercise price $1,120
Put (Exercise price $1040
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?
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