Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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Chapter 17, Problem 10PS
Consider a stock that will pay a dividend of D dollars in one year, which is when a futures contract matures. Consider the following strategy: Buy the Stock, short a futures contract on the stock, and borrow
a. What are the cash flows now and in one year? (Hint: Remember the dividend the
stock will pay.)
b. Show that the
c. Call the dividend yield
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Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1.
b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.
Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.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 that 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 relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
Consider a two period economy. You can buy stocks in period 0, and then sell them in period 1. You can also enter into futures contracts in period 0, which expire in period 1.
Suppose a stock has a β of 0.5. The stock pays no dividends, and is trading at $100. The market has an expected return of 10%. The interest rate is 2%. Suppose the CAPM holds. What is the stock’s expected return? What is the expected price of the stock in period 1?
Consider a futures contract on the stock, expiring at t = 1. What is the fair price of the futures contract, in t = 1 dollars?
Suppose you take a long position in the futures contract in period 0 (so, you promise to pay money, in exchange for getting the stock in period 1). When the futures contract expires in period 1, you receive the stock and immediately sell it. What is the expected amount you will pay in money for the stock? What is the expected amount you get from selling the stock?
Since buying single-stock futures appears to be a fairly…
Chapter 17 Solutions
Essentials Of Investments
Ch. 17.4 - Experiment with different values for both income...Ch. 17.4 - 2. What happens to the time spread if the income...Ch. 17.4 - Prob. 3EQCh. 17 - Prob. 1PSCh. 17 - The current level of the S . The risk-free...Ch. 17 - Prob. 3PSCh. 17 - Prob. 4PSCh. 17 - Prob. 6PSCh. 17 - Prob. 7PSCh. 17 - Prob. 8PS
Ch. 17 - Prob. 9PSCh. 17 - Consider a stock that will pay a dividend of D...Ch. 17 - Prob. 11PSCh. 17 - Prob. 13PSCh. 17 - Prob. 14PSCh. 17 - Prob. 15PSCh. 17 - Prob. 16PSCh. 17 - Prob. 17PSCh. 17 - Prob. 18PSCh. 17 - Prob. 19PSCh. 17 - Prob. 20PSCh. 17 - Prob. 21PSCh. 17 - Prob. 22PSCh. 17 - Prob. 23PSCh. 17 - Prob. 24CCh. 17 - a. How would your hedging strategy in the previous...Ch. 17 - Prob. 26CCh. 17 - Prob. 27CCh. 17 - Prob. 1CPCh. 17 - Prob. 2CPCh. 17 - Prob. 3CPCh. 17 - In each of the following cases, discuss how you,...Ch. 17 - Prob. 5CPCh. 17 - Joan Tam, CFA, believes she has identified an...Ch. 17 - Prob. 7CPCh. 17 - Prob. 8CPCh. 17 - Prob. 9CPCh. 17 - Prob. 1WMCh. 17 - Prob. 2WMCh. 17 - Prob. 3WMCh. 17 - Prob. 4WM
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- In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49arrow_forwardA stock is trading at $80 per share. The stock is expected to have a yearend dividend of $4 per share (D1 = $4), and it is expected to grow at some constant rate, g, throughout time. The stock’s required rate of return is 14% (assume the market is in equilibrium with the required return equal to the expected return). What is your forecast of gL?arrow_forwardWhat makes for a good investment? Use the approximate yield formula or a financial calculator to rank the following investments according to their expected returns. Buy a stock for $30 a share, hold it for three years, and then sell it for $60 a share (the stock pays annual dividends of $2 a share). Buy a security for $40, hold it for two years, and then sell it for $100 (current income on this security is zero). Buy a one-year, 5 percent note for $1,000 (assume that the note has a $1,000 par value and that it will be held to maturity).arrow_forward
- Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?arrow_forwardAn analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?arrow_forwardConsider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 1,950, and the June maturity contract is at F0 = 1,951.a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?b. Suppose now that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities?c. By how much does the actual futures price fall below the no-arbitrage bound?d. Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.arrow_forward
- You buy a share of stock, write a 1-year call option with X = $10, and buy a 1-year put option with X = $10. Your net outlay to establish the entire portfolio is $9.50. (a) What is the payoff of your portfolio? (b) What must be the risk-free interest rate? The stock pays no dividends.arrow_forwardYou observe that the settlement price of a one-year futures contract for 1 share of a dividend paying stock is currently at $52. The current stock price is $50 and the risk-free interest rate is 10% p.a. (compounded annually). It is also known that the dividend yield on the stock is 4% p.a. (compounded annually). Set up a strategy to realize an arbitrage profit today and show the initial and terminal cash flows from each position taken in the strategy. Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. Thank you!arrow_forward
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