Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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Textbook Question
Chapter 15, Problem 23PS
Consider the following portfolio. You write a put option with exercise price
a. Plot the value of the portfolio at the expiration date of the options.
b. Now, plot the profit of the portfolio. Hint: Which option must cost more?
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Consider the following portfolio. You write a put option with exercise price 90 and buy a put option on the same stock with the same expiration date with exercise price 95.a. Plot the value of the portfolio at the expiration date of the options.b. On the same graph, plot the profit of the portfolio. Which option must cost more?
Construct a hedge portfolio and by using the binomial option pricing model and find the values of Pu and Pd; and P. Explain your answer and describe the hedge portfolio.
A stock currently priced at $100. One period later it can go up to $125, an increase of 25 percent, or down to $80, a decrease of 20 percent. Assume a put option is available with an exercise price of $100. Consider the example in a two-period world. The risk-free rate is 7 percent. The inputs are summarized as follows
S = 100 d = 0.80 u = 1.25 X= 100 r = 0.07
Consider a portfolio consisting of 6 stocks and 10 put options on the stocks. The current stock price is S0 = 100 and the stike price of the options is X = 100. The stock pricecan take on only two values at maturity T given by Su = 120 and Sd = 90. The risk-free rate is given by 5%.
(1) How many put options with strike price X = 110 are necessary in the portfolio to have a certain payoff at maturity?(2) Find the value of a put option P0 with strike price X = 100.(3) Find the value of a call option C0 with X = 100 by using the Put-Call-Parity. Verify that your answer by calculating the price C0 directly.
Chapter 15 Solutions
Essentials Of Investments
Ch. 15.2 - Plot the rate of return to the call-plus-bills...Ch. 15.2 - Prob. 2EQCh. 15 - Prob. 1PSCh. 15 - Prob. 2PSCh. 15 - Prob. 3PSCh. 15 - Prob. 4PSCh. 15 - Prob. 5PSCh. 15 - Prob. 6PSCh. 15 - Prob. 7PSCh. 15 - The following diagram shows the value of a put...
Ch. 15 - You are a portfolio manager who uses Options...Ch. 15 - An investor purchases a stock for 38 and a put for...Ch. 15 - ll. Imagine that you are holding shares of stock,...Ch. 15 - Prob. 12PSCh. 15 - The common stock of the R.U.I.T. Corporation has...Ch. 15 - 14. The common stock of the C.A.L.L. Corporation...Ch. 15 - Prob. 15PSCh. 15 - Prob. 16PSCh. 15 - Prob. 17PSCh. 15 - Prob. 18PSCh. 15 - Prob. 19PSCh. 15 - In what ways is owning a corporate bond similar to...Ch. 15 - Prob. 21PSCh. 15 - Consider the following options portfolio: You...Ch. 15 - Consider the following portfolio. You write a put...Ch. 15 - A put option with strike price 300 on the Acme...Ch. 15 - You buy a share of stock, mite a one-year call...Ch. 15 - Joe Finance has just purchased a stock-index fund,...Ch. 15 - You write a call option with X=50 and buy a call...Ch. 15 - Devise a portfolio using only call options and...Ch. 15 - Prob. 29CCh. 15 - Prob. 1CPCh. 15 - Prob. 2CPCh. 15 - Prob. 3CPCh. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 1WM
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- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?arrow_forwarda) The cost of a portfolio consisting of a long position in a call option with strike price 50 and a short position in a call option with strike price 80 is zero (both call options are on the same stock and have the same maturity date). True or false? Explain. b) Carefully draw the payoff diagram of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. What reasons could a speculator have for holding such a portfolio (explain in detail)?arrow_forwardWe will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio?c. What is the present value of the portfolio?d. Given that the stock currently is selling at 100, solve for the value of the put.arrow_forward
- If your portfolio includes 35 percent of X, 40 percent of Y and 25 percent of Z, answer the following questions: (a) Calculate the portfolio expected return. (b) Calculate the variance and the standard deviation of the portfolio. (c) If the expected T-bill rate is 3.80 percent, calculate the expected risk premium on the portfolio. (d) If the market index fund has the same expected return as your portfolio, without considering any transaction cost, would you consider selling your portfolio and investing the market index fund instead? Explain your thoughts.arrow_forwardGive typing answer with explanation and conclusion The market portfolio has expected return of 12% and risk of 19%, and the risk-free rate is 5%. According to the CML, what is the portfolio weight for the risky market portfolio if an investor wants to achieve 8.5% return? What about 16.2%? And 19% return?arrow_forwardAn option trader has built a portfolio of three different call options onthe same underlying with the same maturity. The trader has boughtone call with a strike of 20 and also bought a call with a strike of50. The trader has sold two calls with a strike of 35. The currentunderlying price is 35. Tabulate, plot and describe the total payoffsfrom this portfolio. Given your payoff profile, what must be true aboutthe cost of building this portfolio?arrow_forward
- Consider the following portfolio: Long 4 calls with strike price 91.0 and price 21.717 Short 0 calls with strike price 91.0 and price 21.717 Long 0 calls with strike price 106.0 and price 17.807 Short 2 calls with strike price 106.0 and price 17.807 Long 0 calls with strike price 131.0 and price 11.291 Short 2 calls with strike price 131.0 and price 11.291 What is the cost of the portfolio:arrow_forwardWhen the return on the market portfolio goes up by 5%, the return on Stock A goes up onaverage by 8% and when the market portfolio return goes down by 5%, Stock A return goes down by 6%.a) Calculate the beta of this stock.b) Assuming that CAPM holds, calculate the required rate of return on this stock by assigning values forthe risk-free rate and the expected return on the market portfolio depending on your own choice. (The useof the same risk-free rate and market return by different students will be treated as a cheat attempt).arrow_forwarda. Using the data provided in problem 3, determine the return and risk for a portfolio made up of the following three stocks if you want to distribute your investment as follows: 20% in ADRE; 65% in MSFT and 15% in GOOG.b. How would the portfolio be affected if you distributed your investment in the following way: 30% in ADRE; 25% on MSFT and 45% on GOOG?c. Which of the two portfolios would a risk seeking investor prefer and why?arrow_forward
- Assume that the CAPM is true, ?F = 5%, ?M = 15% ??? ?M = 0.1. An investor with $10,000 to invest builds a portfolio, Q, of T-bills and the market portfolio. This means that a. it would be possible for the investor to obtain a return of 17% on portfolio Q. b. if portfolio Q were composed of short-selling $2,000 in T-bills and the remainder is the market portfolio, then ρQM = 1, βQ = 1.2 and σQ = 0.12. c. to obtain a return of 17% from portfolio Q the investor would need to invest $12,000 in the market portfolio. d. all of the above are true. e. only (a) and (b) above are true.arrow_forwardUse the Black-Scholes Model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $35, (3) time toexpiration is 4 months, (4) annualized risk-free rate is 5%, and (5) varianceof stock return is 0.25.arrow_forwardAn investor buys a 6-month European put option with K, = $75 for $10, buys a 6- month European put option with K3= $85 for $5, and sells two 6-month European put options with K₂ = $80 for $7. what is the total payoff and profit on the entire portfolio/strategy using BUTTERFLY spread. please show calculation of payoff.arrow_forward
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