1. Which of the following statement(s) is (are) true regarding the replicating portfolio of a call stock option: a. For each call, the number of shares of the stock held in the replicating portfolio can be negative. b. For each call, the number of shares of the stock held in the replicating portfolio will be 0.5 always. c. The replicating portfolio should give you the same payoff as the option for the next period. d. The market price of the replicating portfolio will always be equal to the market price of the call option. e. The replicating portfolio will consist of the underlying stock only.

1. Which of the following statement(s) is (are) true regarding the replicating portfolio of a call stock option: a. For each call, the number of shares of the stock held in the replicating portfolio can be negative. b. For each call, the number of shares of the stock held in the replicating portfolio will be 0.5 always. c. The replicating portfolio should give you the same payoff as the option for the next period. d. The market price of the replicating portfolio will always be equal to the market price of the call option. e. The replicating portfolio will consist of the underlying stock only.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Correlation = -1 Stock A B Rate of return Required: a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be formed to create a "synthetic" risk-free asset?) (Round your answer to 2 decimal places.) Yes No X Answer is not complete. Expected Return 9% 13% % Standard Deviation 45% 55% b. Could the equilibrium rƒ be greater than rate of return?
You write a put option with X = 100 and buy a put with X = 110. The puts are on the same stock and have the same expiration date.a. Draw the payoff graph for this strategy.b. Draw the profit graph for this strategy.c. If the underlying stock has positive beta, does this portfolio have positive or negative beta?
Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows: Correlation = -1 Stock Rate of return B O Yes ● No Expected Return Required: a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be formed to create a "synthetic" risk-free asset?) (Round your answer to 2 decimal places.) % 6% 12% Standard Deviation 25% 75% b. Could the equilibrium rf be greater than rate of return?
2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.
V3. By looking at the sensivities of your portfolio to δs = -$2 and δσ = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.)
Suppose Stock A has B = 1 and an expected return of 11%. Stock B has a B = 1.5. The risk- free rate is 5%. Also consider that the covariance between B and the market is 0.135. Assume the CAPM is true. Answer the following questions: a) Calculate the expected return on share B. b) Find the equation of the Capital Market Line (CML). c) Build a portfolio Q with B = 0 using actions A and B. Indicate weights (interpret your result) and expected return of portfolio Q.
Which has more value, (a) a portfolio composed of call options on ten different stocks or (b) a single call option on a portfolio composed of the same ten stocks? Assume the exercise price of (b) is equal to the sum of the exercise prices of the call options in (a) and that the expiration dates are identical. Explain your answer!
Given the following information, predict the put option's new price after the stock's volatility changes. Initial put option price = $6 Initial volatility = 25% Vega = 13 New volatility = 18% (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r
Data: S0 = 102; X = 115; 1 + r = 1.1. The two possibilities for ST are 146 and 84. Required: The range of S is 62 while that of P is 31 across the two states. What is the hedge ratio of the put? Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio? Given that the stock currently is selling at 102, calculate the put value.
1. An option is trading at $5.26, has a delta of .52, and a gamma of .11. what would the delta of the option be if the underlying increases by $.75? What would the delta of the option be if the underlying decreases by $1.05? Explain.
Reconsider the determination of the hedge ratio in the two-state model, where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for the following exercise prices: (a) 120, (b) 110, (c) 100, (d) 90? (e) What do you conclude about the hedge ratio as the option becomes progressively more in the money?
1. (Please make it quick) Draw payoff diagrams of the following portiolios as functions of the stock price ST. Show clearly the payoff from each individual security. Make sure to preserve the prices/values/premia appropriately, which are given as follows: Strike price K1 = 50 K2 = 75 K3 = 100 Price of the call 9 7 4 Price of the put 3 6 8

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