Problem 16-9 (Algo)We will derive a two-state call option value in this problem. Data: S = $210; X = $220; 1+r=1.10. The two possibilities for ST are $250and $130. The portfolio consists of 1 share of stock and 4 calls short.Required:a. The range of S is $120 while that of C is $30 across the two states. What is the hedge ratio of the call? (Round your answer to 2decimal places.)Hedge ratioAnswer is complete and correct.0.25b. Calculate the value of a call option on the stock with an exercise price of $220. (Do not use continuous compounding to calculatethe present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediatecalculations. Round your answer to 2 decimal places.)Answer is complete but not entirely correct.Call value$ 27.27

Part 2: Explanation:a. Step 1: Calculate the range of the stock price (S) and the call option price…

Answered: Problem 16-9 (Algo) We will derive a…

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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9. You are currently holding portfolio M. You are considering combining M with se- curity X, Y, or Z. There are three possible scenarios listed in the table below. (For instance, in scenario 1 which happens with 20% probability, M will deliver a return of -20%). Scenarios 1 3 Probability 20% 50% 30% Return of M -20% 0% 30% 15% 5% -5% Return of X -10% 0% 5% 5% 5% 0% Return of Y Return of Z (a) Which of X, Y, and Z is a risk-free security when considered on a standalone basis? (b) Now, you are considering investing 90% in your current portfolio M and in- vesting 10% into X, or Y, or Z.' Suppose your goal is only to reduce portfolio risk and you do not care about portfolio return. Which of X, Y, or Z will you choose, and why? (c) Recall that you can short securities in forming your new portfolio. Is it pos- sible to reduce portfolio risk by combining M and X by choosing appropriate portfolio weights? If so, please give examples of such portfolio weights. 'For instance, if you choose X,…
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.
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13.
16. Assume the betas for securities A, B, and C are as shown here. (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Security A B C .673 Beta If you have a portfolio with $30,000 invested in each of Investment A, B, and C, what is your portfolio beta? Using the portfolio beta and assuming a risk-free rate of 5%, what would you expect the return of your portfolio to be if the market earned 20.8% next year? Declined 19.6%? The beta of your portfolio is (Round to three decimal places.) The return of your portfolio to be if the market earned 20.8% is If the market earned 20.8%, the value of your portfolio is $ The return of your portfolio to be if the market declined 19.6% is If the market declined 19.6%, the value of your portfolio is $ 1.62 0.63 - 0.23 (Round to the nearest dollar.) %. (Round to two decimal places and enter as a negative number if the return decreased.) %. (Round to two decimal places and enter…
a) 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)?
You want your portfolio beta to be 1.16. Currently, your portfolio consists of $3,000 invested in stock A with a beta of 1.64 and $2,000 in stock B with a beta of 0.75. You have another $5,000 to invest and want to divide it between an asset with a beta of 1.48 and a risk-free asset. How much should you invest in the risk-free asset? Multiple Choice O O O O 1575 1500 225 1230 510
If the beta of Asset A is 2.2, the risk free rate is 2.5%, and the expected return on Asset A is 8%, what is the expected return on the market (Note: you want to use CAPM)? Group of answer choices 7.28% 5.00% 8.00% 16.80%
QUESTION 2. Consider a stock valued So at time t = 0, and taking only two possible values S1 = S, or Si = S1 at time t = 1, with S, < I1. a) Compute the initial portfolio allocation (a, 3) of a portfolio made of a units of stock and $B in cash, hedging the call option with strike price K e [S,,3¡] and claim payoff Si – K if Si = 3ı C = (Si – K)* $0 if S = S1, at time t = 1. b) Show that the risky asset allocation a satisfies the condition a € [0, 1]. c) Compute the Superhedging Risk Measure SRMc' of the claim C = (S1 – K)+.
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?
PLEASE ANSWER CORRECTLY ALL THE FALLOWING ******MAKE SURE YOU DONT NOT GIVE ME THE WRONG ANSWERS
A. An option is trading at $5.03. If it has a delta of -.56, what would the price of the option be if the underlying increases by $.75? What would the price of the option be if the underlying decreases by $.55? B. What type of option is this and how? C. With a delta of -.56, is this option ITM, ATM or OTM and how?

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