Consider the discrete-time binomial tree model with three periods of length 1, i.e. T = 3 and t = 0, 1, 2, 3. In each period the price can move up or down, St+1 is either uSt or dSt. Assume that the factor for moving up is u = 4/3, the factor for moving down is d = 3/4, and that the interest rate is r = 0.0. The initial stock price is So = 1. (a) Compute the price process (i.e. prices at all times and states) for a European Put option on the stock with strike price K = 1 and maturity T = 3. ΤΗ Σίμο St + (K – with ST (b) Compute the price at time t = 0 of the Australian option K- K = 1. Note: As this option is path dependent, you will not be able to use the recursive method, nor will you be able to use the CRR formula.

Consider the discrete-time binomial tree model with three periods of length 1, i.e. T = 3 and t = 0, 1, 2, 3. In each period the price can move up or down, St+1 is either uSt or dSt. Assume that the factor for moving up is u = 4/3, the factor for moving down is d = 3/4, and that the interest rate is r = 0.0. The initial stock price is So = 1. (a) Compute the price process (i.e. prices at all times and states) for a European Put option on the stock with strike price K = 1 and maturity T = 3. ΤΗ Σίμο St + (K – with ST (b) Compute the price at time t = 0 of the Australian option K- K = 1. Note: As this option is path dependent, you will not be able to use the recursive method, nor will you be able to use the CRR formula.

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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Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A(βA) to beta of B(βB).
Assume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15 a. If σM = 16%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) = ???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (βA) to beta of B (βB).
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Question 2. Foreign exchange marketsStatoil, the national…
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.
Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (bA) to beta of B (bB). please show all workings and not merely : Ra = 1/2 rbRf = 1/4 Ra
Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Suppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price? Solutions:
Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO
According to CAPM, the expected rate of return of a portfolio with a beta of 1.0 and an alpha of 0 is:a. Between rM and rf .b. The risk-free rate, rf .c. β(rM − rf).d. The expected return on the market, rM.
If put A has T = 0.5, X = 50, sigma = 0.2, and a price of 10, and put B has T = 0.5, X = 50, sigma = 0.2, and a price of 12, which put is written on a stock with a lower price (and why)?

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