Problem 4. Consider tuo scenarios, wi with probability and w with probability Suppose that thereturn on sonie security is Kretum on another security is Kuch that the tu0 socurities hane the same risk= -2% in the first scenario and K = 6% in the second scenario. If the= -3% in the first scenario, find the return K in the other scenario

Here, w1 is 1/4 or 25% w2 is 1/4 or 75% K1w1 of first security is -2% K1w2 of first security is 6%…

Answered: Problem 4. Consider two scenarios, wi…

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 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.)
The beta of a risk-free security is _____ and the beta of the overall market is _____: a. 0; 1. b. 0; 0. c. 1; 0. d. 1; 1.
The beta of the risk free security is: a) 0 b) > 0 but < 1 c) 1 d) > 1
2. Suppose that you have a riskfree asset and N risky assets for investment. The rate of return on the riskfree asset is r,, while the (Nx1) vector of the rate of return on the N risky assets is r, which is multivariate normal, i.e., r N(u, E). Your utility function for a portfolio that consists of the riskfree asset and the N risky asset is u(r,)=r,-=o, 2 Suppose that the sum of investment proportions on the riskfree and risky assets is one. Answer the following question. A. What is your optimal investment proportion in the risky assets? How is your investment on the riskfree asset affected by different values of 2? B. Suppose that there is only one risky asset i. Show the effects of the Sharpe ratio (4,/0, ) on the investment proportion in the risky asset.
Assuming your utility function U = E(r) - Ao². Consider the investments shown in the table. If your risk aversion coefficient is -2, which investment would you choose? Investment E[r] #1 #2 #3 #4 #2 #3 #4 #1 12% 15% 15% 24% σ 40% 40% 30% 40%
There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.
Two sets of security X and Y have the following characteristics. Security X Probability Return Securty Y Probability Return 0.1 30% 0.5 -20% 0.2 20% 0.25 10% 0.4 10% 0.30 20% 0.2 05% 0.30 30% 0.1 -10% 0.10 40% Required. Calculate the expected return for each Security. Calculate the standard deviation for each security.
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
Based on the following probability distribution, what is the security’s expected return? State Probability r 1 0.2 –5.0% 2 0.4 10.0 3 0.4 30.0
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.)
Consider a one-period model with N = {1,2,3} and two risky assets S1, S2 whose with current prices are 71 = 42 and 12 = 23 respectively. At time one, the price of S1 is believed to be either 44, 43, or 40 while the price of S2 is believed to be either 27, 22, or 20. Suppose that the risk-free interest rate is 3%. What is the unique risk-neutral probability measure Q in this situation? Select one: О а. Q(1) — 0.35, Q(2) — 0.27, Q(3) — 0.38 O b. Q(1) = 0.63, Q(2) = 0.34, Q(3) = 0.03 Ос. Q(1) — 0.25, Q(2) — 0.62, Q(3) — 0.13 O d. Q(1) = 0.35, Q(2) = 0.62, Q(3) = 0.03
The beta of the risk-free asset is: 0.5 1.0 -1.0 2.0

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