Question 5. You can invest in two risky assets, rị and r, and one risk-free asset, rf . The tworisky assets are uncorrelated, and values are E[r] = 8%, E[r2] = 6%, Var[r] = 10%,Var[r2] = 3%,and rf = 3%If you have a mean-variance optimizer with a risk aversion A = 2, what is the optimal portfolio?

The optimal portfolio can be found by solving the mean-variance optimization problem: Maximize:…

Question 5. You can invest in two risky assets, r₁ and r2 and one risk-free asset, r. The two risky assets are uncorrelated, and values are E[ri] = 8%, E[r₂] = 6%, Var[r₁] = 10%,Var[r₂] = 3%, and rf = 3% If you have a mean-variance optimizer with a risk aversion A = 2, what is the optimal portfolio?

Question 5. You can invest in two risky assets, r₁ and r2 and one risk-free asset, r. The two risky assets are uncorrelated, and values are E[ri] = 8%, E[r₂] = 6%, Var[r₁] = 10%,Var[r₂] = 3%, and rf = 3% If you have a mean-variance optimizer with a risk aversion A = 2, what is the optimal portfolio?

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. Suppose you plan to form your overall investment portfolio in two steps: STEP 1: Choose a portfolio of stocks with a zero position in the risk-free asset. STEP 2: Allocate your money between the portfolio from Step 1 and the risk-free asset. Suppose you can borrow and lend as much as you want at the risk-free rate in Step 2. Let Erp be the expected return of the Step 1 portfolio. Let Var(rp) be the variance of the return of the Step 1 portfolio. Let rf be the risk-free rate. How will you form the Step 1 Portfolio? Set the Step 1 portfolio to maximize Erp SettheStep1portfoliotominimizeVar(rp) Set the Step 1 portfolio to maximize Erp - Var(rp) Set the Step 1 portfolio to maximize the ratio Erp/Var(rp) Set the Step 1 portfolio to maximize the ratio (Erp- rf)/Var(rp) None of the above.
True or false? Beta of MSFT is 0.7 and beta of RCL is 1.33. One can conclude that unsystematic risk of RCL is higher than unsystematic risk of MSFT.
Asset A has an expected return of 20% and a standard deviation of 25%. The risk free rate is 10%. What is the reward-to- variability ratio (Sharpe ratio)? O 40 O .50 O .75 O.80
Assume that the risk-free rate, RF, is currently 9% and that the market return, rm, is currently 16%. a. Calculate the market risk premium. b. Given the previous data, calculate the required return on asset A having a beta of 0.4 and asset B having a beta of 1.8.
Calculate the optimal risky portfolio for the following cases when short-sales are allowed. Compute its expected return and the standard deviation of its returns. 1. Two risky assets: Rp = 3, R' = [6, 9], and 4 5 5 20 2. Three risky assets: Rp = 4, R' = [5,9, 8], and [10 0 0 E=0 40 0 0 20 3. Three risky assets: Rp = 5, R' = [12, 9, 8], and 40 10 -5] E= 10 20 0 5 0 30 4. Five risky assets: Rp = 2, R' = [5, 3, 18, 9, 2], and %3D 2 16 0. -12 5 -12 20 16 10 7 14 27 14 9. -13 8. 7 27 13
An investment has been found to have two different IRRs, one at 14% and the other at 20%. When a required return of 17% is used, the NPV of the investment is negative. Knowing this: a. What range of required returns will generate a negative NPV? b. What range of required returns will generate a positive NPV?
4. Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expected rates of return are 1, 2, and 3, respectively. For this example, short sales are allowed. Do the following: a. Find the minimum variance portfolio for the following desired expected portfolio rates of return: 1.0, 1.5, 2.0, 2.5, and 3.0. b. Sketch these on the return versus risk plot (you will need to use the standard deviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), where wi are the weights). c. Suppose we have a risk-free asset with a return of 2%. Modify your plot for b.
Which of the following statements are correct? I.The standard deviation is a measure of risk.II.The variance of yearly returns is roughly the variance of monthly returns multiplied with 12.III.To decide whether asset A is more risky than asset B we can either use their standard deviations or their variances. Group of answer choices II and III only I, II and III I and II only I and III only
Which of the following regression outcomes indicates the asset with the greatest total risk? • large beta, small R² • small beta, large R² • small beta, small R² large beta, large R² .
10) Given an optimal risky portfolio with expected return of 15%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL? A) 0.64 B) 0.27 C) 0.08 D) 0.38 E) 0.36 Provide explanation for the correct answer.
We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
Asset X has an expected return of 6% and a variance of 0.001. Asset Y has an expected return of 12% and the same variance as X (i.e., 0.001). The returns of assets X and Y are uncorrelated, and the risk-free rate is 3%. Find the variance of the highest Sharpe ratio portfolio that can be formed of the two risky assets X and Y.

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