3. Consider the following information for two assets that are perfectly negatively correlated: Expected Return Standard Deviation 10 16 Asset A B 8 11 What is the minimum standard deviation that can be achieved by forming a portfolio of these two assets? Explain (either analytically with math or in words).

3. Consider the following information for two assets that are perfectly negatively correlated: Expected Return Standard Deviation 10 16 Asset A B 8 11 What is the minimum standard deviation that can be achieved by forming a portfolio of these two assets? Explain (either analytically with math or in words).

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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The expected value, standard deviation of returns, and coefficient o below.) \table[[Asset A],[Possible Outcomes,Probability,Returns (%)
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.
Consider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.
Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.
Consider the following linear regression model: (R₁-r)= a; + b(RMkt - rf) + e; The b; in the regression: O measures the deviation from the best fitting line and is zero on aver- measures the sensitivity of the security to market risk. measures the diversifiable risk in returns.
You are given the following data about Asset A and Asset B. Asset A Asset B Expected returns 8.6% 7.9% Standard Deviation 3.8% 4.6% Assuming that an investor is to choose between Asset A or Asset B, explain which asset a rational investor will choose. c) With the use of a diagram, explain why an investor will always choose a point on the SML line.
Expected retun and standard deviation. Use the following information to answer the questions: a. What is the expected return of each asset? b. What is the variance and the standard deviation c. What is the expected return of a portfolio with 1 1 Data Table d. What is the portfolio's variance and standard de - X Hint Make sure to round all intermediate calculatio Swers yo (Click on the following icon D in order to copy its contents into a spreadsheet.) a. What is the expected return of asset J? (Round to four decimal places.) Return on Return on Return on Probability of State State of Asset J in Asset Kin State 0.200 0.140 0.040 Asset L in Economy State State Вoom 0.28 0.070 0.260 0.180 Growth 0.37 0.25 0.070 Stagnant 0.070 0.060 -0.210 Recession 0.10 0.070 -0.100 Print Done
Which of the following statements is correct? Select one: a. Assuming a correlation coefficient of 0 between two assets, the portfolio’s standard deviation will be lower than the weighted average of the individual assets’ standard deviation. b. Assuming a correlation coefficient of +1 between two assets, the portfolio’s standard deviation will be lower than the weighted average of the individual assets’ standard deviation. c. Assuming a correlation coefficient of +1 between two assets, the portfolio’s standard deviation will be the same as the weighted average of the individual assets’ standard deviation. d. Both A and C. Clear my choice
9) The measure of risk in a Markowitz efficient frontier is A) specific risk. B) standard deviation of returns. C) reinvestment risk. D) beta. Provide explanation for the accurate answer.
Given the following probability distribution for assets X and Y, compute the expected rate of return, variance, standard deviation, and coefficient of variation for the two assets. Which asset seems to be a better investment?
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.
Suppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.

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