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##### expected returns and the standard deviation Solution and computation

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solution

**Question**

Question;1. Consider the following scenario analysis involving asset;A and asset B;Economic Condition;Probability;Return on X;Return on Y;Boom;0.1;30%;12%;Accelerated Growth;0.2;20%;10%;Normal Growth;0.4;15%;9%;Slowdown;0.2;10%;8%;Recession;0.1;-50%;-4%;a) Compute the expected returns and the standard deviation;of returns for both assets. Then compute the correlation coefficient between;the returns on the two assets.;b) Find the expected return and the standard deviation of;the minimum variance portfolio of A and B, when short-selling is allowed.;2. There are two risky assets and one risk-free asset;available for INVESTMENT. The two risky assets have the following features;Asset X has an expected return of 25% and a variance of returns of 625%2;(0.04). Asset Y has an expected return on 20% and a standard deviation of;returns of 20%. The covariance between the returns on X and Y is 500%2;(0.0500). Short selling risky assets is NOT allowed. The risk-free asset OFFERS;a return of 8%.;a) Plot the expected returns and standard deviations of;returns of the three assets in a graph. Draw the set of feasible portfolios of;only the RISKY assets onto the same graph. Please note: no need to very;accurate in your drawing of the assets or the feasible set.;b) What is the optimal combination of risky assets that a;risk-averse investor should hold? (Remember that there is also a risk-free;asset available ? no calculations, just describe).;c) What level of standard deviation risk does an investor;have to hold in order to achieve an expected return of 18% on their portfolio?;3. You are given the following data on the returns of;companies D and E;Company D;Company E;Expected rate of return;20%;18%;Standard deviation of returns;40%;24%;The correlation coefficient between the returns on D and E;is rDE = 0.35.;a) What is the expected return and the standard deviation of;the MVP (round to two decimal places)?;Assume that D?s beta is bD = 1.4 and E?s beta is bE = 1.2;and the variance of MARKET returns is 200%2 (0.02).;b) What fraction of each company?s risk is firm-specific?;4. You have been provided with the following data on the;securities of three firms, the MARKET portfolio and the risk-free asset;Security;?i;?iM;?i;A;0.13;0.12;X1;0.90;B;0.16;X2;0.40;1.10;C;0.25;0.24;0.75;X3;MARKET;0.15;0.10;X4;X5;Risk-free asset;0.05;X6;X7;X8;where is the average;realized return of asset i in the recent past (equal to its expected return;today),?i is the standard deviation of asset i's returns,?iM is the;correlation of asset i's returns with the MARKET returns and?i is the beta of;asset i. Assume the CAPM holds true.;a) Fill in the missing values X1,?,X8 in the table without;using the information on average realized returns.;b) Provide an evaluation of the INVESTMENT performance of;the three firms and make justified investment recommendations.

Paper#48841 | Written in 18-Jul-2015

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