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##### Computation of expected returns and the standard deviation

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Question;1. Consider the following scenario analysis involving asset;A and asset B:Economic ConditionProbabilityReturn on XReturn on YBoom0.130%12%Accelerated Growth0.220%10%Normal Growth0.415%9%Slowdown0.210%8%Recession0.1-50%-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 DCompany EExpected rate of return20%18%Standard deviation of returns40%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 MARKETreturns 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 MARKETportfolio and the risk-free asset:Security?i?iM?iA0.130.12X10.90B0.16X20.401.10C0.250.240.75X3MARKET0.150.10X4X5Risk-free asset0.05X6X7X8where 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 MARKETreturns 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.;="msonormal">

Paper#48940 | Written in 18-Jul-2015

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