Consider the following information for three stocks, Stocks X, Y, and Z. The ret

Question

Consider the following information for three stocks, Stocks X, Y, and Z. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

STOCK EXPECTED RETURN STANDARD DEVIATION BETA
X 9.00% 15% 0.8
Y 10.75 15 1.2
Z 12.50 15 1.6

Fund P has half of its funds invested in Stock X and half invested in Stock Y. Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) What is the market risk premium ( - )? Round your answer to two decimal places.

Explanation / Answer

Here, Take Q has invested 1/3 of its funds in each of the three stock. Therefore here we can calculate the Expected return for Q funds.       Expected return   = W1*r1 + W2*r2 + W3*r3       Here, W1 , W2 , W3 are wighted of the funds invested, That is 1/3 and r1 , r 2 and r3 are expected return on the Stock X , Y and Z.       Expected return    = 1/3 * 9.00% + 1/3 * 10.75% + 1/3 * 12.50                                      = 3.00% + 3.58% + 4.17%                                      = 10.75%.       Expected return for the Q's investment is 10.75%. Here, expected return is equal to the required rate of return, From CAPM      Required rate of return   = Risk free rate + Market risk premium* beta. Calulation of Beta of the portfolio:            Portfolio beta     = W1*b1 + W2*b2 + W3*b3       Here, b1, b2, b3 are beta value of the individual stocks.           Portfolio beta      = 1/3*0.8 + 1/3*1.2 + 1/3 * 1.6                                         = 1.2                Here risk free rate is 5.5%.                  10.75% = 5.5% + Risk premium * 1.2                    5.25%    = Risk premium*1.2                   Risk premium = 5.25%/1.2                                             = 4.375% Therefore the market risk premium is 4.37%            Portfolio beta     = W1*b1 + W2*b2 + W3*b3       Here, b1, b2, b3 are beta value of the individual stocks.           Portfolio beta      = 1/3*0.8 + 1/3*1.2 + 1/3 * 1.6                                         = 1.2                Here risk free rate is 5.5%.                  10.75% = 5.5% + Risk premium * 1.2                    5.25%    = Risk premium*1.2                   Risk premium = 5.25%/1.2                                             = 4.375% Therefore the market risk premium is 4.37%

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