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	10.32	%	15	%	0.9
Y	11.28		15		1.1
Z	13.68		15		1.6

Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 6%, and the market is in equilibrium. (That is, required returns equal expected returns.)

What is the market risk premium (r_M - r_RF)? Round your answer to two decimal places.
%

What is the beta of Fund Q? Round your answer to two decimal places.
  

What is the expected return of Fund Q? Round your answer to two decimal places.
%

Answer 1

Standarod Stock Expected Return Deviation Beta 10.32% 11.28% 13.68% 15% 15% 15% 0.9 1.1 1.6 As Per CAPM, required return of stocks can be calculated as r(s)-r + β* (rm-r.) 10 Since market is at equillibrium, therefore expected return will be equal to the required return 12 Since required return, risk free rate and beta of each stock is known then market risk premium can be calculated as follows: (rm-ri) 14 15 16 17 (r(s) /B Risk free rate 696 Standard 19 Stock Expected Return Deviation Beta 10.32% 11.28% 13.68% 15% 15% 15% Risk Premium 4.80% 4.80% 4.80% 0.9 1.6 Hence Market Risk Premium is 4.80% Calculation of Beta of the portfolio The beta of a portfolio is the weighted sum of the beta of individual assets. 26 27 29 Portfolio Beta, A, Σ11, XB 31 32 Where w is the weight of individual asset and A is the corresponding asset beta Stock Beta Weight 35 36 37 38 39 0.9 1.1 1.6 33% 33% 33% Portfolio Beta 1.20 SUMPRODUCT (D35:D37,E35:E37 41 42 43 Hence Portfolio Beta is 1.20

Calculation of Expected Rate of return Portfolio return can be calculated as follows: 45 Expected portfolioreturn, rp- 47 Where wiand r are the weights and return of assets A 50 51 52 53 54 Weight and returns of the stocks of the portfolio are as follows: Expected Return Weights 10.32% 33.33% 11.28% 33.33% 13.68% 33% 57 Hence Portfolio return is calculated as follows: Portfolio expected return -Sum of product of weight and return of each asset 11.76% :SUMPRODUCT(D55:F55,D54:F54) Hence Portfolio return is 11.76%