Please show your work Given the following probability distributions for Stocks A
ID: 2645929 • Letter: P
Question
Please show your work
Given the following probability distributions for Stocks A and B, and the market portfolio, M: State Probability Return on A Return on B Return on M Bust 015 -015 0.00 -0.12 Normal 0.50 0.12 0.06 0.08 Boom 0.35 0.20 0.10 0.16 You construct a 2-stock portfolio by investing $9,000 in Stock A and $6,000 in Stock B. (a) Compute the expected rate of return, beta, and standard deviation of the 2-stock portfolio. given that Stock A has a beta of 1.61 and Stock B has a beta of 0.36. (b) Compute the required (CAPM) rate of return on the 2-stock portfolio, and explain your investment recommendation on this 2-stock portfolio according to the CAPM analysis, given that the risk-free rate and the inflation rate are, respectively, 0.015 and 0.020.Explanation / Answer
Expected rate of return of the two Stock portfolio = W1R1+W2R2+....+WnRn
Expected rate of return of the two Stock portfolio
Weights of the two Stock = 60:40
Bust = E(Rp) = (.6)x(-0.25)+(.4)x(0)
Bust= E(Rp) = -0.15
Normal E(Rp) = (.6)x(0.12)+(0.4)x(0.06)
Normal E(Rp) = 0.096
Boom E(Rp) = (.6)x(0.20)+(0.4)x(0.10)
Boom E(Rp) = 0.16
Expected rate of return of the portfolio = (0.15)x(-0.15)+(0.50)x(0.096)+(0.35)x(0.16)
Expected rate of return of the portfolio = -0.0225+0.048+0.056 = 0.0815 or 8.15%
Beta of the two Stock Portfolio = (1.61 x 0.60)+(0.36 x 0.40) =1.11 (Beta of Indivdual Stock multiplied by their weights and Added together to arrive at portfolio beta
Standard Deviation of the Two Stock Portfolio
=0.15*(-0.15 - 0.0815)^2+0.50*(0.096-0.0815)^2+0.35*(0.16-0.0815)^2
=(0.01030075)^1/2 = 0.00515 = 0.52%
E(r) = Risk free Rate+beta of stockx(Market return-Risk free rate)
E(r)=0.015+1.11*(0.0815 - 0.015)
E(r) = 0.088815 or8.89% adjusted for infaltion = (1+Return)/(1+infaltion rate)-1
= (1+0.089)/(1+0.020) - 1
=0.067 or 6.76%