Portfolio returns and deviations. Consider the following information on a portfo
ID: 2624092 • Letter: P
Question
Portfolio returns and deviations. Consider the following information on a portfolio of three stocks:
State of Probability of Stock A Rate of return Stock B ROR Stock C ROR
Economy State of Economy
Boom .25 .02 .32 .60
Normal .60 .10 .12 .20
Bust .15 .16 -.11 -.35
a. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio
Explanation / Answer
Expected return of A = (.25 *2%) + 0.6*10% + (.15 *.16) = 8.90%
Stock B:
Expected return of B = (.25 *32%) + 0.6*12% + (.15 *(-.11))= 13.55%
Stock C
Expected return of C = (.25 *60%) + 0.6*20% + (.15 *(-.35))= 21.75%
Portfolio:
Expected return in Boom = 40%*0.02 + 40%*0.32+ 20%*0.60= 25.60%
Expected return in Normal = 40%*0.1 + 40%*0.12+ 20%*0.20= 12.80%
Expected return in Bust= 40%*0.16 + 40%*(-0.11)+ 20%*(-0.35)= -5%
Expected return of portfolio = 40%*8.9% + 40%*13.55%+ 20%*21.75%= 13.33%
Portfolio variance = 0.25*(25.60%-13.33%)^2 + 0.6*(12.80%-13.33%)^2 + 0.15*(-5%-13.33%)^2=0.008821
Portfolio standard deviation = sqrt(0.008821)= 9.39%
b. expected risk premium on the portfolio = 13.33%-3.75%= 9.58%