Question

The following table provides stock return distributions in the coming year for three companies, A, B, and C.

State of Economy	Probability of State of Economy	Stock A Rate of Return	Stock B Rate of Return	Stock C Rate of Return
Normal	0.65	14.3%	16.7%	18.2%
Recession	0.35	-9.8%	5.4%	-26.9%

(a) Consider a portfolio that is invested 40 percent in Stock A, 30 percent in Stock B, and the remainder in Stock C. What is the expected return on the portfolio?

(b) What is the standard deviation on the portfolio returns above?

Answer 1

a) Expected return of Portfolio in Normal=40%*Return of Stock A+30%*Return of Stock B+30%*Return of Stock C
=40%*14.3%+30%*16.7%+30%*18.2% =16.19%
Expected return of Portfolio in Recession=40%*Return of Stock A+30%*Return of Stock B+30%*Return of Stock C
=40%*-9.8%+30%*5.4%+30%*-26.9% =-10.37%

Expected Return on Portfolio =0.65*16.19%+0.4*-10.37% =6.3755% or 6.38%

b) Standard Deviation of Portfolio Returns =(0.65*(16.19%-6.3755%)^2+0.35*(-10.37%-6.3755%)^2)^0.5 =12.68%