Question

Returns and Standard Deviations - Consider the following information:

State of Economy	Probability of State of Economy	Rate of Return If State Occurs
		Stock A	Stock B	Stock C
Boom	.10	.35	.45	.27
Good	.60	.16	.10	.08
Poor	.25	−.01	−.06	−.04
Bust	.05	−.12	−.20	−.09

1. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio?

2. What is the variance of this portfolio? The standard deviation?

Answer 1

a. Expected return of Boom =30%*0.35+40%*0.45+30%*0.27 =36.60%
Expected return of Good =30%*0.16+40%*0.10+30%*0.08 =11.20%
Expected return of Boom =30%*-0.01+40%*-0.06+30%*-0.04 =-3.90%
Expected return of Boom =30%*-0.12+40%*-0.20+30%*-0.09 =-14.30%

Expected Return of the portfolio =0.10*36.60%+0.60*11.20%+0.25*-3.90%+0.05*-14.30% =8.69%

b. Variance of this portfolio =0.10*(36.60%-8.69%)^2+0.60*(11.20%-8.69%)^2+0.25*(-3.90%-8.69%)^2+0.05*(-14.30%-8.69%)^2
=0.014773

Standard Deviation =0.014773^0.5 =12.15%