Question

Rate of Return If State Occurs State of Probability of State of Economy Economy Stock A Stock B Stock C .55 .06 14 Boom Bust .45 .34 -.07 10 .02 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the variance of a portfolio invested 22 percent each in A and B and 56 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 161616.)

a. is 10.65% but I'm not sure how to solve for the variance.

please write out your solution and don't use excel:)

Answer 1

b. The expected Return in case of boom =22%*0.06+22%*0.14+56%*0.34 =23.44%
The expected Return in case of bust =22%*0.10+22%*0.02+56%*-0.07 =-1.28%
Expected Return =0.55*23.44%+0.45*-1.28% =12.316%
Variance =0.55*(23.44%-12.316%)^2+0.45*(-1.28%-12.316%)^2=0.015124