Consider the following information: Rate of Return If State Occurs State of Prob

Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .64 .10 .18 .36 Bust .36 .10 .04 .07 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. What is the variance of a portfolio invested 15 percent each in A and B and 70 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) Variance

Explanation / Answer

Expected return for each stock=prob1*return1 +prob.2 *return2

Avg. all the expected returns to achieve portfolio return with equal weights

Calculate variance for each stock by summing Prob.*(Return-Expected return)^2 for eg. for stock B=(0.64*(0.18-0.13)^2+0.36*(0.04-0.13)^2)=-0.0045

Once Variance for each stock is calculated, calculate the port variance =sum of all Weight^2*Variance=0.15^2*0 +0.15^2*0.004516+0.70^2*0.042624=0.020987

Probability A B C Boom 0.64 0.1 0.18 0.36 Bust 0.36 0.1 0.04 -0.07 Expected Return 0.10 0.13 0.21 Portfolio return 14.49% Variance 0 0.004516 0.042624 Weight 15% 15% 70% Weight wise Variance 0 0.000102 0.020886 Port. Variance 0.020987

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