Question

Consider the following information: Rate of Return if State Occurs Probability of State of Economy 0.76 State of Economy Stock A Stock B Stock C 0.25 Вoom 0.33 0.09 0.15 Bust 0.24 0.19 -0.01 Requirement 1 What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.) (Click to select) Requirement 2: What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.) (Click to select)

Answer 1

calculate the expected return of each individual stock.

• 0.76 x 0.33 + 0.24 x 0.15 = 0.2868 = 28.68%
• 0.76 x 0.25 + 0.24 x 0.19 = 0.2356 = 23.56%
• 0.76 x 0.09 + 0.24 x -0.01 = 0.66 = 66%

multiply each individual expected stock return by the assigned weight

• 28.68% x (1 / 3) = 9.56%
• 23.56% x ( 1 / 3) = 7.83%
• 66% x ( 1 /3 ) = 22%

sum of the products for the expected return

• expected portfolio return = 9.56% + 7.83% + 22% = 39.39%

2: calculate the expected returns for the portfolio in the boom and bust states.

• ( 0.20 x 0.33 ) + ( 0.20 x 0.25) + (0.60 x 0.09) = 16.4%
• (0.20 x 0.15) + (0.20 x 0.19) + (0.60 x -0.01) = 6.2%

calculate the total portfolio expected return  

(0.76 x 16.4%) + (0.24 x 6.2%) = 13.9%

calculate deviation of boom and bust portfolios expected return.

16.4% - 13.9% = 2.5%

6.2% - 13.9% = 7.7%

square the deviation of the boom and bust portfolios

2.5%² = 0.000625

7.7%² = 0.005929

multiply each square deviation by its respective probabilitty

• 0.000625 x 0.76 = 0.000475
• 0.005929 x 0.24 = 0.00142296

sum of products for variance

• portfolio variance = 0.000475 + 0.00142296 = 0.00189796 = 0.18%