The probability the economy will boom is 20 percent,while it is 70 percent for a normal economy,and 10 percent for a recession.Stock A will return 18 percent in a boom,11 percent in a normal economy,and lose 10 percent in a recession.Stock B will return 9 percent in boom,7 percent in a normal economy,and 4 percent in a recession.Stock C will return 6 percent in a boom,9 percent in a normal economy,and 13 percent in a recession.What is the expected return on a portfolio which is invested 20 percent in Stock A,50 percent in Stock B,and 30 percent in Stock C?
A)7.40 percent
B)8.25 percent
C)8.33 percent
D)9.45 percent
E)9.50 percent

Question

Quizplus · Accepted Answer

To calculate the expected return on the portfolio, we multiply the returns of each stock by their respective probabilities and portfolio weights, then sum these products. For Stock A: $E[A] = 0.20 \times 18\% + 0.70 \times 11\% + 0.10 \times (-10\%)$. For Stock B: $E[B] = 0.20 \times 9\% + 0.70 \times 7\% + 0.10 \times 4\%$. For Stock C: $E[C] = 0.20 \times 6\% + 0.70 \times 9\% + 0.10 \times 13\%$. Then, calculate the weighted average for the portfolio: $E[Portfolio] = 0.20 \times E[A] + 0.50 \times E[B] + 0.30 \times E[C]$. Plugging in the numbers and calculating gives an expected return of 8.25 percent.

The Probability the Economy Will Boom Is 20 Percent,while It