Question

Consider the following information about Stocks A and B: Rate of Return if State Occurs State of Probability of Economy State of Economy Stock A Stock B Recession 0.26 0.03 − 0.34 Normal 0.56 0.20 0.14 Irrational exuberance 0.18 0.09 0.54 The market risk premium is 5 percent, and the risk-free rate is 3 percent. (Round your answers to 2 decimal places. (e.g., 32.16)) The standard deviation on Stock A's return is percent, and the Stock A beta is . The standard deviation on Stock B's return is percent, and the Stock B beta is . Therefore, based on the stock's systematic risk/beta, which Stock is "riskier".

Answer 1

Stock A:

Expected Return = 0.26 * 0.03 + 0.56 * 0.20 + 0.18 * 0.09
Expected Return = 0.1360 or 13.60%

Variance = 0.26 * (0.03 - 0.136)^2 + 0.56 * (0.20 - 0.136)^2 + 0.18 * (0.09 - 0.136)^2
Variance = 0.005596

Standard Deviation = (0.005596)^(1/2)
Standard Deviation = 0.0748 or 7.48%

Expected Return = Risk-free Rate + Beta * Market Risk Premium
0.1360 = 0.03 + Beta * 0.05
0.1060 = Beta * 0.05
Beta = 2.12

Stock B:

Expected Return = 0.26 * (-0.34) + 0.56 * 0.14 + 0.18 * 0.54
Expected Return = 0.0872 or 8.72%

Variance = 0.26 * (-0.34 - 0.0872)^2 + 0.56 * (0.14 - 0.0872)^2 + 0.18 * (0.54 - 0.0872)^2
Variance = 0.08591616

Standard Deviation = (0.08591616)^(1/2)
Standard Deviation = 0.2931 or 29.31%

Expected Return = Risk-free Rate + Beta * Market Risk Premium
0.0872 = 0.03 + Beta * 0.05
0.0572 = Beta * 0.05
Beta = 1.14

The standard deviation on Stock A's return is 7.48 percent, and the Stock A beta is 2.12. The standard deviation on Stock B's return is 29.31 percent, and the Stock B beta is 1.14. Therefore, based on the stock's systematic risk/beta, which Stock I is "riskier".