Consider the following information about Stocks A and B: Rate of Return if State

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 0.25 0.06 0.30 Normal 0.45 0.18 0.06 Irrational exuberance 0.30 0.12 0.45 The market risk premium is 8 percent, and the risk-free rate is 6 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, Stock A or B is "riskier".

Explanation / Answer

Answer a.

Stock A:

Expected Return = 0.25 * 0.06 + 0.45 * 0.18 + 0.30 * 0.12
Expected Return = 0.132 = 13.20%

Variance = 0.25 * (0.06 - 0.132)^2 + 0.45 * (0.18 - 0.132)^2 + 0.30 * (0.12 - 0.132)^2
Variance = 0.002376

Standard Deviation = (0.002376)^(1/2)
Standard Deviation = 0.0487 = 4.87%

Expected Return = Risk-free Rate + beta of Stock A * Market Risk Premium
0.132 = 0.06 + beta of Stock A * 0.08
beta of Stock A = 0.90

Answer b.

Stock B:

Expected Return = 0.25 * (-0.30) + 0.45 * 0.06 + 0.30 * 0.45
Expected Return = 0.087 = 8.70%

Variance = 0.25 * (-0.30 - 0.087)^2 + 0.45 * (0.06 - 0.087)^2 + 0.30 * (0.45 - 0.087)^2
Variance = 0.077301

Standard Deviation = (0.077301)^(1/2)
Standard Deviation = 0.2780 = 27.80%

Expected Return = Risk-free Rate + beta of Stock A * Market Risk Premium
0.087 = 0.06 + beta of Stock A * 0.08
beta of Stock A = 0.34

Answer c.

Stock B is least symmetric and Stock A is most symmetric

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