Suppose you observe the following situation State of Probabi

Suppose you observe the following situation: State of Probability of Return if State Occurs Economy State Stock A Stock B Boom .17 ? .05 ? .06 Normal .72 .18 .17 Bust .11 .46 .31 a. Calculate the expected return on each stock. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return Stock A % Stock B % b. Assuming the capital asset pricing model holds and Stock A’s beta is greater than Stock B’s beta by .31, what is the expected market risk premium? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Solution

Answer a.

Stock A:

Expected Return = 0.17 * (-0.05) + 0.72 * 0.18 + 0.11 * 0.46
Expected Return = 0.1717
Expected Return = 17.17%

Stock B:

Expected Return = 0.17 * (-0.06) + 0.72 * 0.17 + 0.11 * 0.31
Expected Return = 0.1463
Expected Return = 14.63%

Answer b.

Stock A:

Expected Return = Risk-free Rate + Beta of Stock A * Market Risk Premium
0.1717 = Risk-free Rate + Beta of Stock A * Market Risk Premium

Stock B:

Expected Return = Risk-free Rate + Beta of Stock B * Market Risk Premium
0.1463 = Risk-free Rate + Beta of Stock B * Market Risk Premium

Subtracting above equations:

0.0254 = Market Risk Premium * (Beta of Stock A - Beta of Stock B)
0.0254 = Market Risk Premium * 0.31
Market Risk Premium = 0.0819
Market Risk Premium = 8.19%