Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Recession .04 .097 .102 Normal .72 .114 .133 Boom .24 .156 .148 The market risk premium is 7.4 percent, and the risk-free rate is 3.1 percent. The beta of Stock A is and the beta of Stock B is .

The beta of Stock A is 1.25 and the beta of Stock B is 1.41.

Explanation:

First we will calculate the expected return and then we will use the CAPM equation to find the required beta of both stocks.

The formula for Expected return = p1 *r1 + p2*r2 + p3*r3 . Where p1, p2, p3 are the probabilities & r1, r2 and r3 are the returns for stock

For Stock A

Now, putting the given values of probabilities & returns in the above  

Expected return = (0.04 * 0.097) + (0.72 * 0.114) + (0.24 * 0.156)

Expected return = 0.00388 + 0.08208 + 0.03744  

Expected return =  0.1234

As per CAPM, Expected or required return = Risk free rate + Beta * Market risk premium  

0.1234 = 3.1% + Beta * 7.4%

0.1234 = 0.031 + Beta * 0.074

0.1234 - 0.031 = Beta * 0.074

0.0924 = Beta * 0.074

Beta = 0.019752 / 0.074

Beta = 1.25

Stock B

Expected return = (0.04 * 0.102) + (0.72 * 0.133) + (0.24 * 0.148)

Expected return = 0.00408 + 0.09576 + 0.03552 = 0.13536

As per CAPM equation

0.13536 = 3.1% + Beta * 7.4%

0.13536 = 0.031 + Beta * 0.074

0.13536 - 0.031 = Beta * 0.074

0.10436 = Beta * 0.074

Beta = 0.10436 / 0.074

Beta = 1.41

c.

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