Question

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 ________.

		a) 1.25; 1.41
		b) 1.47; 1.76
		c) 1.21; 1.76
		d) 1.25; 1.89
		e) 1.47; 1.41

Answer 1

Option (A) is correct

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 is:

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 formula, we get,

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

Expected return = 0.00388 + 0.08208 + 0.03744 = 0.1234

As per CAPM,

Expected or required return = Risk free rate + Beta * Market risk premium

Putting the given values in the above formula, we get,

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 = 1.41