Question

Stock a has a beta of 1.47 while stock b has a beta of 1.08 and an expected return of 13.2 percent. what is the expected return on stock a if the risk-free rate is 4.5 percent and both stocks have equal reward-to-risk premiums

Answer 1

The expected return of stock A is 16.34%.

The formula for computing expected return according to CAPM is:

Expected Rate of Return = Rf +β (Rm-Rf)

The underlined term (Rm - Rf) in the equation above is known as the reward-to-risk premium. This represents the excess return earned by an investment over and above the risk free rate.

From the data given in the question, we can arrive at the reward-to-risk premium of stock b.

Let the reward to risk premium (Rm - Rf) be 'x'.

Substituting the values in the CAPM equation we get,

0.132 = 0.045+1.08x

Solving for x we get,

0.087= 1.08x

x = 0.080555556 (0.087/1.08)

Now, we substitute this value of 'x' again in this CAPM, but this time with stock a's beta.

Expected Return = 0.045+ (1.47 × 0.080555556 )

= 0.045 + 0.118416667

= 0.163416667 or 16.34%