Question 13.S-TP.4: CAPM Suppose the risk-free rate is 8 percent. The expected r...

Fundamentals of Corporate Finance

CAPM Suppose the risk-free rate is 8 percent. The expected return on the market is 16 percent. If a particular stock has a beta of .7, what is its expected return based on the CAPM? If another stock has an expected return of 24 percent, what must its beta be?

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Because the expected return on the market is 16 percent, the market risk premium is .16− .08 = .08, or 8%. The first stock has a beta of .7, so its expected return is .08 + .7 × .08 = .136, or 13.6%.

For the second stock, notice that the risk premium is .24% − .08 = .16, or 16%.
Because this is twice as large as the market risk premium, the beta must be exactly equal to 2. We can verify this using the CAPM:

E(R_{i})= R_f + [E(R_{M})-R_{f}]\times \beta _{i}

.24 = .08 + (.16 − .08) × $\beta _{i}$

$\beta _{i}$ = .16/.08

= 2.0

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