Question

Question: Stock Y has a beta of 1.4 and an expected return of 15.1 percent. Stock Z has a beta of .7 and an expected return of 8.6 percent. If the risk-free rate is 5.0 percent and the market risk premium is 6.5 percent, the reward-to-risk ratios for stocks Y and Z are 7.21%  and 5.14 % percent, respectively. Since the SML reward-to-risk is ________ percent, Stock Y is undervalued  and Stock Z is overvalued.

Answer 1

Substituting the value given for each stock in CAPM [E(R)] formula, we would get:

E(R) = Risk free rate + (Beta * Market risk premium)

So, accordingly for Stock Y:

E(RY) = 0.05 + (1.4 * 0.065)

= 0.05 + 0.091 = 0.141 or 14.10%

It is given in the problem that the expected return of Stock Y is 15.1%, but according to the CAPM, the return of the stock based on its level of risk should be 14.10%. This means the stock return is too high, given its level of risk. Stock Y plots below the SML and is undervalued. In other words, its price must increase to decrease the expected return to 14.10%.

For Stock Z, we would get:

E(RZ) = 0.05 + (0.7 * 0.065)

= 0.05 + 0.0455 = 0.0955 or 9.55%

The return given for Stock Z is 8.6%, but according to the CAPM, the expected return of the stock should be 9.55% based on its level of risk. Stock Z plots below the SML and is overvalued. In other words, its price must decrease to increase the expected return to 9.5%.