Stock Y has a beta of 1.5 and an expected return of 13 percent. Stock Z has a be

Question

Stock Y has a beta of 1.5 and an expected return of 13 percent. Stock Z has a beta of 0.95 and an expected return of 10.3 percent.
Required: What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? Stock Y has a beta of 1.5 and an expected return of 13 percent. Stock Z has a beta of 0.95 and an expected return of 10.3 percent.
Required: What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? Stock Y has a beta of 1.5 and an expected return of 13 percent. Stock Z has a beta of 0.95 and an expected return of 10.3 percent.
Required: What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other?

Explanation / Answer

expected return=Risk free rate+Beta*(MArket rate-Risk free rate)

Y:

0.13=Rf+1.5*(Rm-Rf)

0.13=1.5Rm-0.5Rf

Hence Rm=(0.13+0.5Rf)/1.5

Z:

0.103=Rf+0.95*(Rm-Rf)

0.103=0.95Rm+0.05Rf

0.103=0.95(0.13+0.5Rf)/1.5+0.05Rf

0.103=0.08233+0.3167+0.05Rf

Hence Rf=(0.103-0.08233)/(0.3167+0.05)=5.64%(Approx)

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