Question 13.S-TP.3: Risk and Return Suppose you observe the following situation:...

If we compute the reward-to-risk ratios, we get (.22 − .07)/1.8 = .0833, or 8.33% for Cooley versus 8.4% for Moyer. Relative to that of Cooley, Moyer’s expected return is too high, so its price is too low. If they are correctly priced, then they must offer the same reward-to-risk ratio. The risk-free rate would have to be such that:

(.22 − R_{f})/1.8 = (.2044 − R_{f})/1.6

With a little algebra, we find that the risk-free rate must be 8 percent:

.2% − R_{f} = (.2044 − R_{f})(1.8/1.6)
.22 − .2044 × 1.125 = R_{f} − R_{f} × 1.125
R_{f} = .08, or 8%