Problem 13-18 Reward-to-Risk Ratios [LO4]

Problem 13-18 Reward-to-Risk Ratios [LO4]

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.​

  

There are two ways to correctly answer this question. We will work through both. First, we can use the CAPM. Substituting in the value we are given for each stock, we find:

E(RY) = .050 + .065(1.4) = .1410, or 14.10%

It is given in the problem that the expected return of Stock Y is 15.1 percent, but according to the CAPM, the return of the stock based on its level of risk, the expected return should be 14.10 percent. This means the stock return is too high, given its level of risk. Stock Y plots above the SML and is undervalued. In other words, its price must increase to reduce the expected return to 14.10 percent. For Stock Z, we find:

E(RZ) = .050 + .065(.7) = .0955, or 9.55%

The return given for Stock Z is 8.6 percent, but according to the CAPM, the expected return of the stock should be 9.55 percent 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 9.55 percent.

We can also answer this question using the reward-to-risk ratio. All assets must have the same reward-to-risk ratio. The reward-to-risk ratio is the risk premium of the asset divided by its β. We are given the market risk premium, and we know the β of the market is one, so the reward-to-risk ratio for the market is .065, or 6.5 percent. Calculating the reward-to-risk ratio for Stock Y, we find:

Reward-to-risk ratio Y = (.151 – .050)/1.4 = .0721

The reward-to-risk ratio for Stock Y is too high, which means the stock plots above the SML, and the stock is undervalued. Its price must increase until its reward-to-risk ratio is equal to the market reward-to-risk ratio. For Stock Z, we find:

Reward-to-risk ratio Z = (.086 – .050)/.7 = .0514

The reward-to-risk ratio for Stock Z is too low, which means the stock plots below the SML, and the stock is overvalued. Its price must decrease until its reward-to-risk ratio is equal to the market reward-to-risk ratio.