Stock Y has a beta of 1.8 and an expected return of 18.2 percent. Stock Z has a beta of .8 and an expected return of 9.6 percent. If the risk-free rate is 5.2 percent and the market risk premium is 6.7 percent, the reward-to-risk ratios for stocks Y and Z are

The reward to risk ratio for stock Y is 7.22%

The reward to risk ratio  for stock Z is 5.50%

Explanation:

First and foremost, it is very important to note that the reward-to-risk ratio of a stock is the risk premium paid by the stock divided by its asset Beta.

The risk premium is calculated as stock expected return minus risk free rate

The risk premium is denoted by (rm – rrf) in Capital Asset Pricing Model of Modgiliani and Miller

For stock Y risk premium is 18.2%-5.2%=13%

For stock Z risk premium is 9.6%-5.2%=4.40%

For stock Y reward to risk ratio=13%/1.8=7.22%

For stock Z reward to risk ratio=4.40%/0.8=5.50%

Hence stock Y has a higher reward to risk ratio

Y=1.05    Z=0.91

Explanation:

We calculate the risk for the stocks first

Ry=5.2+1.8(6.7)=17.26

Rz=5.2+0.8(6.7)=10.56

Then we calculate the reward for every risk the stock takes

so Y= 18.2/17.26

       =1.05

   Z=9.6/10.56

      =0.91

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