A stock has an expected return of 10.2 percent, the risk-free rate is 3.9 percent, and the market risk premium is 7.2 percent. What must the beta of this stock be? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Beta= 0.88

Explanation:

The Capital Asset pricing Model (CAPM) can be used to determined the beta.

According to the Capital Asset pricing Model the return on equity is dependent on the level of reaction of the the equity to changes in the return on a market portfolio.

These changes are captured as systematic risk. The magnitude by which a stock is affected by systematic risk is measured by beta.  

Under CAPM, Ke= Rf + β(Rm-Rf)  

Rf-risk-free rate (treasury bill rate), β= Beta, Rm= Return on market.  

Ke- expected return.

Note that (Rm-Rf) is known as equity risk premium

Using this model,  

10.2%= 3.9% + β× (7.2%)

0.102=0.039 + 0.072β

collect like terms

0.072β = 0.102 -0.039

0.072β = 0.063

Divide both sides by 0.072

 β = 0.063 /0.072

β= 0.875

Beta= 0.88

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