Question

The required return on a stock is 15.25% while the required return on the market portfolio is 10%. If the real risk-free rate is 0.6% and investors expect an inflation rate of 2.4%, what is the beta of the stock?

Answer 1

ERi ​= Rf ​+ βi ​( ERm ​− Rf ​)

where:ERi​=expected return of investment

         Rf​=risk-free rate

         βi​=beta of the investment

        (ERm​−Rf​)=market risk premium​

15.25% = 3% + βi ( 10% - 3% )

12.25% = 7% βi

βi = 1.75

NOTE : The risk free rate given in the question is real so the risk free return for our beta calculation will be after adding inflation rate i.e. 0.6% + 2.4% = 3%.

If risk free rate given in the question is nominal then we ignore the inflation rate as it already included the effect of inflation premium.