Question

5. You are using regression analysis to estimate the equity beta for an electric utility. Suppose the risk-free rate of return is zero, and you run the CAPM regression, obtaining a constant term equal to 0.5 and a slope parameter equal to 0.8. Have you implemented the CAPM regression correctly? Explain why or why not.

Answer 1

Yes, we have implemented the CAPM regression correctly. Calculating Beta is not dependend on whether risk free rate value is zero or not.

Beta formula is given by ;

Beta(β)= Covariance(Re,Rm)/Variance(Rm)

From the equation it can be seen that Beta is the sensitivity of the individual stock returns compared to market returns.

ie; we can find beta by simply running a regression against the market return as independend parameter and stock returns as dependend parameter. The slope of this regression is Beta which can be used in CAPM model to find out the expected returns of the stock.

Hence even if Risk free rate is zero, the approach to calculate beta through regression will be correct and can be used in CAPM model. Provided regression is done with stock return and market index returns and not with stock price and market index.

Once Beta is calculated we can change CAPM Model to Rs=Rf+Beta(Rm-Rf)

Rs=Stock returns ; Rf=Risk free rate ; Rm=Market return/market index return

since Rf=0 in this scenario; Rs=Beta*Rm