capm - Excess, Residual and Active Return

in CAPM. What's the difference between these different types of returns?

• Active return


• Excess return


• Residual return

Answer

Active return: $R-R_m$ i.e. your security (or portfolio) compared to the market portfolio. Used to judge performance before the CAPM was invented

Excess return: $R-R_f$ the security compared to the risk free rate, appears on the left hand side of the CAPM equation.

Excess return on the market: $R_m-R_f$, appears on the right hand side

In words the CAPM says that "there is a linear relationship between the excess return and the excess return on the market" $R-R_f=\beta(R_m-R_f)+\epsilon_i$

Residual return: $R-R_f-\beta(R_m-R_f)$ i.e. the part of your return which the CAPM does not explain, or your outperformance versus the CAPM; its estimated value over a period of time is called Alpha. This is what is advocated to measure performance under the CAPM.