Active, Excess, and CAPM Residual Returns

Summary

The document distinguishes three return measures used to assess a security or portfolio. Active return compares an investment’s return with the market return. Excess return compares it with the risk-free rate, while market excess return is the market’s return above that same benchmark. These quantities serve different roles and should not be treated as interchangeable.

Under the CAPM, an asset’s excess return is modeled as beta times the market’s excess return plus an unexplained residual. Subtracting the modeled market component from the asset’s excess return gives residual return: the portion not explained by CAPM. The answer connects an estimated residual over a period with alpha and describes it as performance relative to the model. It provides definitions and the CAPM relationship, but no empirical example or guidance on estimation choices, benchmark selection, or statistical uncertainty.

Key ideas

• Active return is the investment return minus the market return.
• Excess return is the investment return minus the risk-free rate.
• Market excess return is the market return minus the risk-free rate.
• CAPM explains excess return as beta times market excess return plus a residual.
• Residual return is the component left unexplained by CAPM and is related to estimated alpha.

Tags

# Excess, Residual and Active Return


# Excess, Residual and Active Return












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

- Active return

- Excess return

- Residual return

## Answer by nbbo2 (score 11, accepted)

https://quant.stackexchange.com/a/25627

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.