Interpreting Jensen’s Alpha in a CAPM Regression with Zero Intercept

Summary

The document explains Jensen’s alpha as the return component an asset earns when the modeled factor returns are zero. In a CAPM setting, alpha indicates whether an asset’s return exceeded or fell short of the amount associated with its market risk: positive alpha suggests outperformance, negative alpha underperformance, and zero alpha returns in line with the model. The discussion is conceptual and gives no empirical test or worked example.

It highlights that the intercept’s interpretation depends on whether the regression models raw returns or excess returns over the risk-free rate. For raw returns, the intercept may naturally reflect the risk-free rate; for excess returns, the answer argues that a zero alpha is consistent with market efficiency. This is a brief explanation rather than a complete derivation, and it does not address estimation uncertainty, model assumptions, or other factors that could affect alpha.

Key ideas

• Jensen’s alpha represents the return component when modeled factor returns are zero.
• Positive or negative alpha indicates performance above or below the return implied by modeled risk.
• The intercept’s interpretation changes depending on whether the regression uses raw or excess returns.
• A zero alpha in an excess-return model is presented as consistent with market efficiency.

Tags

# What is the intuition of CAPM model with Intercept at 0?


# What is the intuition of CAPM model with Intercept at 0?












I only have a very general theory-based knowledge on Jensen's Alpha. I'm very curious about Capital Asset Pricing Model with intercept at 0. May I know what is the intuition behind this? What does it indicates actually, and why it needs to be 0?

## Answer by Question Anxiety (score 3)

https://quant.stackexchange.com/a/55162

Jensens $\alpha$ stays for return or risk premia, which the asset pays when all factor returns are zero. The $\alpha$ hence tells you if you were rewarded accordingly to the risk taken. If $\alpha$ is zero then you were rewarded fairly for the risk taken (compared to the market), when its negative you earned too little for the risk taken and when its positive you earned more than the risk taken. Now the question is if you are actually addressing the return of the asset or the excess return of the asset over the risk free rate. In the first case the $\alpha$ most naturally corresponds to the risk free rate. In the latter case in my understanding $\alpha$ needs to be zero such that the market is efficient.

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.