Why Asset Pricing Factors Need Not Be Excess Returns

Summary

The note explains that an asset pricing factor does not have to be an excess return or even a traded portfolio. In a one-factor model where the factor is itself an excess return, its risk price can be read directly from its average value: the factor has a loading of one on itself. This makes the model’s risk-price calculation especially convenient.

For a nontraded variable such as GDP, the factor may still be considered, but its price of risk is not determined by that simple self-pricing relation. The note says additional equations are needed to identify it. It offers this distinction as a conceptual explanation, without providing a full model, empirical example, or guidance on choosing and testing candidate factors.

Key ideas

• An asset pricing factor does not have to be an excess return or a traded portfolio.
• When a factor is an excess return, its own loading is one, so its price of risk equals its expected value in the stated one-factor setup.
• A nontraded variable such as GDP can be considered as a factor, but its risk price requires additional equations.
• The explanation addresses identification of the risk price rather than how to select or validate a factor.

Tags

# Asset pricing model factor need to be excess return?


# Asset pricing model factor need to be excess return?












In John Cochrane's Asset Pricing book and his video lecture, he states that asset pricing factors need to be excess returns, a traded portfolio. Is there a reason for that? I can't find explanation anywhere. GDP is not tradable, can GDP be a asset pricing factor?

## Answer by Igor Pozdeev (score 7, accepted)

https://quant.stackexchange.com/a/42563

AP factors do not need to be excess returns. In case they are, corresponding prices of risk are conveniently equal to average factor values, since "factors price themselves":

$$E[R_i] = \beta_{i} \cdot \lambda_f, \\ E[f] = 1 \cdot \lambda_f, \\ \Leftrightarrow \\ \lambda_f = E[f],$$

where there is just one factor $f$, $\beta_i$ is the loading of asset $i$ thereon, $\lambda_f$ is the price of risk.

On the other hand, what is the price of risk for GDP? You'll need an additional set of equations to determine it.

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