Asset Pricing with Omitted Factors

Standard estimators of risk premia in linear asset pricing models are biased if some priced factors are omitted. We propose a three-pass method to estimate the risk premium of an observable factor, which is valid even when not all factors in the model are specified or observed. We show that the risk premium of the observable factor can be identified regardless of the rotation of the other control factors, as long as they together span the true factor space. Motivated by this rotation invariance result, our approach uses principal components of test asset returns to recover the factor space and additional cross-sectional and time-series regressions to obtain the risk premium of the observed factor. Our estimator is also equivalent to the average excess return of a mimicking portfolio maximally correlated with the observed factor using appropriate regularization. Our methodology also accounts for potential measurement error in the observed factor and detects when such a factor is spurious or even useless. The methodology exploits the blessings of dimensionality, and we therefore apply it to a large panel of equity and non-equity portfolios to estimate risk premia for several workhorse factors.

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