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Abstract:
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We propose a new framework for return predictability and asset pricing based on a “prediction matrix,” which yields optimal linear strategies (principal portfolios). Decomposing the problem into alpha and beta, we show that the eigenvectors of the symmetric part of the prediction matrix provide optimal factor exposures (principal exposure portfolios), while the antisymmetric part provide alpha to the factor (principal alpha portfolios). The framework provides a new test of asset pricing models: exposures to the pricing kernel must correspond to a prediction matrix that is symmetric with positive eigenvalues (i.e., no alpha). We implement the framework empirically using several data sets, finding significant alpha to standard factors out-of-sample.
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