Principal Component Analysis and the Cross-Sectional Variation of Returns

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Abstract: We utilize Principal Component Analysis (PCA), a dimensionality reduction technique, on a set of 142 risk factors, including macroeconomic factors, proposed in financial literature to construct factor models with high explanatory powers when analysing the cross-sectional variation of portfolio returns. We apply a Fama and Macbeth (1973) two-pass regression to estimate risk premia commanded by our principal components. We perform a static PCA, which is what we call the conventional application of PCA, and a rolling window PCA, where the data is split into overlapping windows and where the PCA constructs principal components separately in each window. This allows us to construct two sets of factor models: one set from the static PCA, and one set from the rolling window PCA. The benchmark model for our research is the Fama and French (2015) five-factor asset pricing model. Our results suggest that both sets of factor models outperform the benchmark model in capturing the cross-sectional variation of returns. Furthermore, we find that the addition of macroeconomic factors adds explanatory power to our models. Finally, we find that the factor models from the rolling window PCA do not outperform the factor models from the static PCA.

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