Principal Component Analysis and Portfolio Optimization

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Principle Component Analysis (PCA) is one of the common techniques used in Risk modeling, i.e. statistical factor models. When using PCA to estimate the covariance matrix, and applying it to portfolio optimization, we formally analyze its performance, and find positive results in terms of portfolio efficiency (Information Ratio) and transaction cost reduction. We also propose using PCA to manage beta against alpha, and show how to apply the idea within Black-Litterman framework. Finally, we invent the technique 'Mean-Reverting PCA' to improve the stability of conventional PCA analysis.