An Empirical Study of Markowitz’s Optimal Portfolio Using Principal Component Analysis: Standard Deviation, VaR and ES as Risk Measures

This study presents a new application of Singular Value Decomposition(SVD), which is related to Principal Component Analysis(PCA), to Markowitz’s mean-variance optimal portfolio and further test its empirical applicability. In the past period(2000~2004), efficient frontiers(Markowitz, 1952) were derived with two different covariance matrixes from stock returns in KOSPI200, namely original covariance matrix and SVD-applied covariance matrix. These covariance matrixes were also used to draw efficient frontier in the future period (2005~2007). Expected returns are arithmetic averages in a corresponding period. The results showed that an actual efficient frontier in the future period is closer to the frontier from SVD-applied covariance matrix than the frontier from original covariance matrix. Employing other risk measures such as Value-at-Risk and Expected Shortfall than standard deviation presented the same results and confirmed the usefulness of SVD to optimal portfolio.