Abstract
The eigen decomposition of Toeplitz matrix, with exponential correlations as its elements, to model empirical correlations of US equity returns is investigated. Closed form expressions for eigenvalues and eigenvectors of such Toeplitz matrix are available. Those eigenvectors are used to design the eigenportfolios of the model. The Sharpe ratios and PNL curves of eigenportfolios for stocks in Dow Jones Industrial Average (DJIA) index for the period from July 1999 to Nov. 2018 are calculated to validate the model. The proposed method provides eigenportfolios that closely mimic the eigenportfolios designed based on empirical correlation matrix generated from market data. The modeling of empirical correlation matrix brings new insights to design and evaluate eigenportolios for US equities and other asset classes.
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