Eigenportfolios of US Equities for the Exponential Correlation Model
24 Pages Posted: 19 Jan 2021
Date Written: January 23, 2019
In this paper, the eigendecomposition of a Toeplitz matrix populated by an exponential function in order to model empirical correlations of US equity returns is investigated. The closed-form expressions for eigenvalues and eigenvectors of such a matrix are available. These eigenvectors are used to design the eigenportfolios of the model, and we derive their performance for the two metrics. The Sharpe ratios and proﬁt-and-loss curves (P&Ls) of eigenportfolios for twenty-eight of the thirty stocks in the Dow Jones Industrial Average index are calculated for the end-of-day returns from July 1, 1999 to November 1, 2018, several different subintervals and three other baskets in order to validate the model. The proposed method provides eigenportfolios that mimic those based on an empirical correlation matrix generated from market data. The model brings new insights into the design and evaluation of eigen portfolios for US equities and other asset classes. These eigenportfolios are used in the design of trading algorithms, including statistical arbitrage, and investment portfolios. Here, P&Ls and Sharpe ratios of minimum variance, market and eigenportfolios are compared along with the index and three sector exchange-traded funds (XLF, XLI and XLV) for the same time intervals. They show that the ﬁrst eigenportfolio outperforms the others considered in the paper.
Keywords: exponential correlation model, Toeplitz matrix, eigende composition, principal component analysis, Karhunen–Loeve transform (KLT), eigen portfolios, market portfolio, minimum variance portfolio, exchange-traded fund (ETF); Sharpe ratio, market exposure, proﬁt and loss (P&L) curve.
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