Spectral Portfolio Theory

44 Pages Posted: 3 Jun 2016

See all articles by Shomesh Chaudhuri

Shomesh Chaudhuri

Massachusetts Institute of Technology

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Date Written: June 2, 2016

Abstract

Economic shocks can have diverse effects on financial market dynamics at different time horizons, yet traditional portfolio management tools do not distinguish between short- and long-term components in alpha, beta, and covariance estimators. In this paper, we apply spectral analysis techniques to quantify stock-return dynamics across multiple time horizons. Using the Fourier transform, we decompose asset-return variances, correlations, alphas, and betas into distinct frequency components. These decompositions allow us to identify the relative importance of specific time horizons in determining each of these quantities, as well as to construct mean-variance-frequency optimal portfolios. Our approach can be applied to any portfolio, and is particularly useful for comparing the forecast power of multiple investment strategies. We provide several numerical and empirical examples to illustrate the practical relevance of these techniques.

Keywords: Portfolio Theory, Portfolio Optimization, Spectral Analysis, Cycles, Active/Passive Decomposition

JEL Classification: G11, G12, C32, E32

Suggested Citation

Chaudhuri, Shomesh and Lo, Andrew W., Spectral Portfolio Theory (June 2, 2016). Available at SSRN: https://ssrn.com/abstract=2788999 or http://dx.doi.org/10.2139/ssrn.2788999

Shomesh Chaudhuri

Massachusetts Institute of Technology ( email )

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Andrew W. Lo (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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Cambridge, MA 02142
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781 891-9783 (Fax)

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National Bureau of Economic Research (NBER) ( email )

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Cambridge, MA 02138
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Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Stata Center
Cambridge, MA 02142
United States

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