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Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization

Gábor Papp, Fabio Caccioli and Imre Kondor

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The optimization of a large random portfolio under the expected shortfall risk measure with an ℓ 2 regularizer is carried out by analytical calculation for the case of uncorrelated Gaussian returns. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition where this error would otherwise blow up. In the data-dominated region, where the number N of di?erent assets in the portfolio is much less than the length T of the available time series, the regularizer plays a negligible role even if its strength η is large, while in the opposite limit, where the size of samples is comparable to, or even smaller than the number of assets, the optimum is almost entirely determined by the regularizer. We construct the contour map of estimation error on the N/T versus η plane and find that for a given value of the estimation error the gain in N/T due to the regularizer can reach a factor of about four for a suffciently strong regularizer.

Keywords: cavity and replica method; quantitative finance; risk measure and management (search for similar items in EconPapers)
JEL-codes: F3 G3 G32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-rmg
Date: 2019-01-04
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Published in Journal of Statistical Mechanics: Theory and Experiment, 4, January, 2019, 2019(1). ISSN: 1742-5468

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