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

Papp, Gábor, Caccioli, Fabio and Kondor, Imre (2019) Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization. Journal of Statistical Mechanics: Theory and Experiment, 2019 (1). ISSN 1742-5468

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Identification Number: 10.1088/1742-5468/aaf108

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.

Item Type: Article
Additional Information: © 2019 IOP Publishing Ltd and SISSA Medialab srl © CC BY 3.0
Divisions: Systemic Risk Centre
Subjects: H Social Sciences > HG Finance
H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Date Deposited: 20 Mar 2019 15:39
Last Modified: 18 Jul 2019 23:08
URI: http://eprints.lse.ac.uk/id/eprint/100294

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