Portfolio optimization under expected shortfall: contour maps of estimation error

Caccioli, Fabio, Kondor, Imre and Papp, Gábor (2015) Portfolio optimization under expected shortfall: contour maps of estimation error. Systemic Risk Centre Discussion Papers (49). Systemic Risk Centre, The London School of Economics and Political Science, London, UK.

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Abstract

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-the-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confi dence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.

Item Type:	Monograph (Discussion Paper)
Official URL:	http://www.systemicrisk.ac.uk/
Additional Information:	© 2015 The Authors
Divisions:	Systemic Risk Centre
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G10 - General
Date Deposited:	21 Jun 2023 14:48
Last Modified:	16 Sep 2023 00:03
URI:	http://eprints.lse.ac.uk/id/eprint/119463

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