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Portfolio optimization under Expected Shortfall: contour maps of estimation error

Caccioli, F; Kondor, I; Papp, G; (2018) Portfolio optimization under Expected Shortfall: contour maps of estimation error. Quantitative Finance , 18 (8) pp. 1295-1313. 10.1080/14697688.2017.1390245. Green open access

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Abstract

The contour maps of the error of historical and parametric estimates of the global minimum risk for large random portfolios optimized under the Expected Shortfall (ES) risk measure are constructed. Similar maps for 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-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 confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.

Type: Article
Title: Portfolio optimization under Expected Shortfall: contour maps of estimation error
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/14697688.2017.1390245
Publisher version: https://doi.org/10.1080/14697688.2017.1390245
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Expected shortfall, Estimation error, Replica met
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10047474
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