Evaluating the Precision of Estimators of Quantile-Based Risk Measures

31 Pages Posted: 19 Jun 2007

See all articles by John Cotter

John Cotter

University College Dublin; University of California, Los Angeles (UCLA) - Anderson School of Management

Kevin Dowd

Nottingham University Business School (NUBS)

Date Written: 2007

Abstract

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions.

Keywords: Value at Risk, Expected Shortfall, Spectral Risk Measures, Moments

JEL Classification: G15

Suggested Citation

Cotter, John and Dowd, Kevin, Evaluating the Precision of Estimators of Quantile-Based Risk Measures (2007). Available at SSRN: https://ssrn.com/abstract=994524 or http://dx.doi.org/10.2139/ssrn.994524

John Cotter

University College Dublin ( email )

School of Business, Carysfort Avenue
Blackrock, Co. Dublin
Ireland
353 1 716 8900 (Phone)
353 1 283 5482 (Fax)

HOME PAGE: http://https://johncotter.org/

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

Kevin Dowd (Contact Author)

Nottingham University Business School (NUBS) ( email )

Jubilee Campus
Wollaton Road
Nottingham, NG8 1BB
United Kingdom

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