An Optimal Tail Selection in Risk Measurement

Małgorzata Just and Krzysztof Echaust
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Małgorzata Just: Department of Finance and Accounting, Poznań University of Life Sciences, 60-637 Poznań, Poland
Krzysztof Echaust: Department of Operations Research and Mathematical Economics, Poznań University of Economics and Business, 61-875 Poznań, Poland

Risks, 2021, vol. 9, issue 4, 1-16

Abstract: The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications.

Keywords: optimal tail selection; threshold; extreme value theory; Value at Risk; Expected Shortfall (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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