Estimation of Value-at-Risk using Weibull distribution – portfolio analysis on the precious metals market

Dominik Krężołek

doi:10.5604/01.3001.0015.2731

Dominik Krężołek University of Economics in Katowice, Department of Demography and Economic Statistics, ul. Bogucicka 3, 40-287 Katowice, Poland ORCID:https://orcid.org/0000-0002-4333-9405 Przegląd Statystyczny. Statistical Review, vol. 68, 2021, 2, pages: 38-52 Published online: 18 October 2021 DOI 10.5604/01.3001.0015.2731

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ARTICLE

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ABSTRACT

In this paper, we present a modification of the Weibull distribution for the Value-at- Risk (VaR) estimation of investment portfolios on the precious metals market. The reason for using the Weibull distribution is the similarity of its shape to that of empirical distributions of metals returns. These distributions are unimodal, leptokurtic and have heavy tails. A portfolio analysis is carried out based on daily log-returns of four precious metals quoted on the London Metal Exchange: gold, silver, platinum and palladium. The estimates of VaR calculated using GARCH-type models with non-classical error distributions are compared with the empirical estimates. The preliminary analysis proves that using conditional models based on the modified Weibull distribution to forecast values of VaR is fully justified.

KEYWORDS

risk analysis, Value-at-Risk, metals market, GARCH-type models, two-sided Weibull distribution

JEL

C32, C58, G11, G17

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