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

1208 Views 46 Downloads

ARTICLE

(English) PDF

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

REFERENCES

Alexander, C., & Sarabia, J. M. (2012). Quantile uncertainty and value-at-risk model risk. Risk Analysis, 32(8), 1293–1308. https://doi.org/10.1111/j.1539-6924.2012.01824.x.

Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1.

Cheema, M. A., Faff, R., & Szulczyk, K. R. (2020). The 2008 global financial crisis and COVID-19 pandemic: How safe are the safe haven assets?. Covid Economics, (34), 88–115. https://cepr.org/content/covid-economics-vetted-and-real-time-papers-0#block-block-10.

Chen, Q., & Gerlach, R. H. (2013). The two-sided Weibull distribution and forecasting financial tail risk. International Journal of Forecasting, 29(4), 527–540. https://doi.org/10.1016/j.ijforecast.2013.01.007.

Chen, Y., & Qu, F. (2019). Leverage effect and dynamics correlation between international crude oil and China’s precious metals. Physica A: Statistical Mechanics and its Applications, 534, 1–13. https://doi.org/10.1016/j.physa.2019.122319.

Cheung, K. C., & Yuen, F. L. (2020). On the uncertainty of VaR of individual risk. Journal of Computational and Applied Mathematics, 367, 1–14. https://doi.org/10.1016/j.cam.2019.112468.

Chinhamu, K., Huang, C. K., Huang, C. S., & Chikobvu, D. (2015). Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market. International Business & Economics Research Journal, 14(1), 107–122. https://doi.org/10.19030/iber.v14i1.9035.

Chkili, W., Hammoudeh, S., & Nguyen, D. K. (2014). Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory. Energy Economics, 41, 1–18. https://doi.org/10.1016/j.eneco.2013.10.011.

Christoffersen, P. F. (1998). Evaluating Interval Forecasts. International Economic Review, 39(4), 841–862. https://doi.org/10.2307/2527341.

Daníelsson, J., Jorgensen, B. N., Samorodnitsky, G., Sarma, M., & de Vries, C. G. (2013). Fat tails, VaR and subadditivity. Journal of Econometrics, 172(2), 283–291. https://doi.org/10.1016/j.jeconom.2012.08.011.

Ding, Z., Granger, C. W. J., & Engle, R. F. (1993). A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance, 1(1), 83–106. https://doi.org/10.1016/0927-5398(93)90006-D.

Doman, M., & Doman, R. (2009). Modelowanie zmienności i ryzyka: Metody ekonometrii finansowej. Kraków: Wolters Kluwer Polska.

Dowd, K. (1999). Beyond Value at Risk: The New Science of Risk Management. Chichester: John Wiley & Sons.

Krawczyk, T. (2017). Modelowanie ryzyka inwestycyjnego. Zastosowania praktyczne z wykorzystaniem arkusza kalkulacyjnego Excel i programu GRETL (2nd edition). Warszawa: Wydawnictwo CeDeWu.

Krężołek, D. (2020). Modelowanie ryzyka na rynku metali. Katowice: Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach.

Kupiec, P. H. (1995). Techniques for Verifying the Accuracy of Risk Management Models. The Journal of Derivatives, 3(2), 73–84. https://doi.org/10.3905/jod.1995.407942.

Salisu, A., Raheem, I., & Vo, X. (2021). Assessing the safe haven property of the gold market during COVID-19 pandemic (MPRA Paper No. 105353). https://mpra.ub.uni-muenchen.de/105353/.

Trzpiot, G. (2004). O wybranych własnościach miar ryzyka. Badania Operacyjne i Decyzje, 14(3–4), 91–98. http://www.ord.pwr.wroc.pl/index.php?s=archive.

Wang, C., Zhang, X., Wang, M., Lim, M. K., & Ghadimi, P. (2019). Predictive analytics of the copper spot price by utilizing complex network and artificial neural network techniques. Resources Policy, 63, 1–17. https://doi.org/10.1016/j.resourpol.2019.101414.

Włodarczyk, B. (2017). Prognozowanie zmienności stóp zwrotu na rynkach złota i srebra z uwzględnieniem efektu asymetrii i długiej pamięci. Studia i Prace WNEiZ US, (50/1), 231–247. https://doi.org/10.18276/sip.2017.50/1-17.

Yu, W., Yang, K., Wei, Y., & Lei, L. (2018). Measuring Value-at-Risk and Expected Shortfall of crude oil portfolio using extreme value theory and vine copula. Physica A: Statistical Mechanics and its Applications, 490, 1423–1433. https://doi.org/10.1016/j.physa.2017.08.064.

Zijing, Z., & Zhang, H. K. (2016). The dynamics of precious metal markets VaR: A GARCHEVT approach. Journal of Commodity Markets, 4(1), 14–27. https://doi.org/10.1016/j.jcomm.2016.10.001.