Issue: 2014/Vol.24/No.2, Pages 59-79


Henryk Gurgul, Artur Machno

Full paper (PDF)    RePEC

Cite as: H. Gurgul, A. Machno. The optimal portfolio under VaR and ES. Operations Research and Decisions 2014: 24(2), 59-79. DOI 10.5277/ord140203

An analysis of the dependence structure among certain European indices (FTSE100, CAC40, DAX30, ATX20, PX, BUX and BIST) has been conducted. The main features of the financial data were studied: asymmetry, fat-tailedness (leptokurtosis), variability and mutual dependence. We have fitted a regime switching copula based model including asymmetric and fat-tailed copulas. All the indices are left-skewed and fat-tailed. Large indices are more skewed and less fail-tailed. The findings suggest that size of a market has an influence on its properties. A particular behaviour of the Turkish market suggests the importance of geographical factors. It is also suggested that the maturity of a market is insignificant in the analysis. Another important conclusion drawn from our empirical investigation is that VaR is a less exact risk measure than ES. However, the dynamics of the temporal and statistical properties of both measures are similar.

Keywords: value at risk, expected shortfall, interdependence, regime copulas, vine copula

Received: 17 September 2013    Accepted: 14 January 2014