Value-at-Risk (VaR ) has become a standard risk measure for financial risk management due to its conceptual simplicity, ease of computation and ready applicability. Nevertheless, VaR has been criticised for having several conceptual problems (Yamai & Yoshiba, 2005): - VaR measures only percentiles of profit/loss distributions and disregards any loss beyond the VaR level (this is the 'tail risk' problem), - VaR is not coherent, since it is not subadditive. To remedy the above problems, Artzner et al. (1997) have proposed the use of Expected Shortfall (ES) which is defined as the conditional expectation of loss for losses beyond the VaR level. ES is also demonstrated to be subadditive, which assures its coherence as a risk measure. The aim of this paper is a comparative analysis of selected Polish equity open-end mutual funds' portfolios using the estimators of risk measures Value-at-Risk and Expected Shortfall. The authoress focuses on the application of relative return - VaR(gamma VaR) and return - ES(gamma ES) measures to give examples of risk estimation in a bear market period using daily data from July 4, 2007 to February 17, 2009. The overall WIG index fell from 66951.73 (July 4, 2007) to 21274.28 (Feb 17, 2009). It lost 68.22% during the period investigated. Relative risk measures can be used to rank the investment funds in order of their risk exposure, particularly during a bear market period.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.