Value at Risk (VaR) Historical Approach: Could It Be More Historical and Representative of the Real Financial Risk Environment?

Abstract

The purpose of this paper is to suggest a new approach that improves the conventional Historical Value-at-Risk (HVaR) estimations’ accuracy and can be easily applied by anyone. The main assumption for the newly suggested method is “the more representative to the financial conditions the data inputs are, the better the VaR estimations”. Volatility is assumed to be the criterion for the “representative to the financial conditions” definition. In practice, the newly suggested approach does not use the previous x days observations as data inputs in the estimation process (as the HVaR does), but the last x filtered volatility (fv) observations of a “representative to the current financial conditions dataset”. Depending on the volatility value, each observation is classified in several regimes, from which the VaR is estimated depending on the examined day’s volatility. This way the HVaR approach is more historical. The empirical findings using data from the US and the Eurozone stock market show that the newly suggested filtered volatility approach not only significantly improves the VaR estimations, but also makes these estimations much more representative of the real financial conditions. The results using the filtered volatility approach are comparable to some previously documented VaR estimations that adopt advanced econometric models. In this point, we should note advanced econometric models have the drawbacks that are not usually applied in financial markets industry because of their complexity. The newly suggested approach: (i) popularizes some of the most advanced econometric techniques, (ii) improves the VaR estimations accuracy, and (iii) enables financial risk analysts and portfolio managers to estimate the risk-return under several volatility regimes in order to help them to apply their desired investment strategy. Finally, this paper not only examines accuracy using the traditional/conventional tests [1], but also suggests some new measures for the comparison amongst different VaR models and their ability to accurately estimate the real financial risk.