VAR assessment under nongaussian distribution of returns

Abstract

The study aims to assess the impact of violation of the assumption about normality of the investment portfolio returns on its risk measures. The article is focused on the Value at Risk (VaR) metric required by major regulatory authorities for bank risk assessment. Using historical share prices of several Russian companies it is shown that the assumption about returns normality is not supported by statistical tests. It is also shown that the empirical distribution of the assets returns is described by Johnson’s distribution. The Kolmogorov-Smirnov test supports the obtained results. The tests proposed by the authors allow estimating the loss in accuracy in parameters calibration of the autoregressive model, obtained by using the maximum likelihood method when the asset returns have non-gaussian distribution. It was found that the loss in the accuracy lies in the range [22%, 26%] for absolute returns and in the range [33%, 38%] for relative returns depending on the autoregression parameter which varies in the range [–0.9, 0.9]. The error of ten-day VaR estimation was calculated for 1% (99%) and 5% (95%) significance levels. At a significance level of 5% (95%) the VaR metric obtained under the assumption that the asset returns have normal distribution is lower than the true value by 7% (6%) for absolute returns and 4% (13%) for relative returns, which indicates strong underestimation of the portfolio risk. At a significance level of 1% the metric is conservative exceeding the true value by 12.5%.