Stock market risk measured by VaR nad CVaR: A comparison study

Abstract

VaR and CVaR are effective quantitative measurement of market risk. These measures can quantify the risk of unexpected changes within a given period. In this paper, we examine the market risk of four stock indices: the Czech PX, the Austrian ATX, the London FTSE, and the American S&P 500. First, the returns of these indices are approximated using two distributions showing semi-heavy tails: a t- distribution and a normal inverse Gaussian distribution. For comparison, the normal and empirical distributions are also included since they often work as convenient alternatives. Subsequently, the VaR99 and CVaR97.5 values corresponding to four candidate distributions are calculated for each index. We also analyze the ability of theoretical distribution to approximate the left tail behavior of stock market indices returns. It turns out that the normal distribution is not suitable for this purpose. Furthermore, it appears that CVaR97.5 is higher (in absolute value) for all indices than the corresponding VaR 99, which may require higher need for economic capital, which banks should allocate.