Measuring Risk in Value-at-Risk Based on Student’s t-Distribution

Distributional assumptions of financial return data are an important issue for asset-pricing and portfolio management as well as risk controlling. In order to capture the departure of empirical observations of financial return data from normality the Student’s t-distribution has been proposed as an alternative fat-tailed distribution in the literature. In this paper we (i) briefly summarize the Student’s t-distribution; (ii) compare the tail behavior of the Student’s t-distribution with empirical data; and (iii) discuss some implications of the empirical results on the risk management based on Value-at-Risk. We also suggest a simple statistic as a measure of tail-thickness based on the sample quantile and the first absolute moment.