A Method to Quantify Risks of Financial Assets: An Empirical Analysis of Japanese Security Prices

Abstract

This study investigates unconditional distributions of daily log-returns of Japanese security prices from a comprehensive point of view. The purpose of this article is to estimate a risk distribution of stocks in terms of Value-at-Risk (VaR) in order to select low risk securities from many securities. Daily log-return time series of 1,340 Japanese companies listed on the first section of Tokyo Stock Exchange are examined during the last one decade. I develop a method to estimate VaR by both the maximum likelihood estimation procedure under a q-Gaussian assumption and analytical form of its cumulative distribution function. It is confirmed that they are fitted to q-Gaussian distributions (Student t-distributions) with Kolmogorov-Smirnov test. It is found that the complementary cumulative distribution function of VaR has a power-law tail with its characteristic exponent depending on values of the VaR percentile.