An Estimation of Portfolio’s Value-at-Risk with Copula: Empirical Evidence from Laos Securities Exchange

Abstract

This research aims to examine the application of copula in estimating portfolio’s VaR of the two most actively traded stocks (BECL and EDL-Gen) registered in the LSX which can describe the overall movement of the Laos stock market transactions during November 2019 to February 2024. The daily returns of both stocks were calculated to figure out the potential marginal distributions that were well describing the behavior of stock’s return. The chi-square and Anderson-Darling tests would be applied to assess a goodness-of-fit between historical time series of daily return and the possible probability distributions which were normal, Student-t, log-normal, logistic, triangular, Gumbel, Fréchet, Weibull, generalized beta, and generalized extreme value distributions. The tested results were found that the Gumbel distribution, extreme value distributions type-I, was well suit to describe the behavior of each stock’s returns. The method of maximum likelihood estimation was then employed to estimate parameters of the Gumbel distributions. In accordance with the variance-covariance matrix of both stocks, random samples from a multivariate normal distribution were then generated. The tail-independent Gaussian copula, which permits negative dependency and correlation matrix of the generated random samples were used to compute stock’s returns. Based on equally weighted average of all individual estimated stock’s returns held in the portfolio, the portfolio’s returns were recalculated in a number of 1,000 times. Then, the portfolio VaRs based on normality assumption and copula method were estimated in according with 95%, 97.5% and 99% levels of confidence respectively. We found that the Gaussian copula VaR was marginally lower than the normality VaR for all given levels of confidence respectively. This can be implied that the Gaussian copula VaR was not consistently aligned with the conservative portfolio investment where investing in low-risk securities is prioritized. Even though, the portfolio based on low-volatility stocks was formulated, the Gaussian copula VaR was not favorable for risk-averse investors to measure the worse loss depending on the current position.