Comparison of Traditional and Copula based Value-at-Risk with Low Volatility Equity Portfolio: Empirical Evidence from Laos Securities Exchange

Abstract

While eleven stocks are currently registered and traded in the Laos Securities Exchange (LSX), risk regarding market volatility is kind of tricky to measure. Value-at-risk (VaR) is a popular statistical measure for the return of financial assets that are normally distributed. However, the distribution of a portfolio’s return is uncommonly characterized by the assumption of joint normality that many classical financial theories are assumed. Therefore, the copula is employed to draw out a multivariate probability distribution. This research aims to compare the performance between the traditional and copula based VaR with the two most actively traded but low volatility stocks (BECL and EDL-Gen) registered in the LSX between November 2019 to November 2020. The daily returns were calculated to evaluate the possible marginal distributions that were well describing the behavior of stock’s return. The 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 are normal, student-t, log-normal, logistic, triangular, Gumbel, Fréchet, Weibull, generalized beta, and generalized extreme value distributions. The tested results found that the Gumbel distribution, extreme value distributions type-I, was well suit to describing the behavior of both stock’s returns. The maximum likelihood estimation method was then used to estimate parameters of the Gumbel distributions.  The random samples from a multivariate normal distribution were generated based on variance-covariance matrix of both stocks. The Gaussian copula, which is tail independent and also allows for negative dependence, and correlation matrix of the generated random samples were used to generate 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 10,000 times. Then, the portfolio VaRs based on normality assumption and copula were estimated in according with 95%, 97.5% and 99% levels of confidence respectively. The VaR based on Gaussian copula was slightly 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.