Calculating Portfolio Risk with Copula: An Application on BIST100 and USD Exchange Rates
Keywords:
copula, VaR, Shapiro-Wilk test, Kolmogorov-Smirnov testAbstract
VaR analysis provides a way to measure and manage financial risk and the potential loss from an investment or portfolio over a period of time. For this reason, it is used as a popular risk management tool for financial institutions and investors. The aim of this study is to provide some insights to investors by making financial risk estimation through the multivariate copula method. In the study, the combined distribution of the daily return rates of the assets in a portfolio consisting of BIST100 and USD/TL rates is modeled using the copula method. This common distribution is used to calculate portfolio VaR. The main reason for using the copula method in the study is that it is based on fewer assumptions than the standard VaR calculation method, which assumes a multivariate normal distribution for asset price returns. As a result of the analysis, the correlation structure that best fits the basic data was modeled with t-copula. This obtained t-copula describes a certain correlation structure of the multivariate normal distribution. As a result of the analysis, the VaR of the portfolio at 99% confidence level was calculated and compared with the VaR results of the portfolio, which is considered to be a multivariate normal distribution. Analysis results show that portfolio risk ratio decreases as USD/TL weight increases in a portfolio consisting of BIST100 and USD/TL.
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