Modeling the dependence between equity returns and foreign exchange rates in Kenyan financial markets: a copula approach

Abstract

The dependence structure between financial assets is critical in risk management and portfolio diversification. Using the copula approach, this study sought to investigate the dependence structure between the Kenyan stock market and the foreign exchange market over the period 2011 to 2022. We first estimated marginal distributions by the ARMA-GARCH model with normal, student t, and skewed t distributions. To model dependence between the return series, we used elliptical copulas (Gaussian, student t) and Archimedean copulas (Gumbel, Clayton, Frank). We also compared the best-fit copula with the time-varying student t copula and time-varying Gaussian copula. The best-fit copula was later used to measure portfolio tail risk. Parameter estimation was based on inference for margins technique. The best-fitting marginal model and copula were selected using AIC and BIC. Our findings show that the ARMA(1,1)-GARCH(1,1)-t distribution model was the best fit for margins. Student t copula was the best fitting copula. We found the existence of symmetric dependence and tail dependence between the variables. Portfolio risk is measured using VaR. The analysis suggested that the choice between the equally weighted portfolio and the Global Minimum Variance portfolio depends on the investor’s risk tolerance and investment objectives. While a more conservative approach might favor the Global Minimum Variance portfolio, investors seeking to balance risk and return might find the equally weighted portfolio or a mix of assets according to the optimal weights more suitable.

Keywords: Dependence, Copula, Foreign Exchange, Equity returns, Portfolio risk, Marginal distributions, Value at Risk