Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange

Mitigation of risk in a security-trading environment is one of the strategies that every investor would want. Stock prices keep on changing from time to time and it is difficult for participants to predict share price direction. It is therefore appropriate for any trader to use the risk minimization strategies. One of the strategies is to estimate the amount of money a trader is willing to lose in a given period. This project uses the concept of copula to describe the dependency structure of portfolio returns selected from the Nairobi Securities Exchange. The Copula concept works towards modeling the dependency structure of high volatile data by separating the univariate distribution of their respective marginals. Dependencies in a volatile data enables one to assess the relationship that appears in the extreme values of historically sampled data. The study started with selecting an optimal portfolio from the Nairobi Securities Exchange using the Capital Asset and Pricing Model. The chosen optimal portfolio involved companies from different sectors, thus implying minimization of unsystematic risk. The next step involved estimating the systematic risk based on the historical data of the optimal portfolio selected. Different types of copula-based models were fitted then compared to each other to assess the dependencies measures, the goodness of fit of the model, and backtest of the Value-at-Risk. The main findings were that the Tawn type 1 copula was the best copula-based model for modeling the dependence structure of the portfolio returns. Additionally, the backtesting results also show that this model had the highest coverage of the exceedances.