Applying a genetic algorithm to international diversification of equity portfolios: A South African investor perspective

This paper uses the genetic algorithm (GA) approach to generate a portfolio optimisation scenario of a South African investor who seeks to maximise return from investing in S&P500, FTSE100, NASDAQ, DOWJONES, CAC40 and the DAX from January 1, 2005, to January 31, 2008, but facing exchange rate risk. The GA searches for the optimal solution in the entire set of financial constraints without looking for partial derivatives of the utility function. Whereas most financial problems require a non-linear and time-varying model, the GA, with its survival principle of offspring chromosomes, is better suited to this type of problem than local optimisation methods. The performance of the GA is compared with two non-linear models, namely the quadratic mean-variance (QMV), which maximises the portfolio mean-variance, and the quadratic variance minimisation (QVM), which minimises the portfolio variance. The results show that neither the QMV nor the QVM takes into account the domestic investors' risk attitude towards investing in foreign equities and therefore does not provide any international diversification benefits. In addition, the bootstrapping scenario of 10,000 simulations reveals that neither the QMV nor the QVM outperforms the GA in terms of Sharpe ratio and flexibility in dealing with investors' risk attitude towards investing in foreign equities denominated in foreign currencies.