This paper analyses the optimal investment strategy in the stock markest of a selected group of South American countries: Mexico, Brazil, Argentina, and Chile. The Markowitz efficiency frontiers are derived based on daily stock market index returns expressed in US dollars, for the period of January 1, 1988 through December 23, 1993. In addition to the Markowitz algorithm, the low partial moment algorithm is used. The benefits of international diversification are studied from the perspectives of an American investor who can invest both in the U.S. and in the South American stock markets. The paper assesses the risks and rewards of investing in these countries based on both foreign exchange as well as sovereign risks. It is shown that the optimal portfolio derived provides a risk-adjusted return that is better or, as good as, the return realizable from investing in stock markets with lesser degrees of risk. The optimal portfolio is calculated based on stock-market returns for the emerging South American countries mentioned, with the S&P 500 Index incorporated into the analysis. The portfolio's performance is then measured using various portfolio evaluation techniques.