This paper examines the strategy of investing in seven Latin American emerging stock markets: Mexico, Brazil, Argentina, Colombia, Peru, Venezuela, and Chile. International Portfolio investment gradually increased during the late 1980s and the 1990s in this region. Investors willing to assume the additional risk present in these markets have been well compensated. Yet, many market analysts have indicated that such markest are somewhat of an abnormality, in that they tend to be characterized as thin, narrow and driven by poorly informed individuals rather than by fundamentals. The optimization algorithms include Markowitz variance-covariance and lower partial moment. The optimal portfolios are evaluated using criteria such as terminal wealth, Sharpe utility measure, Treynor and Jensen measures, and reward to semi-variance. In addition, portfolios which employed ̄rst, second and third degree stochastic dominances are presented. It is shown that possesing a diversified international portfolio which includes Latin American stocks is beneficial.