There is a large body of knowledge concerning the cointegration of international stock markets. In light of such a concept, this study attempts to provide an answer to the international portfolio optimization problem. It is likely that investors’ preferences for mean, variance, skewness and kurtosis may vary over time. One investor may choose to give more weight to profits, while another may choose variance or skewness over return. To achieve multi-objective optimization, the study uses the polynomial goal programming (PGP) model. It is the first study of its kind to consider the closing stock indices of BRICS (Brazil, Russia, India, China and South Africa) economies from January 2010 to December 2016, by assigning various weights to individual BRICS countries under an alternative MVSK (mean, variance, skewness, kurtosis) framework. It notes that two cornerstones of BRICS (India and China) show an investment pattern such that when potential investors approach India as a favourable country to invest in stocks, Chinese portfolio returns move the other way, and vice versa.