Over the past two decades, a number of studies have examined the benefits of diversifying equity investments internationally, particularly into emerging markets. In the portfolio construction process, many researchers have criticised Markowitz's Portfolio Theory because of its inherent assumptions such as symmetric and constant correlations. In this study, we use a conditional copula model to estimate the time-varying asymmetric correlations of stock markets and construct optimal portfolios by using estimated correlations. We find that optimised portfolios provide significant benefits for both Australian and the US investors. Out-of-sample results show Copula model provides results closer to the in-sample-estimated benefits of diversification. The results have important implications for portfolio managers who seek to diversify into emerging markets.