This paper studies stock market returns in twelve countries with a special focus on Asian stocks and the Asian crisis. Under the turbulent conditions in 1997 and 1998, our approach is a conservative and cautious one. Specifically, we construct an international portfolio using a shortfall constraint approach designed to minimise the 'probability of loss'. We also use the tail index based on the Extreme Value Theory to analyse the distribution of extreme returns particularly those included in the left tail. The approach adopted here represents one of the recent developments in finance that explicitly accepts a departure from the long tradition of Normal distribution assumption, and it corresponds directly with the recent trend in the finance industry in emphasising the value-at-risk approach for risk management. We find, despite the great turmoil during the Asian crisis, that Asian stocks remain viable investment opportunities to the US investors. An ex ante optimal portfolio constructed using a simplistic method and based on information available in the previous month, outperformed, in every aspect, a portfolio consists of only US stocks. With more sophisticated techniques for forecasting returns and risk, and with the Asian economies on course to a full recovery, this result can only be stronger. Other findings in this paper include a positive relationship between correlation and volatility and a negative relationship between correlation and returns. During stock markets downturn, both correlation and volatility are likely to go up eroding some of the benefits of international diversification.