This study identifies the impact of three natural disasters on cointegrating relationship among selected world stock market indices. The study further suggests the best international diversification strategy in case of the occurrence of an extreme event from the perspective of an Indian investor. A vast amount of research suggests that international portfolio diversification helps to spread the risk of any adversity occurring in a particular country as the correlations among stocks in various countries are lower as compared to local securities. But the disagreement nevertheless is that in a number of instances, diversifying internationally might not be effective. To fill this research gap, the study employs Johansen multivariate cointegration test to evaluate change in the financial linkages between selected stock market indices during the pre- and post-one year event period for three events to include China Earthquake of 2008, Japan earthquake and tsunami of 2011 and the US Hurricane Sandy of 2012. The study further compares performance of different portfolio diversification strategies, viz., Naive 1/N portfolio construction technique, Markowitz modern portfolio theory and cointegration-based portfolio construction method with the aid of Sharpe's ratio. The study finds that with the help of cointegration analysis, effective portfolio selection can be done to seek maximum diversification benefit.