Emerging market policy makers have been concerned about the financial stability implications of financial globalization. These concerns are focused on behavior under stressed conditions. Do tail events in the home country trigger off extreme responses by foreign investors - are foreign investors `fair weather friends'? In this, is there asymmetry between the response of foreign investors to very good versus very bad days? Do foreign investors have a major impact on domestic markets through large inflows or outflows - are they ‘big fish in a small pond'? Do extreme events in world markets induce extreme behavior by foreign investors, thus making them vectors of crisis transmission? We propose a modified event study methodology focused on tail events, which yields evidence on these questions. The results, for India, do not suggest that financial globalization has induced instability on the equity market.