The study sets out to clarify the scope for international diversification of share portfolios that is open to investors in the CEE member-states of the EU. A steady decrease in interest rates can be observed in most countries in the region, unsurprisingly, as these rates must converge on those of the Euro zone before the Euro is introduced. Falling interest rates increase the importance of stock markets, as the fall in the yield of low-risk bonds makes equity investment more attractive. The research was based on a comprehensive database covering 17 countries: 8 new CEE members of the EU, Russia, and 8 countries with developed capital markets. The 1997-2003 period was examined for characteristics of the stock-market yields and risks in these countries, along the scope for reducing risks and enhancing yields with internationally diversified portfolios. Three strategies for optimizing portfolios and a method of choosing a so-called naive portfolio were assessed using a so-called ex ante reverse-testing procedure. The results obtained for the developing CEE stock markets were compared with those of developed markets and various distinguishing marks of the developing-market portfolios were identified.