The objective of this paper is to assess the investment opportunities emerging in the newly developing stock markets of Eastern Europe. The Czech Republic, Hungary, and Poland, representative of the emerging stock markets of Eastern Europe, are examined from the perspective of a US investor who invests solely in the US markets. During the period November 24, 1994 to May 12, 1995, the most advantageous investment strategy is derived using optimization algorithms, comparing the optimal portfolio in the stock markets of a select group of Eastern European countries against the S&P 500 Index, representative of the US stock markets. Based on market volatility, sovereign risks, and foreign exchange the risks and rewards of investing in these countries are appraised. The results show that the risk-adjusted return, yielded from the optimal portfolio, exceeds or equals the return realizable from investing in stock markets with lesser degrees of risk.