Common stochastic trends among major international stock price indices has been a very intensively analyzed issue mainly as a result of the 1987 stock market crash and the need for policy coordination in financial markets. This paper investigates the existence of common stochastic trends among an emerging equity market, the Cyprus Stock Exchange and three mature equity markets namely ASE, LSE and NYSE. The main finding of our analysis is that there is evidence of one long-run relationship among the four equity markets and therefore three common stochastic trends. We use the Gonzalo and Granger (1995) methodology to identify, estimate and test for the number of common trends that leads to permanent changes among the four stock markets. Furthermore, we identify as driving forces of the system the ASE, LSE and NYSE equity markets while the emerging stock market of Cyprus does not enter significantly the common trends. Finally, we show that although cointegration exists there are small long-run benefits from international portfolio diversification since the stock prices adjust very slowly to these common trends.