This paper examines the evidence for the common assertion that the volatility of emerging stock markets has increased as a result of the liberalization of markets. A range of measures suggests that there has been no generalized increase in volatility in recent years; indeed, it appears that volatility may have tended to fall rather than rise on average. The paper also tests for the predictability of long-horizon returns in emerging markets. While there is evidence for positive autocorrelation in returns at horizons of one or two quarters, the autocorrelations appear to turn negative at horizons of a year or more. However, the magnitude of the apparent return reversals is not that much larger than reversals in some mature markets. One interpretation of the results would be that emerging markets have not consistently been subject to fads or bubbles, or at least no more so than in some industrial countries. In general, the liberalization and broadening of emerging markets should lead to a reduction in return volatility as risk is spread among a larger number of investors.