Financial market observers have noted that during periods of high market volatility, correlations between asset prices can differ substantially from those seen in quieter markets. For example, correlations among yield spreads were substantially higher during the fall of 1998 than in earlier or later periods. Such differences in correlations have been attributed either to structural breaks in the underlying distribution of returns or to "contagion" across markets that occurs only during periods of market turbulence. However, we argue that the differences may reflect nothing more than time-varying sampling volatility. As noted by Boyer, Gibson and Loretan (1999), increases in the volatility of returns are generally accompanied by an increase in sampling correlations even when the true correlations are constant. We show that this result is not just of theoretical interest: When we consider quarterly measures of volatility and correlation for three pairs of asset returns, we find that the theoretical relationship can explain much of the movement in correlations over time. We then examine the implications of this link between measures of volatility and correlation for risk management, bank supervision, and monetary policy making.