A nice measure of how equities outside the U.S. are performing is the EAFE ETF (EFA), which taps into stocks across Europe & Australasia Far East. Normally, EFA correlates highly with the S&P 500 Index (SPY). Since March, 2003 (N = 857 trading days), the correlation of 10 day price moves in EFA and SPY has been .74.
Interestingly, when the U.S. and EAFE are highly correlated on a 10-day basis (.925 or greater; N = 84), the next 10 days in SPY average a gain of .87% (58 up, 26 down). This is stronger than the average 10-day gain of .53% (520 up, 339 down).
Conversely, when the U.S. and EAFE are loosely correlated on a 10-day basis (.50 or less; N = 92), the next ten days in SPY average a gain of only .19% (53 up, 39 down).
When the S&P has risen 2% or more in a 10-day period (N = 186), the next 10 days in SPY have averaged a gain of .41% (112 up, 74 down). When the correlation between the U.S. and EAFE has been above average, however (N = 93), the average 10-day gain has been only .25% (52 up, 41 down). When the correlation between the U.S. and EAFE has been below average (N = 93), the average 10-day gain has been stronger at .58% (60 up, 33 down).
What this suggests is that a world that moves in lockstep may have very different implications for future price change than a world that moves in separate directions. Moreover, this relationship appears to be different under bull and bear conditions. This is an area for fruitful research, I suspect.