Change of Correlation Regime in ETFs

Although there is no guarantee that a short ETF will correspond to the inverse of the long portfolio, empirical analysis shows that their values in dollar terms (but not necessarily in terms of daily returns) have been almost perfectly negatively correlated. For example, for calendar year 2007, the correlation of the dollar values of the ProShares Long 2x Russell 200 and the ProShares Short Russell 2000 was -0.97.

This can lead to nice arbitrage opportunities -- we may think. Look at the plot below of two Russell2000 ETFs, one long and one short, as of Dec 31, 2008.

(click to enlarge)

The R squared is 0.791, so correlation is 89%. However, in the last few days of 2008, the corresponding points are those at the bottom left corner, strickling far from the regression line. An arbitrage idea could have been to buy both ETFs, in proportions guided by the slope of the regression line, and to wait until the ETFs retrace or revert to their "natural" relationship. Since both ETFs look cheap in this regression, the trade would gain on both legs irrespective of the movement of the Russell2000. One fund may lose value, but if they did retrace to the red regression line, the gain on one leg would more than compensate for a loss in the other.

Unfortunately, here's what happened since.

Bloomberg shows the 2009 time series in blue. We see that the last few dots of 2008, the bottom leftmost yellow dots, were in fact the beginning of a new correlation regime: the relationship between the short and the long ETFs is still linear, but on a totally different line. What caused this change is a mystery to me, but the putting that trade on at the end of 2008 would not have made any money and possibly lost some.

Interestingly, this is far from limited to the Russell2000 index. Take the S&P500 for example. At the end of 08, the plot was this:

Same observation: the linear relationship is strong (75% of the price of one is explained by the price of the other), and the then-current market was an out-lier. However, we can now see that this was, again, a sudden (and to me, unexplained) change in "correlation regime:"