One of the very few things you can count on in the investment world is that everything will change. Timeless investment truths will become relics. Guidelines that were infallible in the past will suddenly go wrong. Human nature may not change much, but the market itself is a constantly evolving organism. One of the biggest casualties of change is correlation. There are really two problems with correlation.
1. Correlation is often confused with causality. Big mistake. Just because something is related does not mean it has anything to do with the cause. For example, drinking milk is not the cause of heroin addiction, even if you can prove that all heroin addicts drank milk as children.
2. Correlations are unstable. This causes all sorts of problems in mean optimization and strategic asset allocation. The best example I have seen of this recently is a fantastic chart from Bespoke Investment Group that shows a rolling 6-month correlation between the dollar and the S&P 500. Over a ten-year period, the correlation moves from virtually +1.0 to -1.0, not to mention everywhere in between!
Courtesy: Bespoke Investment Group
Shocking isn’t it? Yet this is the one thing you can count on-that everything will change. To me, this is one of the strongest arguments for an adaptive method that adjusts systematically to new conditions. Although it is probably not the only way to go about it, relative strength is a good engine to use for models because it is highly adaptive, robust, and deals well with multi-asset portfolios, which are more and more becoming the norm.
I don’t think that the Bespoke data shows that correlations are unstable. I think it shows that there is a lot of measurement error when estimating correlations.
I’d like to see your mathematical explanation of this measurement error. The concept of correlation is relatively simple. If, for example, the dollar and S&P 500 both go up on a given day, the correlation is +1.0. If they go in a completely opposite direction, the correlation is -1.0. If you did a plot of one-day correlations, it would whip back and forth between +1.0 and -1.0, which is clearly due to the instability of the relationship, not measurement error. (Bespoke attempted to smooth the relationship by using a 6-month lookback period. Their chart shows that even over a 6-month period the correlation whips around a lot. Even 5-year correlations between a lot of asset classes exhibit significant instability.)
The whipping between +1 and -1 is due to measurement error. It’s pretty high! That’s why even a 6 month period still has a lot of whipping. In the linear model y = a + bx + e I define e to be the measurement error. If the standard deviation of e is high then any attempts to estimate b will be swamped by the noisy e even if you take 6 months worth of data.
Your comment assumes that linear regression is the only way to measure the correlation, and that anything away from the regression line is measurement error! (Even a least-squares fit regression line is affected a lot by high standard deviation.) There is a lot of “noise,” but I would contend that the noise reflects an unstable correlation rather than measurement error. As I mentioned earlier, you get significant instability in correlations even with 5-year smoothing. This is why, for example, even a 10-year efficient frontier for stocks/bonds looks completely different for the 1970s, the 1980s, and the 1990s. Are you actually contending that the relationship between stocks and the dollar is stable? (And Bespoke just can’t tell because the measurement error is high?)