Today’s statistical phenomenon has many names – mean reversion, statistical arbitrage, lead-lag structures – but the trading strategy remains the same. We are leaving the Market Timing family of strategies and going further into the deep end of Mean Reversion for this one. Observe this chart:
We see that once we normalize as of a certain date, the Straits Times Index and the Hang Seng Index track each other closely despite their vastly different numerical levels. Plotting the cumulative degree of STI outperformance results in the green line, which has no further purpose than to show that the ratio of FSSTI to HSI hovers pretty much around the level it is at as of 3 Jan 2001 (this ratio is 7.72). Thus, when the FSSTI outperforms the HSI on any particular day, it is likely to underperform the HSI at some future point (not necessarily the following day). With a long/short market neutral bet we can profit from the expected narrowing of this gap, but there are an infinite number of ways to structure your decision rule. The simplest, in my view, is to bet on the ratio reverting back to 7.72, and to keep at it until the ratio is reestablished (Static Ratio Reversion):
This chart is on a log scale so I have added +1 to all values on the green line in order to display it meaningfully. The purple line shows the profits resulting from the Static Ratio Reversion strategy, and although the end result of 381% profit is impressive, it is worthwhile to note that from 2001 to late 2007 the strategy didn’t have any profit to show for all its sophistication. Also, eyeballing the green and purple lines, it is clear that the strategy only makes money when the green line heads toward the 1.000 line, which marks the 7.72 ratio established on 3rd Jan 2001. This highlights the chief difficulty with the Static Ratio Reversion strategy, as it is a strategy that says that the ratio of FSSTI and HSI on any given day is wrong, but the ratio on one particular day (in this one, 3rd Jan 2001), is “right”. Further, it doesn’t allow for any fundamental movement over time in the ratio itself.
The Moving Average Ratio Reversion method solves this by trading based on reversion to a moving average of past ratios, and not one past ratio on one particular day. This can help anticipate movements in the trend far better, as it can be seen that the 7.72 point is quite often off the mark:
With this in mind, is a slower moving average better or a faster moving average? I don’t have the time or presence of mind to derive the relationship between the predictive ability of the moving average of a ratio and the profit from a ratio reversion strategy on that ratio, but empirically we can observe a few data points and make some inferences:
It seems that the mid 2000s loss periods are avoided with longer MA estimations. I need to do further work on this and don’t have the time, but I leave you with the risk/return statistics:
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