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Some Subtle Thoughts on Mean-Reversion and How To Create More Informative Benchmarks

January 21, 2011

Michael Stokes who does excellent work over at MarketSci publishes a very interesting report on the “State of Mean-Reversion.” Equally interesting is work done by Jez Liberty at Automated Trading Systems on the complementary “State of Trend Following.” Both of these reports aim to capture an “effect” via  the performance of similar or correlated strategies. The logic is that such benchmarks should reveal important information at a “20,000 foot level” towards the relative effectiveness of a given style. I am not writing this post to disparage/criticize the excellent work of these bloggers (and Michael especially since this considers mean-reversion only), but rather wish to point out how the benchmarks themselves can create issues in interpretation in ways that are analogous to any type of index product. Some of these issues are so subtle– such as the “rebalancing bonus”  that they deserve their own post. For now, it is important to consider some subtle thoughts on the “philosophy” of mean-reversion as it is often referred to in the blogosphere. In my opinion, there are some layers beneath the onion that many readers have likely taken for granted–or failed to consider.

Ultimately what most of us think of as “mean-reversion” is quite semantic but not necessarily interchangeable. I will spare readers from making a specific definition at this point, but rather mention that it is overly simplistic to have one strategy be representative of a group or constitute the baseline benchmark for an effect like mean-reversion.  For example, “daily follow-through” or the reverse seems to be the de facto benchmark for most traders as representative of mean-reversion (note that the State of Mean-Reversion is more balanced). In my opinion, daily follow through (or reverse daily follow through as I like to call it) is NOT per se mean-reversion by my thinking. This reflects a more recent evolution in my thinking towards looking at conditional outcomes of specific features of classification. In this case, a daily follow through strategy has features that are different from say an indicator and such differences are not readily obvious. As a consequence, the observed performance (or recent lack therof) of such a strategy as “daily follow through” does not appropriately lead to a linear set of conclusions. The confusion doesn’t stop there:  mean-reversion can still exist profitably at the daily level without conforming to a pattern of positive days leading to negative days and vice versa. Furthermore, the existence of a profitable strategy that fades positive/negative days need not necessarily imply strong mean reversion. Much of this discrepancy can relate to non-linearity in decile/quantile/quartile/median/average behavior in measuring a given effect. In addition, the presence of outliers that tend to occur in high/low volatility or very strong/weak trends can bias various backtest lengths. The environment has a strong conditional effect on the micro-observation of the 1-day lagged performance. Also  the persistence of incorrect signals for long versus short signals as a function of going against the trend can also obscure what is actually going on. That is, long/cash is very different than long/short, and the profitability/losses of one side (ie short) can mask the profitability/losses of the other side (ie long).

At the indicator level,  it is difficult to paint things with the same brush as they too can measure different things, and can have widely diverging performance at times as a function of those differences. The DV2  or DVB indicator had remarkable performance in 2010 while other “mean-reversion” strategies suffered– to hail its superiority as a mean-reversion indicator would be foolish and self-serving but more importantly it also obscures the point: The DVB or DV2 measures a distribution of relative range (close vs high/low) and is not always a mean-reversion indicator! The DVB/DV2  has a tendency to adapt to the current environment and because it does not care about the relative close, it  often signals going long on up days as well as short on down days. This creates substantial “tracking error” to any benchmark such as daily follow through that looks for example at the binary pattern of closing prices over the last two days. The RSI2 also need not be a mean-reversion indicator– in this case because it has very different behavior at a binary level (50/50) versus extremes, and also has very different behavior as a function of time spent at extremes. The RSI is more closely related to daily follow through, yet because of these properties as well as a 2-day parameter, it can also generate material tracking error to such a benchmark. The RSI is also a multi-faceted tool that can be used in for example the reverse direction for strongly trending markets. In other words, high readings can function more accurately as a trend signal–especially in commodities. This negates the stereotype that it must function as a pure mean-reversion indicator. The parameter length of the aforementioned examples in itself is ambiguous as it suggests that mean-reversion is defined by a given lookback–in this case shorter-term. Also missing in this discussion is the profitability or derivative of the strategy–that is conditional performance matters.

To complicate matters even more, the discussion of volatility filters and related measures and their linkage to mean-reversion performance can further obscure the ultimate goal (the subject of the next post). So lets take a step back and consider what we are trying to accomplish. The nuances of “mean-reversion” are truly never-ending-one must understand the calculations of indicators and their concurrent assumptions/drawbacks to understand why things succeed or fail to work. Lets take the RSI2 as a very basic example. The RSI2 is merely an oscillator that captures a relative measurement of the close to close point moves up versus the point moves down. That is, it does not consider the open, the low or the high.  Through the process of re-scaling, this measure is normalized (albeit more akin  to forced nonlinear compression) between 0 and 100. The RSI has some advantages and disadvantages, first the good: 1) it is very sensitive and tends to move coincident with price 2) it is a more normalized measure than using either point moves or returns in the sense that moves are considered in a relative sense versus a pure absolute sense. This makes it easier to create standardized trading rules.  Now the bad: 1) RSI values are still somewhat absolute, and the distribution of values can change over time such that extreme readings become even more infrequent and vice versa, especially as the environment changes (think 2009). 2) one implicitly assumes using an RSI that close to close movements are a stationary and valuable predictor of future reversion– in fact, the relative importance of momentum (close to close) versus range (close versus highs and lows) can shift over both short and long periods of time. They can also have complex interacting effects. An example would be RSI-DV2 divergence, or the diverging performance of the indicators in isolation as a tool for analysis. There is little point in continuing to list the oddities or discrepancies that exist. The point is that mean-reversion is a highly nuanced topic—and cannot be taken advantage of effectively without gaining a deeper understanding of the details.  Perhaps this post is somewhat similar to the movies that end without a clear resolution– such films require the viewer to do some thinking after the fact or have an imagination concerning the possible outcomes. If this post helps you to do the latter in the appropriate context, then you will find yourself become a better system developer–and even a better discretionary trader than uses technical indicators.

3 Comments leave one →
  1. Dave Evans permalink
    January 21, 2011 9:54 am

    Interesting post David

    It is interesting to note the divergence in performance between the DVB and simple sell after an up day type methods. Though linked they both look at different effects. Perhaps its basic human psychology to need to create boundaries around things in order to categorise and understand them.

  2. January 21, 2011 10:29 am

    Thanks for the mention David.

    A bit more background with regards to the index/state of Trend Following report (which in no doubt is different but not opposite to Mean Reversion): some of the underlying reasons why I believe it works quite well in reflecting Trend Following “effectiveness” as a “strategy” are explained there:
    and in the paper from the Conquest Group linked in that post.

    The basic idea is that most CTAs involved in diversified Trend Following correlate fairly well to each other and that they produce more beta to a Trend Following “hypthetical index” than usually assumed, compared to real alpha.

    I am planning a post running a correlation analysis to compare the performance of the index to the big CTAs in Trend Following (which I track as well, ie “TF Wizards”) and the idea is to show that a big chunk of their performance/returns is replicable by building a fairly simple benchmark/hypothetical index.

  3. January 24, 2011 12:57 pm

    To understand mean reversion, one should understand liquidity.

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