Taming Mean Reversion’s Left Tail – Don’t use Stop Losses!

Mean reversion strategies rely on the premise that extremes in price eventually revert to the mean price over time. They are effective during established markets – bull, bear or sideways – but unfortunately do not perform well during market regime changes or tail events. Tail events are outcomes that have a low probability of occurring, but may inflict significant damage to a portfolio when they do. They are those rare but devastating losses caused by persistent and violent price trends that are typically tied to a structural change within a company, such as fraud uncovered in financial reporting for instance. It’s these tail events, specifically negative or left tail events, that present the single largest risk to mean reversion. Thus, the key issue to successfully exploiting mean reversion is to contain the effects of significant losses associated with the left tail.

In this post, I’ll explore the performance profile of mean reversion, examine tail risk and share some methods that can be used to mitigate tail risk. Interestingly, the common approaches to controlling risk, such as the use of stop losses, actually make matters worse. I’ll share alternatives that prove more effective.

Mean Reversion’s Performance Profile

Before we discuss methods to mitigate the tail risk inherent in mean reversion, lets first take a look at the performance profile of a simple mean reversion strategy and discuss what is meant by tail risk. The return distribution below is from a long only mean reversion strategy that enters stocks on short-term weakness and exits on short-term strength. It does not use stop losses. We’ll examine the use of stops next, for now, I want to focus on the trade return distribution, which is typical of mean reversion.

Examining the return distribution below, it’s clear that short-term mean reversion strategies enjoy high winning rates – the green bars represent positive returns, and make up the majority of the distribution – but small average returns– the most frequent return is captured by the tallest green bar which represents returns between +2% and +3%. This combination of high winning rates and small returns is what feeds the compounding machine and which leads to relatively low volatility and consistent performance. This is a very desirable attribute which resulted in my researching and trading this approach for the last decade.

There is however a dark side to mean reversion (isn’t there always; trading is about compromise) which is associated with the distribution’s strong negative skew in the left tail. This is represented by the greater number of more extreme negative returns relative to the positive returns. For instance, the best performing trade generated +14%, while the worst performing trade resulted in a -23% loss. Moreover, there are 21 positive returns above +10%, but 78 negative returns less than -10%! This is the nasty negative skew in the left tail of mean reversion. For every return greater than +10%, there are 4 negative returns that exceed -10%. These extreme left tail losses can result in significant portfolio damage if not controlled for properly. So how do we manage the risk associated with the left tail? What about stop losses?

Stop Losses – Make Matters Worse!

An obvious starting point to control risk is the use of a stop loss. This seems intuitive since we’re looking to contain extreme losses, but as is often the case in trading, what seems logical does not always work. This is one of those instances. In fact, stop losses make matters far worse, often halving returns and doubling drawdown. Below are the return distributions when implementing a 5% and 10% stop loss respectively.

The distributions clearly show the problem when stops are applied to mean reversion – they lock in the loss of multiple trades that would have otherwise resulted in positive returns or smaller losses if closed with the original exit strategy, which waited for the trade to start its reversion. I’ve run this analysis to include a stop loss as far as 50% away from the entry point, and incredibly performance still deteriorates relative to no stops, albeit marginally. Basically, stop losses are not an effective way to control left tail losses because they tend to be triggered by extreme intraday moves driven by emotion that have a high propensity to reverse. All a stop loss does is guarantee the loss without the ability to participate in the likely recovery. That said, a stop loss may be useful when used in the context of a catastrophic loss. This can be achieved by setting the stop far enough away from price so as not to erode performance, but close enough to prevent catastrophic losses. In our case, 50% would work well.

If stop losses don’t work, how do we control for tail risk in mean reversion? Let’s examine a couple of techniques that have proven to be effective.

Position Size for the Left Tail

Set your trade size at a level that would not result in material losses if the worst hypothetical trade return were exceeded by a factor of two or three. The strategy discussed above experienced a worse loss of -23%, so by this measure we should allow for losses in our trading of around -50%. With this figure in hand, we can now set a position size that ensures we remain within our loss tolerance band. For instance, if we intend to restrict our worst losses to no more than -10% of equity, then we would allow ourselves a position size of 20% of equity (on a R100K account, that would amount to a R20K position, which would result in a R10K loss, or -10%, if the trade fell -50%). However, keep in mind that multiple extreme losses could occur together, which we need to make provision for.

Limit Sector Exposure

Set limits for the strategy in terms of the amount of exposure that it’s allowed to assume in a single sector. Market moving news tends to effect sectors in their entirety so allowing a strategy to expose itself 100% to a given sector will amplify the effects of the left tail when the sector experiences material game changing events.

Limit Daily Exposure

Markets tend to see very high levels of correlation in the short-term during significant broad market moves, especially when driven by fear to the downside. Therefore, allowing a strategy to gain 100% of its exposure in a single day increases mean reversion’s left tail risk as the strategy is sucked into multiple correlated positions on the same day. It’s far more effective to restrict a strategy’s allocation on any one day to a percentage of equity.

Diversify across the Mean Reversion Curve

This is something our professional platform, QuantLab, does exceptionally well. Instead of allocating capital to a single entry or exit point in each trade, rather look to divide the capital into portions and allocate to different entry and exit points. We will never capture the perfect bottom and top consistently through time, so why allocate capital in such a manner? By spreading capital across multiple entry and exit points, we capture the average trade through time. This has some incredibly powerful performance attributes, not least of which is it helps reduce the impact of tail risk.

Diversify across Everything

Diversify in every possible way to reduce equity exposure to any one idea. Include many mean reversion strategies in many different global markets. Include different non-correlated strategies, like for instance trend following strategies. The idea here is to have as many small positions as possible spread across as many ideas as possible. When you reach this level of diversification, position sizes are so small relative to total equity that even if a trade moves 100% against your portfolio the losses are so small to be almost insignificant.

Employing some or all of these techniques will help to reduce the effects of the nasty left tail inherent in mean reversion. Taken to the extreme, when implementing all the methods discussed, the risk of the left tail is essentially eliminated, or at the very least, significantly reduced. What is however clear is the ineffectiveness of stop losses in short-term mean reversion strategies.

Happy Trading,
PJ

Passionate about generating and sharing quantified trading models that empower individuals to trade successfully. I founded www.sutherlandresearch.com to realise my passion.

3 comments On Taming Mean Reversion’s Left Tail – Don’t use Stop Losses!

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  • Great blog PJ! I would really like to learn more about diversifying across the mean reversion curve. If you could do a blog post with a hypothetical example that would be great. Some question I have is when you mentioned dividing capital into portions and allocating to different entry and exit points. Is this done across all of the portfolio entry and exit signals or is this only done at the asset class level for example currencies, commodities, stocks and interest rates?

    • Thanks for reading, glad you enjoyed. I’ll look to do a post on diversifying across the mean reversion curve at some future point, appreciate your suggestion. If you haven’t listened to the podcast I did with Better System Trader, then you’ll probably find it worth your time since I speak in depth about diversifying across the mean reversion curve. You can access the podcast with the efollowing link http://bettersystemtrader.com/062-mean-reversion-strategies-pj-sutherland/. Briefly, I allocate portions of my capital across different parameter combinations within a portfolio so that my capital is exposed to shallow/medium/deep reversion entries and exits. That way we have a piece for all types of mean reversion and capture the average trade through time removing to a large extents the effects of luck (good and bad), which can be quite significant with single strategy approaches. We are also able to generate more consistent performance as a direct result of being better diversified. Hope that helps.

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