Last Updated on June 19, 2022 by Quantified Trading
Mean Reversion Trading Strategies and Backtest. How do you create or build a trading strategy that is based on reverting to the mean?
? What are the pros and cons of mean reversion trading strategies? Do mean reversion strategies work?
This article gives you some input and advice on how to develop a mean reversion trading strategy and discusses its pros and cons. We cover what mean reversion is, if it works, explain which markets are most mean revertive, and lastly in numerical order explain the main elements worth considering in the creation process. Mean reversion strategies work very well in the stock market.
What is mean reversion in trading?
Mean reversion is the opposite of momentum and trend following. Also called reverting to the mean.
What is momentum?
Momentum is when you go long or short in the same direction as the movement over the last defined periods. For example, a lot of research shows that by going long the best 20 stocks over the last six months and rebalancing monthly, you have had a tremendous edge in the stock market and beaten the indices by a wide margin. This anomaly was revealed in the early 1990s but it has still worked well after it was “discovered”.
A good example of momentum is this strategy we developed by rotating back and forth between the S&P 500 (SPY) and Treasury Bonds (TLT):
The same goes for trend-following, which is also a strategy similar to momentum:
What is mean reversion?
Mean reversion is the opposite of momentum and trend-following. A mean-reverting strategy assumes any trends and moves will reverse and return to the mean. In statistics, this term is called regression to the mean.
Any data or observations that are on the tails of a normal distribution are most likely abnormalities that will sooner or later turn around a revert to the mean. At least that’s the idea (most of the time).
Coin flipping is a perfect example of mean-reversion:
If you flip a coin and assume fair play, there is a 50% chance of tail or head. By flipping 100 times there is a 67% chance that the interval will be 55:45 head or tail (one standard deviation). The chance of being inside 60:40 is 95% (two standard deviations), and 99% of being inside 65:35 (three standard deviations).
However, the more you flip the coin, for example, 10 000 times, the closer you’ll get to the average of 50:50, despite having short-term “runs” that can deviate pretty much from the long-term statistics and probabilities.
This is also called the law of large numbers, which is an important concept in trading.
How can you utilize the coin-flip metaphor in the financial markets?
It turns out certain markets are mean-revertive by nature, while others are not. For example, stocks are highly mean-reverting in the short-term while commodities are much less so. However, the good thing about stocks is that you can successfully apply both momentum and mean-reversion. Moreover, the stock market has many sectors and industries that are not very correlated (business-like).
The latter is not a contradiction. The market is very mean-revertive in the short-term (less than three months), while momentum seems to work best in 3-12 months time frames. When looking at more than 12 months stocks trend, ie. the upward bias from inflation and earnings make stocks go up. The overnight edge has been long and persistent.
Why are stocks mean-revertive?
One possible explanation could be margin, or rather the lack of margin. Why would margin make the market mean-revertive? As stocks go up and down they become more liable to rebalancing, and this means selling those stocks which have risen and buying those which have fallen.
Both hedge funds and mutual funds have mandates on how to operate, both on risk parameters and diversification. Thus, they are obligated to reshuffle their portfolio which is often against the prevailing trend.
Another aspect is short selling and arbitrage. Short sellers short overvalued stocks and buy undervalued stocks, which effectively dampens both upside and downside moves. This also explains why we tend to see the most violent moves to the upside during bear markets: short-sellers run to the exits (they need to buy to cover their positions) and this adds fuel to the fire.
Likewise, arbitrageurs short those which rise in value and buy those which fall in value.
Does mean reversion work? Is mean reversion profitable?
Yes, mean reversion works, but not in all markets. To our knowledge, it works best for stocks and less for other financial assets.
We have published many free strategies on this website that works pretty well, for example, these two:
Some popular mean revertive indicators
The most used indicators are mostly based on mean-reversion, albeit you can use them in many different ways. Here are some samples of what we have written about the most popular indicators (with quantified examples):
- Which oscillating indicator is the best for trading strategies?
- WilliamsVixFix explained – does it work? (Including trading strategies)
- Does the MACD indicator work? (Including strategies)
- Williams %R – does it work?
- How the RSI indicator works
- The internal bar strength indicator (IBS)
- The stochastic indicator – does it work?
- Zweig Breadth Thrust Indicator – how to measure market breadth
Are stock fundamentals mean reverting?
Back in 1994, the academics Josef Lakonishok, Andrei Shleifer, and Robert Vishny wrote a paper called Contrarian Investment, Extrapolation, and Risk, the first study looking at mean reversion in earnings, where they compared past growth rates to future growth rates. Perhaps not surprisingly, they concluded that earnings tend to revert to the mean.
Likewise, mutual funds tend to mean revert: the best funds over the last three years, are not likely to be among the top funds over the next three years and vice versa.
Is volatility mean reverting?
Yes, volatility is highly mean-reverting. As an example, look at this average true range (ATR) of the S&P 500 since the year 2000:
(We have developed an ATR strategy on the S&P 500 which you can order for 99 USD.)
The chart above shows that volatility comes and goes, although it seems to have established itself on a higher level in 2021. When volatility spikes, it tends to cool off and go down after some time, of course depending on your time frame.
Not shown in the chart is that spikes in volatility frequently signal a “blow-off” and a bottom, at least temporarily.
Stop losses and mean reversion
In almost all backtests, you will notice that stop-loss doesn’t work in mean-reverting strategies. The more it goes against you, the better the signal. Thus, stop-losses might be very detrimental to a strategy unless you set a very wide stop-loss. But if you have a very wide stop-loss then you in reality don’t have a stop-loss.
The tendency for stops not to add value applies to trend-following as well. In the brilliant book The Way Of The Turtle, Curtis Faith concluded that stop-losses for most systems don’t improve profitability, nor does it limit the drawdowns. His trend-following systems perform better for all trading performance metrics without any stop at all: CAGR, MAR, Sharpe-ratio, and drawdown.
Jim Simons and the Medallion fund uses many mean-reverting strategies
In Gregory Zuckerman’s unauthorized book about Jim Simons, Zuckerman claims that the managers of the highly successful Medallion Fund consider men revertive strategies as the “low hanging fruit”.
Why would he write that?
Mean-revertive strategies, in principle, are not complex and they are easy to understand: you go against moves in certain directions, either sharp and violent short-term moves or slow long-term moves. It’s easy both to understand and implement. They are also frequent enough to have a meaningful statistical significance.
Sentiment indicators are mean-reverting
Technical indicators are not the only mean-revertive indicators: sentiment indicators are also strongly mean-revertive by nature.
Let’s take one example: the put/call ratio which measures the number of puts and calls traded daily, weekly, or whatever time frame you are looking at. It serves as a measurement of the mood of the markets.
Because puts and calls, in reality, work like insurance, the ratio tends to rise in turbulence and vice versa. The graph below shows the put/call ratio for equities over the last three years:
The ratio measures the mood of the options market. Investors and traders tend to buy puts when equity prices go down, and because of this, the put/call ratio can be used as a sentiment indicator for mean-reversion strategies.
Drawbacks of mean reversion (mean reversion disadvantages – cons)
Every strategy has its pros and cons. What are the main drawbacks of a mean-reverting strategy?
First off, a mean-revertive strategy doesn’t let the profits run: you cut the winners and let the losers run, opposite of what many traders and gurus recommend. Because you aim for a regression to the mean you sell or close the position after a moderate move in your desired direction. You cut the winners.
And, as pointed out above, mean-reversion strategies are not happy when it comes to stop-losses. Mean-reversion works better without stops, and thus you let the losers run.
A third drawback is the profit distribution which is slightly negatively skewed to the left side of the x-axis. Unfortunately, many mean-reverting strategies are not evenly distributed: Most trades are around the mean with many winners, but at the same time a few big losers:
The win ratio is normally very high, but often the distribution has more big losers than big winners. In the pic above we see a high win ratio, but the left tail is “fat” while the right tail is “thin”.
Another key point about mean-reversion is high activity. To get a high CAGR you need to trade quite frequently. This is both positive and negative. The positive is that you normally can get faith in the system because of the big sample of trades. The drawback is, of course, slippage and commissions.
However, the faith in a mean-reverting system can easily grind to a halt when you get the infrequent big loser.
Trend-following strategies normally have the opposite characteristics: fewer trades, lower win ratio, but most likely “thin” left tails and “fat” right tails: more big winners than losers. The biggest risk in trend-following is that your account slowly bleeds to death.
A mean-reversion strategy is more likely to deteriorate quickly. You can make a lot of money for over a year, only to see most or all of it disappear in a brief bear market.
This means that mean-reversion and trend-following require completely different mindsets, risks, and drawdowns.
How to create a mean reversion strategy:
The principles of mean reversion strategies are simple: you buy when something has fallen, and you sell when it has risen in value. In order to measure, you need a benchmark or a mean to create “bands” or levels where you consider going against the move. The principles can’t get any simpler than that.
We end the article by presenting a bullet point list on how to develop a mean-reversion strategy:
- You need an idea or a hypothesis. Make it as precise as possible to a testable hypothesis.
- Get data for the product you want to test. The best data have little to no errors, and preferably including delisted stocks to avoid survivorship bias.
- Make buy and sell rules with as few parameters/variables as possible to avoid curve-fitting the data to the past.
- The exit is important and often overlooked. Mean reversion strategies work best when you sell on strength.
- Test exit with time stops to verify robustness, preferably by using exits based on n-days (time exit).
- Use common sense. Be street-smart, not academic smart. Keep it simple, complexity is for the academics.
- Play with optimization to find out how the strategy performs with other sets of values.
- Test out of sample, preferably on a demo account for a few months.
The best mean reversion strategies
Because mean reversion has worked so well in the stock market for over two decades, most indicators that buy on weakness and sell on strength have worked.
We have covered many of these indicators and included examples and strategies in the articles. Here are a few sample of mean reversion strategies:
- 3 free mean reversion trading strategies (backtested buy and sell signals)
- 10 free swing strategies that work (backtested buy and sell signals)
- S&P 500 mean reversion using IBS and RSI
- The Turnaround Tuesday trading strategy
- A long-term pullback trading strategy in the S&P 500
- Lower highs and lower lows pattern (trading strategy)
- Higher highs and higher lows pattern (trading strategy)
- RSI SPY trading strategy (RSI(2) on SPY)
- 4 Overnight Trading Strategies In The S&P 500 (Strategies From Close To The Next Open)
- RSI QQQ (RSI mean reversion trading strategy QQQ)
- Do candlesticks work? A quantitative test of 23 candlestick patterns
- 3 bullish candlestick patterns that work
- XLP trading strategies (Is XLP good for trading?)
- Larry Connors’ Double Seven strategy (Double 7 trading strategy)
- Larry Connors’ multiple days up and multiple days down strategy
- Larry Connors’ %b strategy (Bollinger Bands)
- Larry Connors’ R3 strategy
- Larry Connors’ RSI 25 & RSI 75 strategy
- Larry Connors’ 3-day high/low strategy
- What happens when stock markets are oversold?
- What happens when stock markets are overbought?
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Mean reversion conclusions
There is no coincidence that Jim Simons indicates that mean-reversion strategies are the “low hanging fruit” in the equity markets. They are both easy to understand, implement, and are for most traders easy to execute. However, it has its drawdowns: you cut the winners and let the losers run.
Mean reversion is often intuitive: buy weakness and sell strengths. Because of this, we recommend mean-revertive systems, as a matter of fact, most of our systems are mean-revertive, but you need to diversify to different time frames, instruments, and by using filters.
How do you build or create a mean reversion strategy? You need to use the most important tool of any trader: statistics to quantify your hypotheses.