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Mean-Reversion in Trend-Following Performance Using a 120-day Lookback

September 19, 2019

In the last post we showed that trend-following tends to be mean-reverting in the short-term. Data analysis also shows that trend-following has an even stronger mean-reverting effect using a 6-month or 120-day window using the same methodology. Take a look at the chart below using the BarclayHedge SG Trend Index:

In the last post I hypothesized that the mean-reversion effect exists because investors tend to chase recent performance. But there is obviously a lot more going on that drives the performance of trend-followers including lower interest rates, higher correlations, and generally less pronounced trends. Certainly monetary policy worldwide has also played a factor. A very good paper by Spring Valley analyzes some of the factors that have affected trend-following performance. Ultimately the data suggests that you need to incorporate this effect into your strategy or asset allocation methodology in order to be more consistently profitable using a trend-following approach.

Mean-Reversion in Trend-Following Performance

September 18, 2019

In a recent post I showed that the momentum factor has been mean-reverting in the short-term, and that this effect can be used to trade both the factor and momentum strategies effectively. An obvious extension is to see whether trend-following as a factor is also mean-reverting. After all, time-series momentum and momentum have been shown to be related in the research.

To represent the trend-following factor I used the data for the BarclayHedge SG Trend-Following Index which captures the profitability of CTAs that follow a systematic trend-following approach. For consistency, I used the same methodology as the original post: I took the 10-day return and smoothed using a 5-period simple moving average in order to reduce noise. I then took the percentile ranking using all history available at each point-in-time of that smoothed return. Oversold was considered to be when the percentile ranking of the return was below the median (<.5) and overbought was when the percentile ranking was above the median (>.5). Positions are held until the percentile ranking goes back above (below) the median. As a third strategy, I tested avoiding the top quartile of performance (<.75) which is a lower turnover and perhaps a more realistic strategy.

In general we see evidence of mean-reversion in trend-following performance (this is true using a wide variety of parameters) which becomes most pronounced starting in early 2014. The strategy of avoiding the top quartile (long when trend-following has not recently been performing very well) has been effective over longer periods of time.

The lesson highlighted in recent posts has been that to be effective in the modern day environment you have to be a contrarian— buying momentum and trend-following strategies after they have had poor performance. The reason this anomaly likely exists is because people tend to hire and fire managers based on recent performance. As a piece of anectdotal evidence: when I was doing consulting work a long time ago, I used to joke with my colleagues that certain clients were particularly adept at timing when to be in or out of strategies: as soon as they were upset, the strategy probably bottomed, and as soon as they wanted to increase their allocation it had probably topped. After making several poor allocation/timing decisions they usually quit the strategy altogether claiming that it was ineffective.

I made a presentation at a conference in 2010 about mean-reversion in strategy performance using a sample of over a hundred different strategies (including both mean-reversion and trend-following as well as many others). My experience in money management after 2010 has been no different. Unfortunately, all marketing is geared toward recent performance so there is a conflict of interest: if you understand that strategies mean-revert in the short-term then you will be marketing most when clients are least likely to make money. AUM flows tend to reflect that this method works well. It is therefore not surprising that DALBAR studies show that the average investor (most of whom have advisors) significantly underperform their risk benchmarks.

Mo Data: Using Mean-Reversion in the Momentum Factor to Time Momentum

September 12, 2019

In the last post we used the data available for the momentum factor using an ETF (ticker: MOM) which seeks to replicate The Dow Jones Thematic Market Neutral Momentum Index to time when to be in or out of high momentum stocks. Alpha Architect recently did some interesting analysis of the distribution of returns for the same momentum index in this post. One of the challenges was the lack of data available for testing. Ideally we would have much more data. To address this issue I found that the Kenneth French Data Library has daily momentum factor returns. To find a tradeable long-only momentum strategy, I used PDP which is the Invesco DWA Momentum ETF and is based on the Dorsey Wright® Technical Leaders Index (DWA Technical Leaders Index). The strategy is to go long PDP when the momentum factor is oversold (<.5) and this is compared to a strategy that goes long PDP when the momentum factor is overbought (>.5). For more details please read the previous post. The results are in the chart below:

Having data prior to 2013 is valuable because we get to see how the strategy performed during the credit crisis in 2008 and also in the beginning of the explosive bull rally from 2009 to early 2010. Clearly mean-reversion in the momentum factor has worked well in timing high momentum stocks since 2007. While not shown, I tested a wide variety of different parameters and found very similar results. To determine whether this is a pervasive effect across history would require extensive testing with synthetic momentum strategies, however my guess is that this has been effective for at least the last 25 years. Ultimately if it works back to 2007, it is clearly worth using and at least watching as part of your trading in either high momentum stocks or their proxy ETFs or mutual funds. However it is worthwhile doing some additional analysis to determine why this strategy works.

When Should You Buy Momentum? Mean-Reversion in The Momentum Factor

September 12, 2019

Recently there was a good post by Bespoke Research highlighting the “Momentum Massacre” that we recently witnessed in the market. High- flying momentum stocks were decimated and the low momentum/losing stocks made a roaring comeback. One of the best ways to track the momentum factor is to look at the ETF ticker symbol: MOM or QuantShares U.S. Market Neutral Momentum Fund. As you can see in the chart below, the momentum factor has taken the elevator down over the past 10-days completely reversing total returns year to date.

This begs the obvious question: can we expect some mean-reversion in performance going forward? As a simple test I took a look at 10-day returns in MOM and smoothed them using a 5-day average to account for some of the noise in closing prices for less liquid ETFs. Then I took the cumulative percentile ranking looking at all data available at each point-in-time of that smoothed 10-day return. What I found was that in the last 8 years (the maximum data available), the momentum factor has been highly mean-reverting. If you bought the momentum factor after smoothed 10-day returns were above the median (.5) you lost money consistently. In contrast if you bought when returns were below the median you made money consistently. Clearly mean-reversion has been a powerful factor driving performance as you can see in the chart below:

To get a sense of how this would benefit investors that follow high momentum stocks, I looked at how using the same mean-reversion oscillator on MOM could be used to time MTUM or iShares MSCI USA Momentum Factor. In the chart below we see that using this oscillator has been a very useful way to time whether to be in or out of high momentum stocks:

When the momentum factor was oversold (<.5) you made almost 17% annualized with a sharpe of 1.74, and in contrast when the momentum factor was overbought- which was nearly 50% of the time- you lost money. One of the obvious questions is whether there is some bias in the momentum methodology unique to MTUM that makes it less generalizable to a more concentrated approach. To address this concern I tested using the oscillator on QMOM or Alpha Architect’s U.S. Quantitative Momentum ETF. While there is a much shorter history the general conclusion is the same: mean-reversion in the momentum factor is a good way to time momentum stocks:

Finally, and perhaps the most interesting test was whether or not the momentum factor on stocks can be used to time asset class momentum. I have read studies in the past that show that the momentum factor is correlated to asset class momentum. If that is the case then we can expect that the oscillator should be effective in timing global asset allocation. To test this I used GMOM or Cambria’s Global Momentum ETF. The chart tells the story below:

Clearly mean-reversion has been effective for timing global asset allocation that uses a momentum approach. What was surprising was just how effective it was. Having more data using proxy strategies to test these hypotheses over a larger sample size would be valuable, but I currently don’t have access to that data on a daily basis going far back in time. Nevertheless, it is still very important to respect current market trends and how they impact investment strategies. In recent times, the effect of mean-reversion in momentum factor is a very real and material driver of performance.

Why might there be a mean-reversion effect in the momentum factor? I think that a lot of stat arb money chases the momentum factor, and to be able to rebalance in order to maintain risk limits and to unwind positions they need to sell when they are profitable and buy back when they are losing money. To do so requires that a lot of retail and other institutional money be chasing or fleeing from momentum in order to provide them with liquidity. Perhaps this “smart money” effect explains why momentum is mean-reverting. In either case trying to explain why this happens would require a very thoughtful and deep analysis in the form of a serious research paper.

Current S&P 500 Economic Model Prediction

September 5, 2019

In responding to feedback, the economic model has been revised for the sake of simplicity to provide a more useable dashboard. The output is the chance of a large correction classified into three categories (low, drawdown>10%, drawdown >15%) and the predicted direction for the S&P500 over the next 90 days ( Bullish: >5% expected return, Sideways: >-5% <5% expected return, Bearish: <-5% expected return). Below is the current update. We will provide some backtests very soon, preliminary results are quite promising. Investor IQ plans to launch a website soon to provide access to this model in real time along with current ETF and stock analytics.

Building a Risk Control Index with Drawdown Protection (Part 1)

July 9, 2019


Both trend-following and absolute momentum are well established methods for managing risk. Another method for managing risk is to use volatility targeting. The former are superior for reducing large drawdowns in bear markets while the latter tends to reduce kurtosis by normalizing the daily bet size. The combination of the two tends to increase the sharpe ratio while generally reducing both kurtosis and skew. For a great review of the subject check out Rob Carver’s post. One of the concepts Rob brings up is that part of the challenge of trend-following and absolute momentum is that they are binary in nature– you are either “all-in” or “all-out” and this is suboptimal.

There are no magical numbers in finance- if the 1 year excess return of the stock market is 1% does this mean that you should have the same conviction as if it is up 10% or more? Clearly the slope has some relationship with forward risk. Is a -1% excess return that much worse than a 1% excess return? These levels are more arbitrary than you think. Exiting or reducing a position can be done profitably at a wide range of levels.

Another disadvantage of binary trend/momentum systems from a variance or luck standpoint is that by going all-in or all-out you can be hurt a lot more by the arbitrary execution timing of any one trade. (One way to reduce this problem is to use multiple lookbacks for a good review see this post by Newfound Research. This is also used within our “Trend Strength” indicator within Investor IQ) In contrast a strategy that employs a continuous position size has the benefit of scaling exposure as a function of conviction and is less susceptible to timing risk.

Lastly, the biggest challenge to trend/momentum systems is that they are not tied directly to any financial or risk-based objective. There is no limit on how much you can lose in any given time frame given either repeated whipsaws or large short-term corrections that occur before your signals trigger. In high momentum markets or situations like 1987, this added tail-risk can be significant as the binary trend/momentum signals will often still be 100% invested.

Risk Control

The concept of risk control is used more frequently in the annuity market or in various programs run by insurance companies to manage equity risk. Typically these are exactly the same as using volatility targeting (see this example here). However, there are more exotic strategies that add a type of dynamic overlay in order to further reduce risk. Regardless of the exact method used, this second layer is designed to be a form of drawdown protection. This feature is important given that a traditional risk control/vol targeting with a moderate risk profile will still have plenty of equity exposure through bear markets.

To build a risk control index with drawdown protection, I propose that investors use a drawdown target or “floor” that has some time frame attached to it. For example, many investors have a risk preference for not losing more than -20% on their portfolio in one year (this choice of floor and lookback is optional). You can directly control for this risk by scaling the size of your positions as a function of the current drawdown of your portfolio’s equity curve. This method roughly mimics a synthetic put option designed to insure losses below -20%. Here are the steps to building a risk control index with drawdown protection. For this example we can call this the “Risk Control 20/20 Index” (20% risk target, 20% drawdown target):

STEP 1: Risk Exposure (RE): Develop a volatility targeting method with a chosen volatility forecast or realized volatility forecast window (I chose 20-day realized historical in this example). Scale positions by target volatility (20% in this case) divided by current volatility whereby there is some maximum leverage permitted (no leverage in this case). Track the equity curve of this strategy for step #2

STEP 2: Drawdown Exposure (DE): Choosing some target drawdown (I chose 20% in this example) the equity “floor” (F) is equal to 1 minus the target drawdown. The current equity level (CE) is the value of yesterday’s risk control/vol target equity curve divided by the maximum price over the past n-days (I chose 1-year for this example). The formula for drawdown exposure (DE) is: MAX((1/(1-F)) x (CE-F)),0)

STEP 3: Total Exposure (TE): The final portfolio exposure that gets applied for the following day is calculated as: TE= RE x DE

The advantage of this approach is that you respond in a continuous manner to market drawdowns while scaling by volatility to improve risk-adjusted returns. Keep in mind that a 20% risk target and a 20% floor is fairly generous, so we can readily compare this Risk Control 20/20 index to standard absolute momentum (1-year return minus t-bills). The results of this comparison applied to the S&P500 index can be seen in the table below using daily execution to avoid bias (the choice of index price data allows for observing action across a wider array of different market regimes):

Both methods have nearly equal performance, but the Risk Control 20/20 index has better risk statistics with lower volatility, higher sharpe ratio and a much lower maximum drawdown. It is hard to see the difference between the two equity curves, but the rolling drawdown analysis is far more revealing:

In this chart you can clearly see that the Risk Control 20/20 Index does a much better job of controlling large drawdowns. In fact, the largest drawdown for absolute momentum occurred in 1987, when momentum was high and the signal failed to change in time for the crash. In contrast, the risk control index gradually shifted to a lower level of equity exposure. There are several other large drawdowns in the last thirty years where the risk control index with drawdown protection was superior owing to its ability to continuously size positions. Of course nothing can prevent against jump risk or large one day declines, but for most cases in theory the risk control index with drawdown protection should provide more explicit protection for investors. In the next post we will look at various methods to improve upon this original method along with some heuristics to make it more practical for real trading.

Investor IQ New Analytics

June 24, 2019

We have added some new analytics to the Investor IQ report. The signals are generated using a composite of 28 different momentum and trend-following signals over time frames ranging from 1-12 months. The number of buy signals determines whether the overall signal is “buy”, “hold” or “sell.” The “Trend Strength” is a new feature which shows the percentage of buy signals across the 28 different momentum and trend systems. This allows users to differentiate between the strength of the trend across ETFs or stocks. The “Volatility Score” is also a new feature which shows the relative volatility ranking (low ranking=lower volatility) from 0-100 across all ETFs or stocks. This can provide insight into relative risk and also allow users to form lower volatility portfolios with relative ease. A visual of the new output can be seen below:

Current S&P 500 Economic Prediction

June 10, 2019

The following is the composite point-in-time prediction for the S&P500 economic forecasting model. Currently the direction has changed from a flat prediction to an up prediction which indicates a resumption of the bullish trend. On the technical side check out our Investor IQ to look at the US Market Summary:

New Feature on Investor IQ: Asset Class Breadth and Relative Strength Summary Statistics

May 28, 2019

One of the new features introduced yesterday on Investor IQ is a summary of the breadth and relative strength of various asset class categories. This helps provide another layer of information for investors to determine which asset classes to focus on and which to avoid. We compile the % of buy signals using a matrix of trend and momentum signals as well as the average RS or Relative Strength using momentum within the asset class category. The best combination is obviously high % of buy signals and high RS. However a high RS with a low% of buy signals indicates caution as not all areas are participating as they would typically in a healthy market. The RS Spread is the difference between the strongest and weakest performer in the category and indicates the degree of opportunity for long/short portfolios within the same asset class. A visual of the current output can be seen below:

The asset class categories are listed in order of average RS. We can see that domestic equity and style,sector and factor components have the strongest relative strength. Traditional equity factors have the highest % buys within the domestic equity category. On the international front things are looking challenging – likely the result of the trade war. The % buys across countries is only 40% which suggests that markets across the globe are broadly struggling right now. This also correlates with the weakness in both breadth and relative strength in the Currency category which only has 14% buys and has the weakest asset class category average RS of only 7. The strongest asset class categories in terms of breadth are bonds and credit which is a trend worth watching. Commodities are the worst performing category in terms of breadth with 0% buys and also are relatively weak with an average RS of 28. The RS Spread of Commodities is the highest across asset class categories which indicates a good opportunity to go long a strong market such as Oil (USO) and short a weak market such as Gas (UNG).

This summary is a good way to keep on top of the market and spot new opportunities to overweight/underweight certain asset class categories.

Current S&P500 Economic Forecasting Model Prediction

May 27, 2019

We introduced our machine-learning economic forecasting model as a neat new way to compress a ton of economic data to gauge the health of the economy in order to predict cyclical (not sentiment driven) drawdowns in the stock market. The current prediction uses two different models:

1) Composite Point-in-time– this model only creates a forecast when all data required by the model is available at the point-in-time that it was available. If the model is waiting on data it will simply carry forward the last prediction made when all data was available. The historical prediction table was generated using this model.

2) Preliminary – this model is trained using the data available and is capable of making forecasts when there is missing data that the Composite model is waiting for. It does this by interpolating the missing data. Currently given that there are three missing pieces of data we can only make a preliminary forecast through the end of June.

Current Prediction- Preliminary

For the prediction period Apr 2019 – Jun 2019, the model predicts the following results based on economic data as of Mar 31, 2019:

  • Is there a reasonable chance of a large correction happening between Apr 2019 – Jun 2019? Not Expected
  • What is the predicted direction of returns between Apr 2019 – Jun 2019? Flat