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Trend Following

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When I was a young account executive with Merrill Lynch in the mid-1970's, I became friendly with the top producer in our office. One day he shared with me one of the secrets of his success – he would only promote stocks if a certain percentage of the Dow Jones Industrial stocks were above their 39-week moving averages. Very few people even knew what moving averages were back then, and there were no PCs for calculating them. So I dug up all the old stock charts I could find with moving averages on them and verified that this moving average filter was incredibly useful. Not long after that, I was accepted into the PhD programs at both the University of Chicago and Wharton. I turned them both down, based in part on the how well this moving average method had done. (I was also impressed with Bob Levy's research on relative strength momentum and the Nick Darvas book describing his remarkable success using rotational momentum.) The efficient market hypothesis, which said the market could not be beat using publically available information, was akin to religion in the academic world at that time. I had frightening visions of being burned at the stake in the University of Chicago quadrangle if I had gone there.

Things have certainly changed since then. During the past 20 years, academics have found strong evidence of profitability using trend following methods, such as moving averages. As with momentum, behavioral finance is what led to serious trend following research by the academic community. A large body of research has now shown that price trends exist in part due to long-standing behavioral biases by investors, such as anchoring and hoarding. Price trends are created when investors initially under-react and subsequently over-react to information because of their strongly ingrained behavioral tendencies. 

There are now over a dozen well-researched academic papers documenting extraordinary risk-adjusted returns from trend following methods. I will provide references in my new research paper on absolute momentum that I am finishing up on now. However, here are three excellent, recently released papers on the subject of trend following:

Market Timing with Moving Averages by Paskalis Glabadanis


A Century of Evidence on Trend-Following Investing by Brian Hurst, Yao Hua Ooi, and Lasse H. Pedersen

The first two papers deal with moving averages applied to U.S. stocks. The third is a simple white paper from the folks at AQR. It features time series (absolute) momentum applied to 59 markets in 4 asset classes: equity indices, bonds, commodities, and currency pairs. The authors use a weighted combination of 1, 3, and 12 month look back periods on data going all the way back to 1903. Their paper provides convincing evidence that trend following absolute momentum is just as robust and pervasive as cross-sectional relative strength momentum.

The expanded version of my paper, Risk Premia Harvesting Through Dual Momentum, shows that absolute momentum is actually more valuable than relative strength momentum. Both enhance returns, but absolute momentum is more effective in reducing expected volatility and drawdown. The best of all worlds is to use them both together.  

Whatchamacallit

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In 1967, Bob Levy came up with the term relative strength in his paper "Relative Strength as a Criterion for Investment Selection." He soon afterwards wrote a book called The Relative Strength Concept of Stock Price Forecasting. Levy showed that stocks which outperformed the market over a pre-specified time period exhibited a type of performance that tended to persist. Relative strength was a good name for this form of investing. When academics got a hold of the relative strength concept in the 1990s, they renamed it momentum. This was unfortunate, since momentum among practitioners also means investing in anything that shows price strength. I still run across this when uninformed investors want to dismiss momentum as something left over from the dotcom days.

In the early days, academics further defined momentum as "cross-sectional momentum," since it was usually studied by sectioning the stock market into deciles or quintiles and comparing the top relative strength "winners" to the bottom relative strength "losers". Recently, researchers have discovered another form of momentum that looks at an asset's performance against its own past price action rather than against the past performance of its peers. I first used this in my 2011 research paper by comparing the performance of risky assets to the relatively stable performance of short-term bonds. This form of momentum was a key feature of my 2012 paper "Risk Premia Harvesting through Dual Momentum." I called it absolute momentum, in contrast to relative momentum. The researchers at AQR were also working on a paper published last year called "Time Series Momentum." To me, time series means something like ARMA or ARCH modeling, in which one studies a series of past prices. Moving averages are a time series. However, in absolute momentum one usually compares the current price to only a single past price in order to determine if the trend is up or down. I also prefer the term absolute momentum because practitioners are used to hearing about relative returns and absolute returns. Relative momentum and absolute momentum follow the same logic.

To confuse matters further, some academics distinguish between only two types of momentum, cross-sectional and time series momentum. However, relative strength momentum across asset classes is neither cross sectional nor time series based. CXO Advisory Group, the research service that tests out different systems and methods, has started calling absolute momentum "intrinsic momentum." We will continue to use the terms relative and absolute momentum. You should be able to follow all the momentum players now without a program. Remember, a rose by any other name….

Maximum Drawdown

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There is a new research paper out by Wes Grey and Jack Vogel that is important not only to momentum investors, but to all investors and researchers. The paper is "Using Maximum Drawdown to Capture Tail Risk." In it, Wes and Jack show that academic anomalies, identified by linear factor models (alpha), are often not great trading strategies.

Wes and Jack select eleven long/short anomalies from academic literature and show that a number of them, despite positive alphas and attractive Sharpe ratios, show very large drawdowns that would likely trigger margin calls and investor withdrawals at inopportune times. Six of the eleven strategies have drawdowns exceeding 50%, with the three worst being 86.1%, 84.7%, and 83.5%. (Long/short stock momentum is the one with an 86% drawdown. Perhaps QuantShares should reconsider calling their long/short momentum stock ETF, the "US Market Neutral Momentum Fund.")

Wes and Jack say it is important for researchers and investors to consider tail risk. They suggest looking at the maximum peak-to-valley loss (drawdown) associated with a time series as a relatively easy way to do this. They have an explanatory video on their Turnkey Analyst blog, along with the Excel VBA macro code and a spreadsheet for calculating maximum drawdown. (There are other good videos there as well, showing how to use Excel for mean variance optimization and how to calculate 3 or 4 factor alpha. Wes and his crew are democratizing investment research.)

Of course, maximum drawdown is not perfect as a risk measure. It is not amenable to traditional statistical analysis, such as confidence intervals. (Given the stochastic nature of financial markets, traditional statistical analysis may not be so accurate anyway.) Maximum drawdown is time dependent – the longer a track record, the more likely that maximum drawdown will increase. Drawdown frequency, as well as magnitude, is also important. Furthermore, maximum drawdown shows only a single past event that may be a chance occurrence and not be representative of what the future may bring.

Other ways of looking at tail risk attempt to deal with these concerns. Conditional value at risk (CVAR) tries to show what a drawdown will most likely look like given an extreme event. Extreme value theory (EVT) tries to identify large deviations from the medians of probability distributions. Both these approaches are computationally challenging and rarely found in finance literature. (I used to compute CVAR myself, but didn’t find it as intuitively appealing as maximum drawdown.)

Wes and Jack have done a great service in showing how the usual ways of evaluating investment opportunities, such as alpha and Sharpe ratios, can be seriously lacking. Neither alpha, nor standard deviation, nor maximum drawdown, represent a complete measure of investment risk. Therefore, what I like to do is take a multi-pronged approach. I use the Sharpe ratio as a measure of the risk efficiency of a strategy. It tells how much excess return we can expect across an equalized amount of volatility.

Maximum drawdown is good in that it gives some indication of extreme tail risk. However, I also look more broadly at strategy drawdown versus benchmarks drawdown under a variety of adverse conditions.

Finally, I examine interquartile ranges and extreme outliers using box plots of the data. You can see all four of these methods at work in my dual momentum paper. I hope other researchers catch on soon and start presenting more than just Sharpe ratio or alpha as their objective function. These often mean little on their own in terms of true risk exposure.Tail risk is important to investors, and it should also matter to researchers.

More Momentum Research Papers

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As the advantages of momentum investing become more widely known, there is naturally more research being done to explore its potential. Some of that research, such as the Moskowitz, Ooi, and Pedersen paper "Time Series Momentum," has been excellent.We prefer to point out and discuss positive things like that, but since this is a blog about momentum, we feel an obligation to also talk about momentum products and research that may be a bit off base (See "Here Comes Market Neutral Momentum…sort of").

At the end of last year, Keller and van Putten issued a paper called "Generalized Momentum and Flexible Asset Allocation." The authors applied absolute and relative momentum to the top 3 of 7 assets using data from 1998 through 2012. They developed their parameters on 8 years of in-sample data from 2005 through 2012, and then validated their results on 7 years of out-of-sample data from 1998 through 2004.

Our first observation is that eight years of data is a very small sample size for determining investment model parameters. Their out-of-sample validation may have held up because momentum is so robust that most parameters over a certain range work out OK. However, back testing on only eight years of data may not give what are really the best parameter values.

Elsewhere, the authors' paper can be rather confusing. Here is an example, "Sometimes our relative momentum is called relative strength (RS, see Faber 2010) or time series momentum (see Thomas 2012). We will also use the term return momentum to contrast better with volatility and correlation momentum."

Time series momentum is different from relative momentum (See my post Whatchmacallit). Furthermore, what they call volatility and correlation momentum has nothing to do with momentum. Momentum is about selecting assets based on persistence in their performance, either against their peers (relative momentum) or against themselves over time (absolute momentum). This makes no sense with respect to volatility or correlation.

The authors actually use volatility and correlation as ranking factors. They do the same with returns, after they select them using relative and absolute momentum.

The authors end up ranking assets using arbitrary weights of 1.0, 0.5, and 0.5 for return momentum, volatility, and correlation, respectively. They do not explain how they came up with these weightings. I would be cautious about using the information in this paper without doing considerably more analysis and back testing.

"Time Series Momentum Versus Moving Average Trading Rules," by Marshall, Nguyen, and Visaltanachoti is an academic paper that attempts to determine if long-only momentum trading rules beat comparable moving average trading rules. They do this by comparing absolute momentum (which they call time series momentum) to comparable (according to them) moving averages of size based quintiles of US stocks using 10, 50, 100, and 200 trading day look-back periods. They have confidence in their comparisons because their correlations between momentum and moving average returns are generally in excess of .8. However, this may have something to do with their use of daily, rather than monthly, return data. Since momentum is an intermediate term anomaly, most researchers study it using monthly returns.

We get correlations ranging from .45 to .47 when comparing 12-month absolute momentum monthly returns to a range of 4 to 32 month moving average monthly returns of the US stock market for the past 38 years. We use a range of moving average lengths because one cannot just use the same look-back period for momentum and moving averages and expect comparable results. The authors hint at this themselves when they say that moving averages enter and exit stocks sooner. Their paper also identifies the average holding periods for look-back intervals of 10, 50, 100 and 200 trading days as 8, 22, 31 and 47 days for moving average rules, and 10, 32, 46 and 83 days for momentum rules. Quicker entries and exits with moving averages means that their lengths should be longer if one expects their performance to match up with the performance of absolute momentum.Choosing the same look-back period does not make absolute momentum and moving averages comparable.

An old investment adage is that moving averages should be plotted half their length behind the current price on a stock chart. A half-span lag means that the look-back period for a moving average would be twice as long as the look-back period for momentum in order for the two to be roughly comparable. The following chart should make this clear.

 

Let's measure absolute momentum from the midpoint of this line at 30 to the endpoint at 50. Absolute momentum measures the difference between the start and end value, which in this case is 20. The computed moving average value from the start of 30 to the end of 50 is 40. The difference between the moving average value of 40 and the end value of 50 is only 10, indicating a weaker trend than was identified using absolute momentum.

However, if we start our moving average twice as far back at the point of 10, the computed moving average value becomes 30 instead of 40, and the difference between it and our end value is now 20, the same as with absolute momentum. The numbers do not always work out exactly this way. The equivalent moving average look-back period depends on the price action along the length of the moving average. However, it is safe to say that using twice the absolute momentum look-back period gives us a better equivalent moving average length. We can see that in Panel D from Table 2 of the paper:

 Table 2
Time-Series Momentum and Technical Analysis Performance and Comparison
         Q1 (Small)            Q2                Q3                Q4              Q5 (Large)
         MA  TSMOM  MA TSMOM  MA TSMOM  MA TSMOM  MA TSMOM
Panel D: Sharpe Ratios
10     0.47     0.38     0.41    0.31    0.42    0.28     0.37    0.25     0.16    0.04
50     0.37     0.26     0.30    0.21    0.28    0.22     0.25    0.19     0.12    0.08
100   0.27     0.19     0.22    0.15    0.21    0.18     0.19    0.16     0.12    0.11
200   0.20     0.13     0.17    0.12    0.17    0.15     0.19    0.14     0.13    0.10     

Stocks are in size-based quintiles from Q1 (small) to Q5 (large). Look-back periods from 10 to 200 days are in the first column. Reading across the rows, the Sharpe ratios are for moving average (MA) and absolute momentum (TSMOM) strategies using the same look-back period. We see, that except for Q5 (large), if we shift the MA strategies up one level so that their look-back periods are twice as long (or longer when going from 50 to 10) as the TSMOM look-back periods, we get an almost exact match of the Sharpe ratios. Based on using such shifted look-back periods that make MA and TSMOM strategies roughly equivalent, one can no longer say that portfolio-timing rules based on moving averages clearly outperform their absolute momentum counterparts.

To compare absolute momentum to moving average trading rules, one should examine a range of values for each. We did this and found that the best performing momentum parameters applied to different assets and different time periods have far less dispersion than the best performing moving average parameters. For this reason, we favor absolute momentum trading rules for its robustness over moving average trading rules. There is also a very large body of research now confirming the validity of momentum strategies from the turn-of-the-century to the present and across many different asset classes.

My New Research Paper on Absolute Momentum

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My newest research paper is now available. It is "Absolute Momentum: A Simple Rule- Based Strategy and Universal Trend-Following Overlay". In it, I show how to use absolute momentum to add value to single asset investments or a 60-40 portfolio by reducing expected volatility and drawdown. I also show how to construct a simple momentum-based parity type portfolio without many of the drawbacks associated with traditional risk parity programs. 

There are other potential uses for absolute momentum as the foundation for a core portfolio or as an overlay for most any portfolio. Absolute momentum is easy to understand and simple to implement. 

My paper last year was to illustrate principles of dual momentum. The Global Balanced Momentum Index (GBMI) on our website illustrates that approach applied to a realistic investment portfolio. Similarly, I now have a Risk Parity Momentum Composite (RPMC) on the website that tracks a model portfolio of asset class indices based largely on the absolute momentum principles in my new paper.  

Sector Rotation and Dual Momentum

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Sector rotation is one of the more popular applications of momentum. The following chart using the eleven Morningstar equity sectors will be featured in my new book on momentum  investing

The equal weight portfolio shows higher returns than the S&P 500 due to mean reversion profits from rebalancing and equal, rather than capitalization, weighting across sectors. The results of both relative and absolute momentum are better than this. They have similar rates of return, but absolute momentum has less volatility and much lower drawdowns, even though relative momentum is more popular than absolute momentum. As expected, dual momentum shows the very best performance. My new book will have more about this. Dual Momentum Sector Rotation (DMSR) performance will be updated monthly on the Performance page of our website.

Morningstar Sector Rotation 1993-2013

Past performance is no assurance of future results. Please see the Disclaimer page of our website for additional disclosures.

The World's Longest Backtest

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Relative strength price momentum is the beneficiary of the world's longest back test. Geczy and Samonov just issued a paper called "212Years of Price Momentum (The World's Longest Backtest: 1801-2012)". Previously, academic studies of U.S. stocks went back to 1926, when the CRSP database began. (Researchers have shown momentum to be effective in British stocks back to the 19th century).

The first two U.S. stocks began trading in 1792. The authors were able to get data on 72 stocks by 1810 and on over 300 stocks by the end of the 1830's.
The most important conclusion of this paper is that the momentum effect has remained statistically significant during 125 out-of-sample years from 1801 through 1926. These results, on more than twice the previous amount of available data, strengthen the evidence that the momentum effect is not a product of data mining.

Specifically, a portfolio that is long the top third and short the bottom third of stocks based on 10 month momentum (prior 12 months of data skipping the last 2) shows an excess return (portfolio return minus the market return) of .4% per month (t stat 4.5) over the last 212 years. Industry momentum is strong and significant as well, with an excess return also of .4% per month (t stat 3.1).  
 

The authors use the same 10-month look back period to determine the state of the market. They find that beta is negative when the market state turns positive. They then see what happens if they dynamically hedge portfolio beta based on market state. This means adding positive beta when the market state turns positive, which is similar to using absolute momentum as a market-timing filter. 

Dynamic hedging increases long-only market excess return from .6% per month (t stat 6.9) to .9% per month (t stat 8.7). So there you have it. Relative strength price momentum has again shown its worth on a long out-of-sample data set and now has the investment world's longest backtest track record. Considering market condition (which we do through absolute momentum) can substantially improve momentum results.

Momentum Tidbits...

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A number of papers have aimed at improving on relative strength momentum in equities by adding enhancements to it, such as analyst coverage, credit rating, business cycle placement, proximity to 52- week highs, and price acceleration. Li-Wen Chen and Hsin-Yi Yu have an interesting new paper called "Investor Attention, Visual Price Pattern, and Momentum Investing" that identifies price acceleration by looking at the concavity or convexity of returns. They do this by regressing price against time squared. Using long/short US stock prices from 1962 through 2011, they find that their exponential application of momentum almost doubles the risk-adjusted profits from conventional momentum. The authors speculate that investors can easily see convex and concave price patterns that investment decisions.

There have been several studies comparing momentum risk-adjusted returns to those of other anomalies. None has come close to momentum. For example, the alpha from momentum has been twice as high as the alpha from value. Michael Nairne in his "Fantasy versus Factors" article has added to this body of evidence with the following charts from 1981 through 2012 that match momentum up with these other factors from the Kenneth French database:  total market, value, small cap, small cap, small cap value, and high quality.








The above studies pertain only to relative strength momentum. Trend following absolute momentum is relevant to the updated Dalbar statistics. Over the past 20 years ending in 2012, the S&P 500 had an annual return of 8.21%, while the average stock mutual fund investor earned 4.25%. Around 1.25% of this under performance is due to mutual fund expenses. Mutual fund investors making poor timing decisions caused the remaining 2.7% of annual under performance. There is a strong propensity for investors to buy near market highs and sell near market bottoms, due to their emotions of fear and greed. Absolute momentum, by reducing downside volatility and truncating potential drawdowns, can make it easier for investors to stay the course and hold on to their investments during unfavorable market periods.




Momentum Combinations

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One can use dual momentum in many ways. In the Performancesection of our website, we show three different applications of dual momentum. The first is our Global Balanced Momentum Index (GBMI), which applies absolute and relative momentum to a simple global stock/bond portfolio.

Next is our Risk Parity Momentum Composite (RPMC) that uses dual momentum in conjunction with a broader class of assets - US and foreign stocks, REITs, Treasury and credit bonds, and gold. This portfolio corresponds roughly with the risk- parity style portfolio in our latest research paper:  "Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend Following Overlay." RPMC uses the return enhancing and risk reducing characteristics of dual momentum to create a risk parity type portfolio without resorting to leverage or a heavy concentration in bonds.  

Finally, in our Dual Momentum Sector Rotation (DMSR) portfolio, we apply dual momentum to the eleven Morningstar U.S. equities sectors. Sector rotation is one of the better-known and more common ways of using momentum. We introduce dual momentum in place of relative strength momentum, which gives us the added benefit of a market-timing overlay. 

Even though all of our strategies use dual momentum, the monthly correlations between these strategies from 1993 (when sector rotation began) until now is not as high as one might expect:

 Correlations
GBMI
DMSR
 GBMI
 -
0.78
 RPMC
0.58
0.60

This means there should be some value in combining them. Below are performance results from combining the GBMI and RPMC strategies. In accordance with modern portfolio theory, the expected return of the combined portfolio lies between the returns of the GBMI and RPMC portfolios, while the expected volatility and maximum drawdown of the combined portfolio is lower than for both portfolios individually. Combining GBMI with RPMC gives us a more conservative overall portfolio:

Jan 1974-Jul 2013[1]
GBMI
RPMC
COMBINED
60/40
Global 60/40
Annual Return
13.41
13.93
13.67
10.49
9.33
Standard Deviation
7.73
7.17
6.68
10.33
9.60
Sharpe Ratio
0.96
1.09
1.14
0.46
0.38
Max Drawdown
-12.57
-8.60
-7.15
-32.66
-33.80

 

We can also take our DMSR sector rotation portfolio and add some parts of the GBMI and RPMC models that are missing from DMSR, such as international equities. The rationale here is twofold. First, bonds have been in a 30-year bull market. With interest rates so low now, bonds are not likely to offer the same returns as they did in the past. This means a more equities oriented portfolio like DMSR might now offer advantages over a balanced stock/bond portfolio like GBMI or RPMC. 

There is a second reason one might prefer a more equities oriented portfolio. Even though bonds historically have a lower risk premium and a lower return than equities, investors have historically used bonds to reduce the downside exposure of their stock/bond portfolios. However, the trend following component of dual momentum can also reduce downside exposure, and can do so without the expected reduction in return from a portfolio that holds a large proportion of bonds. 

There are those who think the stock market is expensive now, based on historic P/E ratio analysis. However, that does not mean the stock market cannot go a higher and become a lot more expensive, as it did in the late 1990s. Markets often will go to extremes. The trend following component of dual momentum can help investors stay in stocks longer and eventually exit without giving back too much of their gains.  
  
Here is the performance of our dual momentum based Enhanced Sector Rotation (ESR) model that adds diversifying elements of GBMI and RPMC to our regular DMSR model: 

Jan 1993-Jul 2013[2]
DMSR
ESR
EQUAL SECTORS
S&P 500
Annual Return
14.35
15.51
10.42
9.10
Standard Deviation
12.16
11.55
13.76
15.33
Sharpe Ratio
0.85
0.99
0.50
0.37
Max Drawdown
-15.50
-14.95
-47.50
-50.95

 

We see from the above examples that the whole can be greater than the sum of the parts, and that we can use dual momentum in a number of different ways. Dual momentum has but one goal - to keep investors in tune with the forces of the markets. Creative combinations of dual momentum can meet the needs of conservative investors, aggressive investors, and those in between.


[1]There are no deductions for transaction or other costs. Maximum drawdown is on a month-end basis. Monthly-rebalanced 60/40 U.S. equities/bond portfolio and 60/40 global equities/bonds serve as benchmarks. 
[2] There are no deductions for transaction or other costs. Maximum drawdown is on a month-end basis. The S&P 500 index and a monthly-rebalanced equally weighted sector allocation serve as benchmarks.

Please see our website Performance and Disclaimer pages for additional disclosures.
Historical data and analysis should not be taken as an indication or guarantee of any future performance.

Momentum Back Testing

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In 1937, Cowles and Jones published the first study showing that relative strength price momentum leads to abnormally high future returns. These findings are just as valid today as they were 75 years ago. Academics have been very diligent in studying momentum further, since it flies in the face of the efficient market hypothesis (EMH). EMH says you cannot beat the market using publicly available information. Hundreds of subsequent tests over the past 20 years have confirmed the veracity of momentum investing. Momentum is slowly gaining the attention it deserves as the investment world's "premier market anomaly" (words of Fama & French).

Last week there was an interview of me on the MyPlanIQ blog. They asked about my work with dual momentum. I did not know at the time that MyPlanIQ intended to use my interview to promote their Tactical Asset Allocation (TAA) model. Since the details of TAA are unknown and proprietary, I cannot comment on the worthiness of their model. What I can say is I have nothing to do with any of MyPlanIQ's models and do not endorse them. 

I have also noticed other advisory services, as well as some managed investment programs, that look like they have been inspired by my momentum research. I would like to make it clear that I am not involved with, nor do I endorse, any outside services. 

There is a natural tendency to take others research, make a few changes to it, and hope you have created a better mousetrap. This often does not work out as expected. Here is why. High quality research is very rigorous. Serious researchers subject their work to peer review and statistical significance testing. They disclose data sources and testing logic so other researchers can replicate their results. For high quality research, data is king. (I have come up with a saying: "One can never have too much money, good looks, or data.") Conscientious researchers are always trying to get as much data as they can for testing purposes.

Fortunately, there has been a large amount of data available for back testing momentum. Academic researchers have consistently shown that momentum works across most markets and on out-of-sample data. Absolute momentum has worked back to the turn of the century[i]. Relative strength momentum has worked all the way back to the beginning of the previous century![ii] This is important for two reasons. First, it leads to greater confidence in the results. Worst-case scenarios, in particular, are highly dependent on the amount of past data that is available. Second, with plenty of data, one can look at segments of the data to see how consistent and stable the results have been over time. We want to see that our overall results are not dependent on just a few good periods of short-term performance. We also want to make sure our results have held up well over time and are still strong.

Another test of robustness is to look at other markets and see if your results hold up there as well. To do this in a meaningful way, you also need plenty of past data. This is why I go to the trouble of using indices instead of ETFs for my back testing. Whenever possible, I test my strategies using index data back to 1972. Data on a reasonable number of ETFs only goes back to 2003. There is a big difference in using forty years rather than ten years of data when you are testing strategies based on monthly price changes. In fact, one should be suspicious of any conclusions derived from using only ten or fewer years of data when evaluating intermediate term strategies like momentum. Yet that is precisely how most practitioners try to tweak and "improve" on my results, or on what they find in other momentum research papers. When working with monthly returns, ten years is not much time. Results can easily be influenced by chance or happenstance, especially if there is not a convincing logical basis for your conclusions. What we can count on is that simple momentum works across many different markets, and it works using a 3 to 12 month formation period. Anything else is speculative and should be subject to rigorous and thorough evaluation that includes as many years as possible of past performance data, confirmation of your results in additional markets, other robustness tests, drawdown analysis, etc.    

There is another problem related to paucity of data, and that is data snooping (data dredging, data fitting) bias. Data snooping is pervasive among practitioners, and not just with respect to momentum. It can happen when you add a new parameter to a model or re-optimize existing parameters. Extensive data dredging and model over fitting can lead to spurious results and regression to the mean. A statistician friend calls this the Grim Reaper, because it can take away all or most of your expected future returns.

Data snooping uses the data twice - first to fit the parameters of the model, and then to tell you how good your model is. Multiple comparisons by means of snooping can lead to spurious correlations. Every data set contains patterns due entirely to chance. When you perform a large number of tests, some of them will invariably produce false results. When the data itself suggests your hypotheses, it is impossible to tell whether the results are just chance patterns. If you do extensive data snooping,  your evaluation criteria need to be much more stringent. 

Some people think that splitting a modest amount of data into a testing set for optimization and a hold out set for subsequent validation will take care of this problem. However, that is not true unless you use carefully constructed randomized out-of-sample tests. Otherwise, as the saying goes, "If you torture your data long enough, it will confess to anything." 

I recently came across someone offering momentum signals based on the same methodology and a very similar portfolio to the one in my first momentum paper. He water boarded the formation period parameters until the model showed an annual return of 41% over the past (guess how long) ten years. Further torturing the model's portfolio composition, he was able to come up with, and now promotes, annual returns of 73% over the past three years! If anyone thinks momentum (or anything else) can realistically provide annual returns of 73%, then I have a lovely bridge I would like to sell you.

If you cannot avoid data snooping bias, there are tests you can perform that will tell you if you have efficient criteria for model selection. One of the best known is White's Reality Check (RC). Others include Hansen's Superior Predictive Ability (SPA) and Benjamini-Hochberg's False Discovery Rate (FDR)tests. Without something like these, you may be data snooping your way to nowhere.  

                                                                                      Data Snoopy


[i] Moskowitz, Tobias J., Yao Hua Ooi, and Lasse Heje Pedersen, 2012, "Time Series Momentum," Journal of Financial Economics 104, 228-250
[ii]Geczy, Christopher and Mikhail Samonov, 2013, "212 Years of Price Momentum (The World's Longest Backtest: 1801-2012)," working paper

CAPE Crusaders?

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In their newest paper, "On the Performance of Cyclically Adjusted Performance Measures," Gray and Vogel challenge the popular belief that the Schiller P/E or Cyclically Adjusted Price Earnings (CAPE) ratio is the best way to look at value. 

CAPE sounds intuitively appealing in that it inflation adjusts and averages earnings across a 10-year business cycle. Gray and Vogel take the Schiller P/E one step further and examine the 10-year inflation adjusted earnings concept with respect to other valuation metrics as well. Here is what they look at:

 10-year average real earnings to market capitalization (CA-EM)
10-year average real book values to market capitalization (CA-BM)
10-year averagerealearningsbeforeinterest,taxes, depreciation, and amortization to total enterprise value (CA-EBITDA/TEV)
 10-year average real free cash flow to total enterprise value (CA-FCF/TEV)
 10-year average real free gross profits to total enterprise value (CA-GP/TEV)

Using NYSE, AMEX, and NASDAQ large and mid-cap data from July 1973 through December 2012, Gray and Vogel find that CA-BM is the best cyclically adjusted valuation metric relative to other valuation metrics. An annually rebalanced equal-weight portfolio of high CA-BM stocks earns 16.6 percent a year and generates the highest Sharpe (.64) and Sortino (.85) ratio among all cyclically adjusted metrics tested. Book-to-market as a valuation measure was popularized by Fama and French in the early1990's. While CA-BM is the marginal top performer over the past 40 years, all cyclically adjusted value measures have outperformed market benchmarks by large margins. Employing monthly rebalancing enhances the performance of all valuation measures. For example, the CA-BM strategy goes from a 16.6 percent compound annual growth rate (CAGR) to a 19.3 percent CAGR.

Last month, our post called Momentum Combinations showed how we can use momentum in different ways to customize portfolios and enhance performance. The Gray/Vogel dynamic duo also looks at integrating momentum with cyclically adjusted valuation measures to enhance returns. Using monthly-rebalanced portfolios, our anti-CAPE crusaders split each valuation decile into high and low momentum. Employing this additional momentum screen adds at least 100 basis points in return while decreasing maximum drawdowns modestly across the different valuation metrics. Holy Momentum, Batman!


Momentum...the Only Practical Anomaly?

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Interest in momentum is growing as it gains recognition as the premier market anomaly. Our purpose here is not to report on every item or research finding related to momentum. We prefer instead to point out those that are most important or interesting often because they seem exceptionally good, or, occasionally, because they seem exceptionally bad.
One exceptionally good piece of research is the working paper by Israel and Moskowitz (I&M) called "The Role of Shorting, Firm Size, and Time on Market Anomalies." This paper has important implications not only for momentum investors, but also for those who are interested in size and value  investment tilts. I&M look at all three with respect to firm size, long or short market exposure, and results stability over time.

Most research papers on relative strength momentum present it on a long/short basis where you buy  winning stocks and short losing ones. In some papers, you can find some long-only results buried in a table somewhere. Except in my papers, it can be challenging to find visual representations or detailed analyses of long-only momentum. However, I&M offer insightful analysis of long-only momentum. It is important to look at long-only results for two reasons. First, most investors are interested only in the long side of the market. Second, in the words of I&M:

Usingdataover thelast86yearsin theU.S. stockmarket(from1926to 2011) and over the last four decadesin internationalstock marketsand other assetclasses(from1972to 2011), wefind that theimportanceofshortingisinconsequentialfor allstrategies when lookingatrawreturns. For an investor who caresonlyaboutrawreturns,thereturnpremia to size, value,andmomentumare dominatedbythe contribution fromlongpositions.

Therefore, even if you are open to shorting, it does not make much sense from a return perspective. 

I&M charts and tables show the top 30% of long-only momentum US stocks from 1927 through 2011 based on the past 12-month return skipping the most recent month. They also show the top 30% of value stocks using the standard book-to-market equity ratio, BE/ME, and the smallest 30% of US stocks based on market capitalization. 


Long-onlymomentum producesan annualinformation ratioalmost threetimeslarger than valueor size. Long-onlyversionsof size, value,and momentumproducepositive alphas, but thoseofsize and value arestatisticallyweak and only exist in the second half of the data. Momentumdelivers significant abnormalperformancerelative tothemarket and does so consistently across all the data.   


Lookingat marketalphas across decile spreads in the table above, thereareno significantabnormalreturnsfor sizeor valuedecile spreadsover theentire1926 to 2011 timeperiod. Alphasfor momentumdecileportfolio spread returns, on theother hand, are statisticallyand economicallylarge


The table above shows alphas across different 20-year periods. (Our recent post called Momentum Backtestingdescribed why it is important to have an abundance of data to segment and use as a robustness check.) Here is what I&M say about these results:

Looking at these finer time slices, there is no significant size premium in any sub period after adjusting for the market. The value premium is positive in every sub period but is only statistically significant at the 5% level in one of the four 20-year periods, from 1970 to 1989. The momentum premium, however, is positive and statistically significant in every sub period, producing reliable alphas that range from 8.9 to 10.3% per year over the four sub periods.

Here is one more table from their paper that shows in more detail the influence size has on momentum and value:


In the words of I&M:

Looking across different sized firms, we find that the momentum premium is present and stable across all size groups—there is little evidence that momentum is substantially stronger among small cap stocks over the entire 86-year U.S. sample period. The value premium, on the other hand, is largely concentrated only among small stocks and is insignificant among the largest two quintiles of stocks (largest 40% of NYSE stocks). Our smallest size groupings of stocks contain mostly micro-cap stocks that may be difficult to trade and implement in a real-world portfolio. The smallest two groupings of stocks contain firms that are much smaller than firms in the Russell 2000 universe.

So there you have it. Momentum returns are strong, stable, and largely unaffected by size over the entire 86-year sample period (and in eight other markets and asset classes.) Long-only value (per the most commonly used metrics), on the other hand, shows positive alpha only among the smallest stocks and insignificant alphas among larger stocks. Since micro-cap stocks are more costly and difficult to trade, most investors, and particularly institutional ones, avoid this area of the market. Not only is momentum the "premier market anomaly" as per Fama & French, but, contrary to popular belief, it may be the only really practical anomaly.
 


Momentum Hierarchy

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The chart below shows how dual momentum, absolute momentum, and relative momentum stack up against one another with our Dual Momentum Sector Rotation model. (No allowance has been made for transaction or other costs.) The light brown line at the bottom of the chart is the S&P500. The dark brown line just above it is an equally weighted average of all the sectors we use. Its shape is similar to the S&P 500, which means that volatility and drawdown are similar to the market's volatility and drawdown. Equal weighting shows modestly higher returns, due to mean reversion profits from monthly re-balancing and equal, rather than capitalization, weighting across sectors.

 Past performance is no assurance of future success. Please see our Disclaimer page.

The purple line shows relative strength momentum. It has higher profits than equal weighting, but retains the performance characteristics of the S&P500. Relative strength momentum typically boosts returns, but does little to reduce volatility or drawdown. It is the best known and most commonly used form of momentum investing.

When we get to the green line representing absolute momentum, things change. Returns are better than with relative momentum. More importantly, the dips representing larger drawdowns flatten out or disappear. Absolute momentum was out of stocks during all of the 2001-02 and most of the 2008-09 bear markets.

In the hierarchy of investment returns, equal weighting with re-balancing beats the S&P500. Relative strength momentum beats equal weighting. Absolute momentum not only beats relative strength momentum, but it is more stable and consistent. If you have to choose just one approach, then absolute momentum looks best. 

However, we are not limited to just one approach. The blue line shows what happens when you combine relative and absolute momentum. Returns improve further while retaining absolute momentum's more attractive risk profile. Dual momentum is where you really want to be.

Introducing Global Equities Momentum

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I feature Global Equities Momentum (GEM) in my forthcoming book, so it is time to introduce it on our website. GEM is a simple but powerful model that switches between the S&P 500 Index, the MSCI All Country World Index ex-US, and the Barclays Capital US Aggregate Bond Index based on dual momentum. GEM is long just equities as long as their trend is positive based on absolute momentum. When the trend of stocks is down, GEM is only in bonds. My book will fully explore the characteristics of this model.

The long run risk premium (and expected return) of bonds is substantially lower than the risk premium of stocks, so stocks are the investment vehicle of choice as long as their trend is positive. There are, however, investors who, for fiduciary or other reasons, need to keep a permanent allocation to bonds. For this reason, we also track our model that maintains 60% in stocks and 40% in bonds. We call this Global Balanced Momentum (GBM). (Formally, we called it the Global Balanced Momentum Index.) GBM applies dual momentum to both stocks and bonds.

Finally, we continue to show the performance of dual momentum applied to US equity sectors. We call this Dual Momentum Sector Rotation (DMSR).  Please check out all three of these models that are now on the Performance Page of our website.

Past performance is no assurance of future returns. Please see our Disclaimer page for other disclosures.

Book Musings

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Now that I have turned my book manuscript into my publisher, I can get back to doing some blog posts. My book's title is Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk. McGraw-Hill will release it in November. If you enter your email address on the right side of this blog where it says "Follow By Email," you will be notified as soon as the book is available.

Putting together the book was an interesting project. Wes Gray, of Alpha Architect, kindly provided me with a book proposal template, and I put a lot of effort into organizing my thoughts. It paid off in that all three publishers I approached offered me a book contract. 

I did not want to limit the book's scope to just momentum, although there certainly is a need for a comprehensive book that explains the salient points of momentum investing. This marks the 40th year since I began my investment career, and I wanted to incorporate other information that I thought might be helpful to investors. The book took on a life of its own soon after I got started. Thanks to the internet, I was able to go deeper into some topics than I had thought possible. Here is a list of chapter titles: 

 DUAL MOMENTUM INVESTING

Chapter 1              World's First Index Fund                         
Chapter 2              What Goes Up…Stays Up                           
Chapter 3              Modern Portfolio Theory Principles and Practices                           
Chapter 4              Rational and Not So Rational Explanations of Momentum
Chapter 5              Asset Selection: the Good, the Bad, and the Ugly 
Chapter 6              Smart Beta, Blind Joe Death, and Other Urban Legends
Chapter 7              Measuring and Managing Risk
Chapter 8              Global Equities Momentum 
Chapter 9              Mo' Better Momentum 
Chapter 10            Final Thoughts 

"Fact, Fiction, and Momentum Investing"

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The AQR posse (Asness, Frazzini, Israel, and Moskowitz) recently issued a working paper that disproves many often-repeated myths about momentum investing, particularly as it applies to individual stocks. The authors back up their reasoning with results from academic papers and publicly available data. Here are the myths they address: 
  •   The momentum anomaly is small and sporadic 
  • ·It works mostly on the short side
  •   It works well only among small stocks
  •   It does not survive trading costs
  •   It does not work for a taxable investor
  •   It is best used as a screen rather than as a regular investment factor
  •   Its returns may not persist
  •   It is too volatile to rely on
  •   Different measures of momentum may give different results
  •   There is no theory or reasonable explanation to support it
 Below is a quick summary of the authors' evidence-based counter arguments:

1)  There is overwhelming evidence from scores of studies showing that momentum returns are remarkably stable and robust.

2)  There is little difference in performance between the long and short sides of momentum based on factor model regressions. Based on average returns versus the market, the long side has contributed more to momentum profits.

3)  As for working only among small caps, this is true only if you replace the word "momentum" with the word "value". Two of the authors, Israel & Moskowitz, wrote an important paper last year called "The Role of Shorting, Firm Size, and Time on Market Anomalies" that clearly showed this. That paper was the subject of my post, "Momentum...the Only Practical Anomaly?"Momentum actually works well across all size stocks and is more robust among large stocks.

4)  A study last year by three of these authors called "Trading Costs of Asset Pricing Anomalies"looked at large institutional trades across nineteen developed markets from 1998-2013. They found the trading costs of momentum to be low, despite a higher turnover than from other factors.

5) Several studies show that even though momentum with individual stocks has 5-6 times the annual turnover of value strategies, momentum actually has a similar tax burden. This is because momentum holds on to winners and sells losers, which avoids short-term gains in favor of long-term ones. Momentum also has a much lower dividend exposure than value.

6)   The authors point to papers showing that momentum works better as a factor-based approach than as a screen-based one.

7)  As for momentum's returns disappearing, one can say the same of any anomaly. Abnormal momentum returns have survived, however, for the past 212 years. Momentum has held up to considerable out-of-sample validation across time, geography, and asset type. The authors point out, "There is no evidence that momentum has weakened since it has become well-known and once many institutional investors embraced it and trading costs declined."

       8) Relative strength momentum is volatile, but the Sharpe ratio (which includes volatility) of momentum still comes up on top. The authors say, "Who are you calling small and sporadic?" (The authors ignore absolute momentum, which significantly reduces expected volatility and drawdown.)

9)  The authors agree that different measures of momentum can give different results, but they point out that this is true of any strategy. Different measures of momentum giving good results is a sign of robustness and not a cause for concern.

10)Momentum can be explained by either risk based or behavioral factors. As long as risks, risk preferences, biases, and/or behaviors do not change, momentum profits should continue unabated as they have for the past 200+ years. (My forthcoming book shows how behavioral biases are part of our DNA and are unlikely to change.)

The authors point out that most of the above myths can be shattered by a quick visit to Kenneth French's data library website. It is refreshing to see the authors, brought up in the Chicago efficient markets tradition, take on the challenge of those who say momentum profits cannot persist (despite plenty of evidence to the contrary) because that would contradict the theory of efficient markets. The authors point out that rejecting data because of a theory (or a one-sided view of the world) can be dangerous. They point to Columbus, Galileo, and the Salem witch trials as examples. Bravo!

The only problem I have with their paper is that the authors, perhaps keenly aware that risk-adjusted  momentum profits from individual stocks have been uninspiring over the past thirty years, repeatedly point out  that momentum works best when it is combined with value. Yet we can easily see in the aforementioned Israel & Moskowitz study that commonly used measures of value hold up only among the smallest stocks, and these are impractical for many investors to hold. Maybe the AQR crew needs to take a closer look at the true value of the emperor's new clothes.

More Time Series Momentum...

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My use of absolute momentum is a key factor in my latest momentum paper. Positive absolute momentum exists when an asset shows a positive excess return over the look back period. Others may call this time series momentum. The more common momentum approach, which appears in most research papers, is cross sectional (or relative strength) momentum, where one asset is compared to its peers, and the strongest is selected. Based on my research, relative strength and time series momentum make for a great combination.

In September of last year, Moskowitz et al wrote a detailed working paper on time series momentum. It showed up on SSRN in June 2012, and I did a blog post calling attention to this paper. Since then, there have been several other working papers dealing with time series momentum. One of the more interesting ones appeared on SSRN earlier this month. It is called Improving Time Series Strategies: The Role of Trading Signals and Volatility Estimators, by Akindynos-Nikolaos Baltas and Robert Kosowski. In it, the authors look at the implications of trading signals and volatility estimators on the profitability of monthly time series momentum strategies. Last December, the authors issued a paper called Momentum Strategies in Futures Markets and Trend-Following Funds, in which they looked at time series momentum patterns across monthly, weekly, and daily frequencies of commodity contracts..

The authors go on to compare various ways of identifying time series momentum. These include whether an asset has been up or down over the look back period, a moving average trend identifier, and several methods based on the t statistic of the regression slope. The most complicated method looks at 30 minute time periods, as well as daily data, in order to add an R Squared cut-off filter. Based on the Ziemba Sharpe ratio, this method looks attractive. However, it also has the highest volatility. Looking at the performance chart of all the methods, the simple up/down method seems to be the most consistent.

I found one of the most interesting parts of their recent paper to be their exploration and comparison of different volatility estimators. These could be useful for risk parity style asset allocations, which I may address in another post.

Value and Momentum Revisited

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Most academic research on momentum deals with individual stocks. Most applications of momentum are also oriented toward individual stocks. The three largest publically offered momentum programs (AQR momentum mutual funds, PowerShares DWA Momentum ETFs, and iShares MSCI USA Momentum Factor ETF) all use individual stock momentum. The only widely-available public program using momentum applied to asset classes was the ALPS Goldman Sachs Momentum Builder that recently went out of business due to lack of interest.

Yet momentum applied to individual stocks is not the ideal way to use momentum. Transaction costs due to high turnover of stock portfolios can negate much of the benefit of momentum investing. Momentum applied to broad-based indexes or sectors, on the other hand, can capture high momentum profits with much lower transaction costs.

Here is a table from my new book Dual Momentum Investing: An Innovative Approach to Higher Returns with Less Risk. (The book can be pre-ordered now from Amazon.) This table shows the performance of the AQR Momentum Index composed of the top one-third of the 1000 highest capitalization U.S. stocks based on 12-month relative strength momentum with a one-month lag. AQR weights their index positions based on market capitalization and adjusts the positions quarterly. For comparison, we show the performance of applying absolute momentum to the Russell 1000 by moving into aggregate bonds whenever 12-month absolute momentum is negative.

Table 9.2 AQR Momentum, Russell 1000, and Russell 1000 w/Absolute Momentum 1980-2013


AQR Momentum Index[1]
Russell 1000Index
Russell 1000 w/Abs Momentum
Annual Return
15.14
13.09
15.92
Annual Std Dev
18.27
15.51
12.57
Annual Sharpe
 0.51
 0.49
 0.80
Max Drawdown
            -51.02
           -51.13
            -23.41

These figures do not account for the 0.7% per year in additional transaction costs for the AQR Momentum Index, would have put it at a disadvantage to even the Russell 1000 index on a risk-adjusted basis. 

The next table shows the AQR Momentum Index, the Russell 1000 Value Index, and a 50/50 combination of value and momentum, which was advocated in the Asness et al. (2013) paper "Value and Momentum Everywhere." This combination is supposed to be desirable due to the negative correlation between value and momentum. We see that value combined with momentum does give a slightly higher Sharpe ratio than either value or momentum alone. However, there is little or no advantage with respect to maximum drawdown, and the results still pale in comparison to simple absolute momentum used with the Russell 1000 Index.

Table 9.3 AQR Momentum, Russell 1000 Value, 50/50 AQR Momentum with Value 1980-2013


AQR Mom Index
Russell 1000 Value Index
50/50 AQR Mom with Value
Russell 1000 w/Abs Mom
 Annual Return
15.14
13.52
14.33
15.92
 Annual Std Dev
18.27
14.87
15.71
12.57
 Annual Sharpe
 0.49
 0.53
 0.55
 0.80
 Max Drawdown
         -51.02
       -55.56
         -51.47
            -23.41

As a further check on the possible worthiness of combining value with momentum, I used the Global Equity Momentum (GEM) model described and tracked on the Performance page of our website. Full disclosure of GEM and instructions on how to use it are in my new book. Using relative momentum, GEM switches between the S&P 500 and the MSCI EAFE when absolute stock momentum is positive. When absolute momentum turns negative, GEM moves into aggregate bonds. 

The table below shows GEM results from January 1974 through August 2014, as well as the results from adding the MSCI USA Value (large and mid-cap) index to GEM as an additional switching option. We see that the inclusion of value into the momentum model adds nothing to the performance of GEM.


GEM
GEM w/Value
Annual Return
17.43
17.24
Annual Std Dev
12.64
12.52
Annual Sharpe
  0.86
0.86
Max Drawdown
            -22.72
              -22.94

Furthermore, as I pointed out in a blog post last year called "Momentum…the Only Practical Anomaly?", Israel and Moskowitz of AQR show in their 2013 paper that value, as it is commonly used, only offers a long-term premium when applied to very small stocks. These stocks are generally unusable by institutional investors. How one can mix individual stock momentum (which may offer nothing special after transaction costs) with value (which may also not be all that it was once thought to be) and create something extraordinary, may be a challenging endeavor. This is especially in true in light of an earlier paper by Daniel and Titman (1999) showing that value strategies are strongest among low momentum rather than high momentum stocks, and momentum strategies are strongest among growth rather than value stocks.

Nevertheless, researchers are nothing if not persistent and imaginative. When it was found that Markowitz mean variance optimization (MVO) gave inconsistent results, researchers tried constraining the inputs, incorporating prior information to shrink the estimates, and even ignoring returns altogether to try to create portfolios that were more robust. In the end, they found that because of estimation error, equal weight portfolios were generally superior to MVO portfolios. The same overreach is true with respect to the Capital Asset Pricing Model (CAPM). This started out as a single factor model that expanded to 3 and then 4 factors. Factor fishing has now come up with more than 80 possible data-mined factors, yet the factor pricing model may still not effectively model the real world. 

Therefore, it didn't surprise me to see recent a paper by Fisher, Shaw, and Titman (2014) called "Combining Value and Momentum" that tries hard to find other ways to use value and momentum together. (Yes, this is the same Titman who co-authored the above paper that showed momentum working better with growth rather than value stocks, and who co-authored the seminal momentum papers of the 1990s with Jegadeesh.)

What is perhaps most interesting are the various findings the authors came up in the course of their research. As the saying goes, the devil is in the details. Here are some of those details.

The authors separate stocks into 2 size categories, large cap corresponding to the Russell 1000 index, and small cap corresponding to all other stocks in the CRSP database from 1975 through 2013. They base momentum on prior 12-month performance skipping the last month. With respect to value and momentum separately, the authors find:
  • Value, as measured by the price-to-book ratio, is beneficial only with small stocks and not with large stocks. This is the same conclusion reached by Israel and Moskowitz using data back to 1926, and who also found it to be true of other valuation measures that had data back to at least the 1930's.
  • Despite high momentum portfolio Sharpe ratios before transaction costs, the high transaction costs associated with momentum portfolio turnover negates much of the difference in Sharpe ratios between large momentum and large value portfolios.
  •  Since small stocks have even higher transaction costs than large stocks, the authors incorporate higher transaction costs to conclude that none of the small momentum portfolio Sharpe ratios are higher than the Sharpe ratios of the small market portfolios.
  • In other words, based on high transaction costs, individual stock momentum may not be very good with either small or large stocks.[2] So all we are left with that provides above market risk-adjusted returns are small value stocks that most investors (and particularly institutional ones) find too expensive and difficult to trade.
The authors then look for ways to salvage momentum by combining it with value in two different ways. The first is to rank firms by momentum and value separately, and then compute an average rank. One signal can outweigh the other, and momentum still has high transaction costs with this approach. 

The authors' second approach is to use momentum as a filter for value-based portfolios. They buy stocks only when value and momentum are both favorable, and they sell stocks only when both factors are unfavorable. Momentum does not trigger trades, but instead influences the portfolios by delaying or avoiding trades. Data mining for the highest ex-post Sharpe ratios with this second approach, the authors find much greater exposure to the value factor. The optimal small cap portfolios, for example, have value allocations of 79% or more. The role of momentum with this approach is very small. 

The authors' first approach gives slightly higher Sharpe ratios when trading costs are low, and the opposite is true if trading costs are high. Of course, we do not know if these Sharpe ratios will continue out-of-sample into the future.

We can avoid the issues of high trading costs and less certain Sharpe ratios if we instead use momentum with indexes or sectors rather than with individual stocks. In our 2012 post called "Value and Momentum…Not Here" we asked if there should be value and momentum everywhere. I didn't think so then, and I see even less reason to believe that now.


[1] http:///www.aqrindex.com
[2] A studylast year by Frazzini, Israel, and Moskowitz looked at large institutional trades across 19 developed markets from 1998-2013. They found the trading costs of momentum to be low, despite a higher turnover than from other factors. On the other hand, a study by Lesmond, Schill, and Zhou (2004) called "The Illusionary Nature of Momentum Profits" showed that transaction costs reduced momentum strategy returns to close to zero. Fisher et al. uses transaction cost estimates that are in between these two. 

The above are hypothetical results, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees. One cannot invest directly in an index.

Giving Investors a Chance

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Researchers estimate that the worldwide cost of investment management is approximately $3 trillion per year. Some of this expense is unavoidable, such as the costs associated with custodial fees and for the periodic re-balancing of portfolios.

However, most of this high expense is in the form of compensation paid to the managers of actively managed mutual funds, hedge funds, and other managed programs. What do investors have to show for this large transfer of wealth from themselves to active money managers? The answer, unfortunately, is "not much." My book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Less Risk, reveals an abundance of research that confirms the general lack of value-added from active investment management.

Lack of performance is due not just from the higher fees and transaction costs associated with active investment management.Institutional investors use disadvantageous periods for the evaluation and selection of their investments. Goyal and Wahal (2008) show that investment managers and their consultants tend to select investments based on performance over the prior three or so years. Yet momentum research papers show 3 to 5 years to be a relatively poor period for performance evaluation. Equity performance tends to be mean reverting over that time frame. A one-year relative evaluation period gives much better results. Vanguard issued a research note last July also documenting poor future performance based on a past 3- year evaluation period.

Making matters worse, yearly reports from Dalbar Inc., a market research firm, indicate poor timing decisions on the part of the investing public. For example, the average US equity investor achieved an annualized return of 5.0% over the past 20 years ending in 2013, which is 4.2% less than the 9.2% average annualized return of the S&P 500.

Investors are emotionally influenced by by market volatility when getting into and out of the markets. Equities have provided investors with the highest risk premium, but they also have been subject to high volatility and extreme drawdown, since few investors have been aware of the risk-reducing benefit of absolute momentum. When investors instead try to dampen volatility through diversification with fixed income or alternative investments with lower inherent risk premiums, they also dampen their long-run expected return.

Some try to boost returns by looking for more of an edge from their equity investments. Historically, investors have used value and small cap portfolio tilts in their attempts to achieve higher risk-adjusted returns.

Yet the latest research shows that small size and high value portfolios may not always provide the higher risk-adjusted returns that investors have been seeking (See our post "Momentum...the Only Practical Anomaly?") Momentum, on the other hand, does provide a proven edge, especially when dealing with indexes rather than individual stocks and when using both absolute and relative momentum together (dual momentum). Unfortunately though, the most popular momentum-based programs use only relative strength momentum, and they apply it to individual stocks, which necessitates higher transaction costs.

I know of one public program that uses dual momentum applied to asset classes. However, their fees are very high, and their portfolio choices leave much to be desired (My book also goes into considerable detail about asset selection, especially with respect to momentum-based portfolios.)

In the future, when the advantages of dual momentum become better known, there may be other dual momentum investment opportunities. However, they may still have fees that are too high, portfolios that are less than ideal, or models based on too little data. The biggest mistakes I see others make are using models that over fit the data and drawing conclusions based on limited amounts (typically around 15 years) of data.

To give investors a better chance to earn decent risk-adjusted returns, my new book fully discloses my simple Global Equity Momentum (GEM) model (see the Performance page of my website) and shows how to use it. GEM has performed well over 40 years of past data under different market conditions using the same approach validated in numerous academic research papers. It has also avoided most bear market equity erosion. For only the cost of a book, any investor can easily utilize GEM to benefit from dual momentum while using a sensible, minimal expense portfolio.

Value Investing Redux

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Believe it or not, I was once a value investor. From an early age I was impressed with the long-run success of such value luminaries as John Neff, Bill Ruane, Walter Schloss, and Max Heine. Being of a contrary temperament, I also liked the idea of buying stocks that were out-of-favor and ignored. Supporting this approach, DeBondt and Thaler (1985) presented evidence that stocks overreact to bad news, and that poor performers over the past 3 to 5 years tend to outperform when moving forward. Value investing also seemed to have representative bias going for it, whereby investors overreact to poor performance and project it far into the future while failing to account for long-run mean reversion.

In 1992, Fama and French presented their groundbreaking paper indicating that value and small cap stocks offered up a risk premium to investors. I, along with the rest of the civilized world, readily accepted this idea. In 1995, Kothari et al. discovered that the the Fama and French results may have been due to sample selection bias. Using a different data source, Kothari et al. found no significant evidence of a positive relationship between value and average returns. However, since Kothari et al. were challenging the work of the highly respected Fama and French, their discovery got very little attention.

What got me away from value wasn't anything about value itself, but rather was my discovery after reading a plethora of research papers on momentum of just how strong momentum is compared with anything else. Looking at relative strength momentum applied to individual stocks showed a much higher premium than from anything else. What I also found is that you can easily apply momentum to different asset classes in order to gain the benefits of diversification, while applying value to asset classes other than equities can be speculative and uncertain.

What really got me excited about momentum though was my own research showing that momentum can be applied not just across different investment opportunities, but to single investments themselves in the form of trend-following absolute momentum.  Absolute momentum not only enhances returns like relative momentum, but it can also dramatically reduce drawdown. As far as I could tell, no other anomaly could do this.

With all these advantages accruing to momentum, I saw no reason to consider any other investment approach. Reinforcing this view in my mind were the surprising results with respect to value in the research report last year by Israel and Moskowitz (See my post "Momentum…the Only Practical Anomaly?"). Working with U.S. equities data back to 1926, the authors said:

The value premium… is largely concentrated only among small stocks and is insignificant among the largest two quintiles of stocks (largest 40% of NYSE stocks). Our smallest size groupings of stocks contain mostly micro-cap stocks that may be difficult to trade and implement in a real-world portfolio.

So value, as popularly derived, was of no practical benefit to investors. On another front, Chen et al. (2011) proposed an asset pricing model in which investment and profitability are the main explanatory variables, rather than value and size. Fama and French (2014) then expanded their established three-factor model to include investment (expected future changes in book equity) and profitability (expected future net income relative to book assets). When doing so, they concluded that value was redundant.

VALUE METRICS

So did all this put a nail in the coffin with respect to value investing? Not necessarily. Israel and Moskowitz looked at value using the popular book-to-market (or price-to-book) ratio. They found similar results using other value measures, such as dividend yield and long-term reversals that had data going back to at least the 1930s. However, these were only singular measures of value.

Dhatt et al. (2001) found that composite measures of value were superior to any individual metric. Moreover, in their book Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, Gray and Carlisle identified a superior valuation metric based on enterprise multiple, defined as total enterprise value (TEV) divided by earnings before interest, taxes, depreciation, and amortization (EBITDA). Here is a table of valuation metric comparisons by Gray using equal weight portfolios sorted into quintiles. Data is from 1971 through 2010 and excludes micro caps. Perhaps use of the enterprise multiple instead of price-to-book (P/B) could restore confidence in the value premium?


VALUE AND QUALITY

Researchers have also found that adding a financial strength or quality metric can substantially improve the risk-adjusted results of value portfolios. Paying attention to these additional factors can help overcome the problem of the "value trap," which happens when stocks remain depressed (and may go bankrupt) because their poor fundamentals warrant it.

Using global data from 1988 through 2012 and U.S. data from 1963 through 2012, Kozlov and Petajisto (2013) found that going long stocks with high quality earnings (based on high return on equity, high cash flow, and low leverage) and short stocks with low quality earnings gave higher Sharpe ratios than a similar value strategy. They also found earnings quality to be negatively correlated with value. The best Sharpe ratio came from combining high quality with value, since there were significant diversification benefits.

Using a different approach, Piotroski and So (2012) came up with a multi-factor scoring method (F-Score) to measure a firm's financial strength. This method was positively correlated with profitability and earnings growth. Piotroski and So found that strategies formed jointly on F-Score and value dramatically outperformed traditional value strategies.

Novy-Marx (2012) found he could simplify the quality factor to just gross profitability, defined as revenues minus cost of goods sold, scaled by assets. Novy-Marx (2013) found on U.S. stock data from 1963 through 2012 that profitable firms generated significantly higher returns (0.31% per month) than unprofitable firms, despite having higher price-to-book ratios. Novy-Marx (2012) also found that joint strategies combining value with Piotroski/So's F-Score, Greenblatt's magic formula, or gross profitability outperformed traditional value, with profitability with value being the strongest combination:


What was particularly impressive here was the reduction in maximum drawdown that came from the joint use of value and profitability due to their large negative correlation. As we can see from the above table, maximum drawdown for large cap strategies dropped from -43% with value alone to -18.9% for value combined with profitability.

The key here is that combining quality with value could help us find stocks that are both reasonably priced and expected to grow. As Warren Buffett said, "Whether we're talking about socks or stocks, I like buying quality merchandise when it is marked down."

WHAT TO DO

Despite the above enhancements to value investing, given the advantages still of dual momentum investing, if I ever get the urge to do value investing, I just lie down until the urge goes away. However, if  I were actually going to add value to my portfolio, it would need to be calculated on a more sophisticated basis than price-to-book, and it would need to be be combined with quality to mitigate the potential value trap problem. More specifically, here is what I would look for in a value fund:

1)    It should combine value with quality and/or profitability screens.
2)    It should determine value based on multiple value metrics and/or a value metric that incorporates the enterprise multiple.
3)    It should re-balance at least quarterly to reduce possible style drift and to increase expected profits.
4)    It should not dilute returns by having an overly broad portfolio. In Chapter 6 of my new book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, I show that many so-called smart beta funds are really closet index funds with a modest stylistic tilt. Unfortunately, most value funds are the same. Even though the value effect is more pronounced in the top 10-20% of value rated stocks, most funds dilute this effect by using the top third or top half of value stocks instead of the more profitable top 10-20%.
5)    The expense ratio should be reasonable. (This is true of all the funds that I use.)
6)    For taxable accounts, ETFs are preferred over mutual funds and hedge funds. Tax liabilities usually only occur when you sell your ETF holdings, whereas mutual funds have yearly taxable distributions of dividends and capital gains.

CANDIDATES

Since value and quality do well together, it is natural to think of actively managed mutual funds when considering investment candidates based on these factors. This is because most active managers use fundamental analysis, which takes into account profitability in the form of financial strength, managerial acumen, competitiveness, quality of earnings, and other judgmental factors, in addition to valuation.

However, most active managers lack transparency so as to give the appearance of possessing proprietary knowledge that is worth paying a premium to access. This means it is usually very difficult to tell if they meet the first two criteria listed above. In addition, active mangers usually charge high fees. The Morningstar average large cap value fund annual expense ratio is 1.16%. Mutual funds also have a drag on their performance  because of reserves held for redemption, and, as mentioned above, thesel funds are generally not tax efficient.

There is one mutual fund, however, that may be worth looking at more closely. It is the AQR Core Equity Fund (QCELX).[1]  This fund meets our first three requirements, since it rebalances monthly and uses three indicators of profitability along with five indicators of value. For good measure, it adds three momentum indicators. QCELX also has a reasonable annual expense ratio of 58 basis points. However, it is not tax efficient, although AQR has plans for a more tax efficient version of the fund. But on the negative side, QCELX currently holds 413 stocks, which is more than 40% of the stocks in its 1000 mid/large cap stock selection universe.

AQR has this same kind of broad participation in their momentum fund, where they hold 47% of the 1000 stocks in their selectable universe. Why they do not target factor profits more aggressively remains a mystery to me. Perhaps they expect so much capital to enter their funds that they anticipate liquidity issues. This may also explain why their portfolios are, for the most part, capitalization weighted instead of value or equal weighted.

In the ETF realm, until this past week there was only fund that qualified with the above criteria. It is the PowerShares Dynamic Large Cap Value ETF (PWV), based on Intellidex methodology. PWV uses a ranking selection method with four indicators of value and four indicators of growth. They subtract the value from the growth rankings and then select the largest negative scores. This process automatically gives PWV some profitability exposure, according to the research of Bridgeway Capital Management. Bridgeway found that a multi-indicator value approach (adding price/cash flow, price/earnings, and price/sales) provided greater exposure to gross profitability than a portfolio based only on price/book.

To help further with profitability exposure, after doing their basic screens, PVW adds weightings for price momentum, earnings momentum, quality, and management action. PVW selects the top 20% of the largest 250 stocks from a potential universe of 2000. This gives them a focused portfolio of just 50 stocks that PVW rebalances quarterly. However, I would  prefer that they derive their portfolio of 50 stocks by selecting the top 10% of the largest 500 stocks instead of the top 20% of the 250 largest stocks. They allocate half their capital equally to the top 15 ranked stocks, and the other half of their capital is divided equally among the remaining 35 stocks. Their annual expense ratio is a reasonable 58 basis points. PVW's performance since inception has been attractive compared to the iShares S&P 500 Value ETF.

                                                      Past performance is no assurance of future success.

This past week another ETF got to the short list of qualified candidates. The new kid on the block is Value Shares U.S. Quantitative Value ETF (QVAL) offered by Wes Gray's Alpha Architect. QVAL incorporates quality in a number of ways. First, it has forensic accounting screens to avoid firms at risk for financial distress or manipulation. Then it filters for financial strength using a modified Piotroski/So F-Score. Finally, QVAL checks for sound business fundamentals through what it calls an "economic moat." This is a screen for firms having sustainable competitive advantages, ala Warren Buffett.

Having written the book on valuation metrics, QVAL's management uses the enterprise multiple. They select just the top 10% of their large cap universe based on value, then drop the bottom half of these based on quality. The remaining 50 stock portfolio is equal weighted and rebalanced quarterly. QVAL's annual expense ratio of 79 basis points is higher than PVW and QCELX, but QVAL is the most focused fund among the three, selecting only the top 5% of quality/value stocks in their mid/large cap universe, compared to PVW's 20% and QCELX's 40%. QVAL represents true active management rather than the more usual "no guts, no glory" approach of most watered down, over diversified funds.

WHAT CAN GO WRONG

Value investing in general poses risks that all investors should be aware of. Chief among them is the high tracking error relative to the overall market. Value can go through sustained periods of under performance, such as during the 1990s. From 1994 through 1999, value underperformed growth by over 10% per year! With focused portfolios of just 50 stocks, PVW and QVAL can potentially have higher tracking error than other value funds. Value investors need to have a very long-term investment horizon and a high tolerance for long periods of under performance.

Value investing with focused portfolios, such as those of PWV and QVAL, is also subject to high volatility and high maximum drawdown, and investors should be prepared for this as well. Unfortunately though, investors can lose sight of this. They can panic and act counter to their best interests when confronted with severe drawdown. In a survey of its members since 1988, AAII found that the highest weight to cash and the lowest weight to equities was in March 2009, right at the bottom of the worst bear market since the 1930s.

There is a way, though, to mitigate this harmful behavior through the use of absolute momentum. (You didn't really think I would write a long post like this  without mentioning momentum, did you?) My research paper on absolute momentum and my new book show how to use trend following absolute momentum to reduce the expected drawdown of any investment opportunity. With that in mind, maybe value and momentum can coexist after all.






[1] This material is for informational purposes only. It is not a recommendation to buy or an endorsement of any securities. Investments involve risk. You should do your own research before investing. Please see our Disclaimer page for additional information.
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