October 2, 2013

Momentum...the Practical Anomaly

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 because they seem exceptionally good or because they seem exceptionally bad.

One 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 interested in size and value based investing.

Most research papers on relative 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. It can be challenging to find visual representations or detailed analyses of long-only momentum. But I&M offer some 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:

Using data over the last 86 years in the U.S. stock market (from 1926 to 2011) and over the last four decades in international stock markets and other asset classes (from 1972 to 2011), we find that the importance of shorting is inconsequential for all strategies when looking at raw returns. For an investor who cares only about raw returns, the return premia to size, value, and momentum are dominated by the contribution from long positions.

So even if you are open to shorting, it does not make much sense from a return perspective. I&M's 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 (I&M find similar results using alternative measures of value having long-term histories, such as dividend yield and long-term reversals).

performance comparison chart

Long-only momentum produces an annual information ratio almost three times larger than value or size. Long-only versions of size, value, and momentum produce positive alphas, but those of size and value are statistically weak and only exist in the second half of the data. Momentum, on the other hand, delivers significant abnormal performance relative to the market and does so across all the data.[1] 

performance table
 According to I&M:

Looking at market alphas across decile spreads in the table above, there are no significant abnormal returns for size or value decile spreads over the entire 1926 to 2011 time period... Alphas for momentum decile portfolio spread returns, on the other hand, are statistically and economically large...


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

comparison table

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 momentum returns are strong, stable, and unaffected by size over the entire 86-year sample period (and in eight other markets and asset classes.) Long-only value shows positive alpha among the smallest stocks and insignificant alphas among larger stocks. Since micro-cap stocks are much 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 it may be the only anomaly that has held up well over the past 86 years.

[1] Before reaching any definitive conclusions, it is important to consider transaction costs with individual stock momentum, since momentum portfolio turnover can be ten times larger than value portfolio turnover.

September 6, 2013

Momentum Back Testing

In 1937, Cowles and Jones published the first study showing that relative strength price momentum leads to abnormally high future returns. Academics have been 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" that is "beyond suspicion" (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 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. This reduces the chance of over fitting the data.

Fortunately, there is now 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 (trend following) 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 cover a wide range of market conditions 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. This kind of robustness testing can reduce the chance of data snooping bias.

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, which is the beginning of fixed income index data. 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 or fifteen 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 well across many different markets using a 3 to 12 month formation period. Anything else 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, parameter sensitivity and 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 often uses the same data more than once. Every data set contains patterns due entirely to chance. When you perform a large number of tests, some of them may produce false results that appear to be good. 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 and a hold out set for cross validation will take care of this problem. However, that is not necessarily true. For example, you could split your data in half then rank your strategies based on looking at only the first half of the data. Going down your list strategies, you might find one that looks decent in both halves of the data. But it is still likely this is just due to chance, and you only have half as much data to use for back testing. Your odds go up if 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."

About 20 years ago there was an infamous study that showed 99% of the return of the S&P500 index could be explained by a multiple regression on butter production in Bangladesh, US cheese production, and the number of sheep in the US and Bangladesh. The author of that paper still gets inquiries asking where to get data on Bangladesh butter production! More recently, a serious research paper (believe it or not) called "Exact Prediction of S&P 500 Returns" links future stock returns to the number of nine year old children in the US.

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 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 significant data snooping bias, there is a False Discovery Rate test you can perform that will tell you if you have efficient criteria for model selection. Without something like this, you may be data snooping your way to nowhere.  

                                                                                      Data Snoopy
picture


[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

August 15, 2013

Momentum Tidbits...

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 the exponential application of momentum almost doubles the risk-adjusted profits from conventional momentum.

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 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 underperformance 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 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.