November 26, 2017

Factor Investing: Costs Do Matter

Progress in science comes when experiment contradicts theory. – Richard Feynman

One of the tenets of modern portfolio theory is that you cannot generally beat the market after transaction costs. Yet academic researchers have shown that momentum consistently beats the market. Other factors besides momentum have also cast doubt on the efficacy of the efficient market hypothesis.

There is one way though that academics can still hold on to the efficient market hypothesis. It is to show that academic research on anomalies does not hold up in the real world after accounting for transaction costs/trading frictions.

Chen, Stanzl & Watanabe (2002) were the first to explore the price impact of large-scale factor investing. They concluded that the maximal fund sizes for factor-based anomalies, especially momentum, to remain profitable are small. Lesmond, Shill & Zhou (2003), Korajczyk & Sadka (2004), Fisher, Shah & Titman (2015), Novy-Marx & Velikov (2015), Beck, Hsu, Kalesnik & Kostka (2016) all came to similar conclusions.

Smart beta type fund sponsors who jumped on the factor bandwagon were not happy to see these results. Similar to what happens when drug companies have academics do trials of their products, fund sponsors had their own researchers look at the capacity of factor-based strategies.

Frazzini, Israel & Moskowitz (2014) work for AQR. They analyzed 16 years of actual trading data ending in 2013. They showed scalable results over this period.  But they show the actual cost of trading as more than 1/3 of gross historical factor returns. This should increase as factor-based investing continues to gain in popularity. Regarding momentum stocks, AQR has been trading non-focused momentum portfolios (over 400 stocks in their large cap U.S. momentum fund). This may not be truly representative of the impact from momentum trading.

Ratcliffe, Miranda & Ang (2016) work for Black Rock. They also contend there is enough capacity for scalable results managing factor-based funds using their high frequency trading market data. To their credit, Ratcliffe et al. added, “The exercise we conduct in this paper is hypothetical and involves several unrealistic assumptions.”

Some argue that trading costs are not an issue by pointing to similar performance between momentum based funds and the momentum indices these funds track. The problem with that argument is the indices themselves may suffer from the impact of trading costs on the stocks that make up those indices.

Chow, Li, Pickard & Garg (2017) show that market impact costs can come from trading at temporarily inpacted prices during index rebalances. This means market impact costs are hidden and cannot be seen in a direct comparison between fund performance and index performance. There is also the potential problem of tracking error issues if funds and their indices are based on different criteria.

Chen and Velikov (2017) in "Accounting for the Anomoly Zoo: A Trading Cost Perspective," show that the post-transaction cost returns of 120 factors are near zero, especially after publication. The average anomaly post-publication net return is only 2 basis points. Even the best net returns are fragile and disappear over time. Poor performance holds across many portfolio constructions including several that use cost mitigation techniques.
Post publication momentum performance has been disappointing over the past 20 years. Battacharya, Li & Sonaer (2016) found that momentum profits from U.S. stocks have been insignificant since the late 1990s.  Hwang & Rubesam (2013) showed that the momentum premium for stocks disappeared in the early 1990s. This was when Jegadeesh & Titman published their seminal study on stock momentum and brought attention to it.

Real World Results

The main drawback of all momentum cost studies, whether academic or industry based, is that they depend on assumptions about future transaction costs and market liquidity. Assessing implementation costs using transaction cost models may be incomplete or misguided. No one can say with any degree of certainty what the future will bring. What Ratcliffe et al. say about unrealistic assumptions is likely true of most, if not all, of these studies.

It is not uncommon for academic finance theories to not hold up well in the real world. The capital asset pricing model (CAPM) and mean variance optimization (MVO) are examples of this. In past blog posts here and here, we highlight factor research using actual fund results. One study we cite by Loughran & Hough (2006) compares the actual past performance of value versus growth mutual funds. After examining fund performance from 1965 to 2001, they conclude that superior long-run performance from value is an “illusion.” They attribute the surprising real time underperformance of small cap value funds to the price impact of trading.

A second study by Arnott, Kalesnik & Wu (2017) applied two-stage Fama-MacBeth regression to the last quarter-century of mutual fund returns. They showed the real-world return for the value and market factors to be half or worse than theoretical factor returns.  On a real-time basis, the momentum factor provided no benefit at all. In support of this, studies here and here show that stock momentum profits have been insignificant since the early or late 1990s.

New Study

Two Duke professors, Patton & Weller (2017), recently came out with a study of real versus theoretical performance of momentum, value, and size factors called “What You See Is Not What You Get: The Costs of Trading Market Anomalies.”

The authors start with a two-stage Fama-MacBeth regression applied to 7320 U.S. domestic mutual funds from January 1970 to December 2016. In the first stage they determine the estimated factor loadings for each fund. In the second stage, they regress the excess returns of all funds against the estimated factor loadings to get the factor premia earned by each fund. They then compare these to the theoretical factor returns.

Implementation Costs

Their regression approach differs from Arnott et al. by focusing more explicitly on implementation costs. From 1970 through 2016, the authors find that annual implementation costs range from 2.2% to 8.5% for momentum strategies. This makes momentum profits inaccessible to typical asset managers, according to the authors.

For value, the authors come up with annual implementation costs of 2.6% to 5%. They report overall that “after accounting for implementation costs, typical mutual funds earn low returns to value and no returns to momentum.”

Implementation costs for both value and momentum are stationary throughout this 46 year period. The authors say industry inflows offset declines in bid-ask spreads and commissions.

In addition to Fama-MacBeth regression, the authors use a second approach called matched pairs analysis. Here they directly compare the compensation for stocks to mutual funds with similar characteristics. They sort stocks into quintiles and match them up with three mutual funds closest to them in factor beta. This is a more direct approach than Fama-MacBeth regression.

Matched pairs analysis shows performance attrition for value and momentum strategies comparable to Fama-MacBeth regression. It also shows high costs to trading small stock portfolios.

In summary, the authors say the implementation gap is large and statistically significant for all the factors they examined. None of the factor strategies earned profits after real-world costs during the 1970 to 2016 period.


The growth of factor-based investing has been explosive and is expected to continue. BlackRock forecasts that factor-based strategic beta investing will reach $1 trillion by 2020 and $2.4 trillion by 2025. Many investment conferences now feature this type of investing.

Continued growth in factor-based investing may very well aggravate any scalability issues associated with factor investing.

August 12, 2017

Book Review: Standard Deviations, Flawed Assumptions, Tortured Data and Other Ways to Lie with Statistics

Years ago, when asked to recommend some good investment books, I often suggested ones dealing with the psychological issues influencing investor behavior. These focused on investor fear and greed, showing “what fools these mortals be.” Here are examples: Devil Take the Hindmost: A History of Financial Speculation by Edward Chancellor, and Extraordinary Popular Delusions and the Madness of Crowds by Charles MacKay.

In recent years, there has been a wealth of similar material in the form of behavioral finance and behavioral economics. I now suggest that investors do an internet search on these topics. To better understand investing and investors, you should be familiar with concepts like herd mentality, recency bias, confirmation bias, overconfidence, overreaction, loss aversion, and the disposition effect.

An enjoyable introduction to this field is Richard Thaler’s Misbehaving: The Making of Behavioral Economics. Here is an extensive bibliography for those who want to do a more in-depth study.

Importance of Statistical Analysis

Now that quantitative investment approaches (factors, indexing, rules-based models) are becoming prominent, you need to also be able to properly evaluate quantitative methods. A lively book on the foundations of statistical analysis is The Seven Pillars of Statistical Wisdom by Stephen Stigler. An engaging and more nuanced view of the subject is Robert Abelson's Statistics As Principled Argument.

What I mostly recommend is Standard Deviations, Flawed Assumptions, Tortured Data and Other Ways to Lie with Statistics by economist Gary Smith.

Smith’s premise is that we yearn to make an uncertain world more certain and to predict the unpredictable. This makes us susceptible to statistical deceptions. The investment world is especially susceptible now that it is more model-based and data driven.

It is easy to lie with statistics but hard to tell the truth without them. Smith takes up the challenge of sorting good from bad using insightful stories and entertaining examples. Here are some salient topics with real-world cases that Smith covers:

•    Survivorship and self-selection biases
•    Overemphasis on short-term results
•    Underestimating the role of chance
•    Results distorted by self-interest
•    Correlation is not causation
•    Regression to the mean
•    Law of small numbers
•    Confounding factors
•    Misleading graphs
•    Gamblers fallacy

Critical Thinking

Smith is not afraid to point out mistakes by the economic establishment.  He mentions  errors by University of Chicago economist Steven Levitt of Freakonomics fame.  Smith also discusses research made popular by two Harvard professors, Reinhart and Rogoff. The professors concluded that a nation’s economic growth is imperiled when its ratio of government debt to GDP exceeds 90%. Smith points out serious problems with their work due to inadvertent errors, selective omissions of data, and questionable research procedures.

Publish or perish can contribute to errors in academic research. Economic self- interest, as in medical and financial research, can also cause errors. Smith helps us see how important it is to look at research critically instead of blindly accepting what is presented.

Theory Ahead of Data

Throughout his book Smith focuses on the potential perils associated with deriving theories from data. He gives examples of the Texas sharpshooter fallacy (aka the Feynman trap). Here a man with a gun but no skill fires a large number of bullets at the side of a barn. He then paints a bullseye around the spot with the most bullet holes. Another version is where the sharpshooter fires lots of bullets at lots of targets. He then finds a target he hits and forgets the rest. Predicting what the data looks like after examining the data is easy but meaningless. Smith says:

Data clusters are everywhere, even in random data. Someone who looks for an explanation will inevitably find one, but a theory that fits a data cluster is not persuasive evidence. The found explanation needs to make sense, and it needs to be tested with uncontaminated data.

Financial market researchers often use data to help invent a theory or develop a trading method.  Theory or method generated by ransacking data is a perilous undertaking. Tortured data will always confess something. Pillaged data without theory leads to bogus inferences.

Data grubbing can uncover patterns that are nothing more than coincidence. Smith points to the South Seas stock bubble as an example where investors saw a pattern - buy the stock at a certain price and sell it at a higher price. But they didn’t think about whether t it made any sense.

Smith addresses those who take a quantitative approach to investing. He says quants have “a na├»ve confidence that historical patterns are a reliable guide to the future, and a dependence on theoretical assumptions that are mathematically convenient but dangerously unrealistic.”

Common Sense

Smith’s solution is to first make sure that one’s approach makes sense. He agrees with the great mathematician Pierre-Simon LaPlace who said probabilities are nothing but common sense reduced to calculation.

Smith says we should be cautious of calculating without thinking. I remember a case at the Harvard Business School where we looked at numbers trying to figure out why Smucker’s new ketchup was not doing well as a mass market item. The reason turned out to be that no one wanted to buy ketchup in a jam jar. We need to look past the numbers to see if what we are doing makes sense.

I often see data-derived trading approaches fit to past data without considering whether the approaches conform to known market principles. If one does come up with models having sensible explanations, they should then be tested on new data not corrupted by data grubbing. Whenever you deviate from the market portfolio, you are saying you are right and the market is wrong. There should be good reasons and plenty of supporting data for believing this is true. [1]


I have seen some take the concept of dual momentum and make it more complicated with additional parameters. They may hold back half their data for model validation. They call this out-of-sample testing, but that is a questionable call.

Do you think you would hear about these models if their “out-of-sample” tests showed poor results? Would they discard their models and move on? Chances are they would search for other parameters that gave satisfactory results on both the original and hold out data.

Momentum is robust enough that a test on hold out data might look okay right from the beginning. But that is likely due to momentum’s overall strength and pervasiveness.  It is questionable whether you really had something better than with a simpler approach. You may have just fit past data better, which is easy to do by adding more parameters.

Keep It Simple

There are some areas I wish Smith had addressed more. First is the importance of having simple models, ala Occam’s razor. Simple models dramatically reduce the possibility of spurious results from overfitting data.

Overfitting is a serious problem in financial research. With enough parameters, you can fit almost any data to get attractive past results. But these usually do not hold up going forward.

In the words of Edsger Dijkstra, "Simplicity is a great virtue, but it is requires hard work to achieve it and education to appreciate it. And...complexity sells better."

In Data We Trust

Smith briefly mentions the law of small numbers popularized bt Kahnemann and Tversky. But I wish Smith had gone more into the importance of abundant data and how it helps us avoid biased results.

According to de Moivre’s observation, accuracy is proportional to the square root of the number of observations. To have half the standard error, you need four times the data.

The stock market has had major regime pattern changes about every 15 years. A model that worked well during one regime pattern may fail during the next. We want a robust model that holds up across all regimes. To determine that, you need plenty of data. In the words of Sherlock Holmes, “Data! Data! Data! I can’t make bricks without clay!”

Theories Without Data

Smith talks a lot about the issue of data groping without theory. But he also mentions the opposite problem of theory without adequate data analysis. Smith cites as an example the limit to growth theories of Malthus, Forrester, and Meadows. Smith contends they did not make any attempt to see whether historical data supported or refuted their theories. Most economists now dismiss these theories.

But Smith may not have considered later information on this topic. Here and here is information that makes this subject more provocative. Smith says it is good to think critically. This is true even when approaching a book as thoughtful as Smith’s.

[1] Even if a model makes sense initially, you need to make sure it continues to do so. Investment approaches can become over utilized and ineffective when they attract too much capital. See here and here

July 14, 2017

Trend Following Research

There have been hundreds of research papers on relative strength momentum since the seminal work by Jegadeesh and Titman in 1993. [1] Relative momentum has been shown to work in and out-of-sample within and across most asset classes. Theoretical results have been consistent, persistent, and robust.

Research on trend following absolute momentum got a much later start. The first paper on “Time Series Momentum” was by Moskowitz, Ooi, and Pedersen (2012). [2]

This was followed by my "Absolute Momentum: A Simple Rules-Based Strategy and Universal Trend Following Overlay" in 2013.

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained.

Since then, there have been other good absolute momentum research papers. But absolute momentum and trend following in general have still not gotten the attention they deserve. Major fund sponsors offer single or multi-factor products using relative momentum. But not a single one incorporates absolute momentum as a trend filter.

Absolute momentum can enhance expected returns just like relative momentum. But, unlike relative momentum, absolute momentum can also reduce expected downside risk exposure. It performs best in extreme market environments, making it an excellent portfolio diversifier.

Moving Averages

Let us look at other trend following research over the past few years. In 2014, Lemperiere et al. applied exponential moving averages to futures since 1960. They examined spot commodities and stock indices since 1800. [3] Their “Two Centuries of Trend Following” showed a t-statistic of 5 on excess returns since 1960 and a t-statistic of 10 on excess returns since 1800. These results were after accounting for the upward drift of the markets. The effect was stable across time and asset classes. There was also no degradation of long-term trend strength in recent years.

In "Timing the Market with a Combination of Moving Averages," Glabadanidis (2016) presented ample evidence of the timing ability of a combination of simple moving averages applied to U.S. stocks.

A comprehensive treatment of moving averages is in a new book Market Timing with Moving Averages: The Anatomy and Performance of Trading Rules  by Valeriy Zakamulin. Zakamulin has already written academic papers on moving average methods.

In the book, Zakamulin analyzed eight different types of moving averages along with absolute momentum. He applied these to stocks, stock indices, bonds, currencies, and commodities since 1857. He showed that these strategies can protect portfolios from losses when needed the most. Zakamulin's conclusion was that trend following represents a prudent investment approach for medium and long-term investors.

What is especially interesting is Zakamulin’s 159-year test on the S&P Composite Index. He looked at the frequency of positive results using a 10-year rolling performance window. Absolute momentum came in first and second place among the strategies tested. It also held 7 out of the top 10 highest positive rankings.

Absolute Momentum

There have been at least a half-dozen noteworthy studies during the past few years that focused on absolute momentum.

In Trend Following with Managed Futures, Greyserman and Kaminski (2014) applied absolute momentum to stock indices, bonds, commodities, and currencies all the way back to 1223! They held assets long or short depending on the trend of the last 12 months. The authors found that trend following was more effective than buy-and-hold. Sizes of the five largest drawdowns were also reduced by an average of one-third.

In “The Trend is Your Friend: Time-Series Momentum Strategies Across Equity and Commodity Markets,” Georgopoulou and Wang (2016) found that absolute momentum was significant, consistent, and robust across conventional asset classes from 1969 to 2015.

In “Trend Following: Equity and Bond Crisis Alpha,” Hamill, Rattray & Van Hemert (2016) applied absolute momentum to global diversified markets from 1960 through 2015. Absolute momentum performed consistently and was particularly strong during the worst equity and bond environments.

In “The Enduring Effect of Time Series Momentum on Stock Returns Over Nearly 100 Years,” D’Souza et al. (2016) found significant profits from absolute momentum applied to individual U.S. stocks from 1927 to 2014 and to international stocks from 1975. Unlike relative momentum, absolute momentum did well in both up and down markets. Absolute momentum fully subsumed relative momentum and was not subsumed by any other factor. The combination of relative and absolute momentum (dual momentum) earned a striking 1.88% per month (t-statistic 5.6).

In “Two Centuries of Multi-Asset Momentum (Equities, Bonds, Currencies, Commodities, Sectors and Stocks),” Geczy and Samonov (2017) applied relative momentum to country indices, bonds, currencies, commodities, sectors, and U.S. stocks over the past 215 years. But they also showed that absolute momentum (which they called “trend”) had highly significant positive results in every asset class.

In “Time-Series and Cross-Sectional Momentum Strategies under Alternative Implementation Strategies,” Bird, Gao, and Yeung (2017) found that both relative and absolute momentum generated positive returns in 24 major stock markets from 1990 through 2012. But absolute momentum was clearly superior. With appropriate cutoffs, absolute momentum outperformed in all 24 markets. The authors concluded that momentum is best implemented using absolute momentum.

A recent study of absolute momentum by Hurst, Ooi, and Pedersen (2017) is an extension of their earlier paper, “A Century of Evidence on Trend-Following Investing.”  In it, the authors studied the performance of trend-following across global markets (commodities, bond indices, equity indices, currency pairs) since 1880. They found in each decade since 1880, absolute momentum delivered positive average returns. This was accomplished with low correlation to traditional asset classes and after adjustments for fees and trading costs.

Absolute momentum performed well across different macro environments and in 8 out of 10 of the largest crisis periods. It performed best during extreme up and down markets in U.S. stocks.


The non-acceptance of absolute momentum as a trend filter by most fund sponsors in the face of strong evidence of its effectiveness has three likely explanations. The first is that research information disperses very slowly through the investment community.  The second is that investors prefer to follow the crowd, even if that means losing more in down markets. They may also be  averse to experiencing trend following whipsaws. The third reason is the possible long-standing bias against trend following. This has been difficult to dislodge, despite strong evidence of its effectiveness. These three tendencies are well-known now in behavioral finance as the slow diffusion of information, herding, anchoring, and confirmation bias.

Based on research results, trend may be the strongest factor. Yet it is also the most ignored. This is good news for those of us using it.

[1] Many academic papers refer to relative momentum as cross-sectional, even though some applications are cross-asset, not cross-sectional.
[2] Academic papers often refer to absolute momentum as time series momentum. But all momentum is based on time series. Geczy and Samonov (2017) repeatedly characterize all momentum as time series momentum in their latest paper.
[3] For a theoretical justification of trend following, see Zhu and Zhou's (2009), “Technical Analysis: An Asset Allocation Perspective on the Use of Moving Averages.”

June 10, 2017

Real Time Factor Performance

According to S&P DJ Indices, 92% of all actively managed stock funds failed to beat their benchmarks over the past 15 years. This should come as no surprise. Similar results were published more than 20 years ago. This information has caused a move away from active stock selection and toward index funds and systematic approaches.

Money managers have recently moved more in the direction of factor-based and so-called smart beta investing. But as I pointed out in my February blog post, “Factor Zoo or Unicorn Ranch?”, there are some potential issues with this type of investing. Not the least of which is the shortfall between actual and theoretical returns.

Theoretical results are in academic papers and all over the internet. Much less information is available on the real-time performance of factor-based investments.

Lack of Real Time Performance Studies

The Loughran and Hough study in 2006 was a rare look at real-time factor performance. In it, the authors showed that there was no significant difference in performance between U.S. value and growth mutual funds from 1965 through 2001. The authors concluded by saying the idea that value generates superior long-run performance is an “illusion”.

This was the only study I could find that examined actual results of popular investment factors. But now there are two other studies. Blitz (2017) in "Are Exchange Traded Funds Harvesting Factor Premiums?" examined the performance of 415 ETFs with at least 36 months of return history as of December 2105. He looked at factor harvesting over the prior 60 months if that much data existed. He concluded that on aggregate, all factor exposures turn out to be close to zero. There is no aggregate alpha there.

Last month Arnott, Kalesnik, and Wu (AKW) published an article called, “The Incredible Shrinking Factor Return.” AKW examined actual versus theoretical performance of four factors well-known to investors using 5323 mutual funds from January 1991 through December 2016. These factors are market, value, size, and momentum

Two Step Approach

To determine their results, AKW did a two stage (Fama-MacBeth) regression.  In stage 1, they regress mutual fund excess returns against standard factor models to determine each fund’s estimated factor loadings. In stage 2, they regress the excess returns of all against the factor loadings to get the factor premium earned by each fund. These are then compared to the theoretical factor returns.

This approach incorporates factor co-variances to determine factor premia. Comparing actual to theoretical performance can reveal data mining, selection, and survivorship biases. It can also identify the effects of management fees, bid-ask spreads, and transaction costs.

In many academic papers, more than half the profits come from shorting stocks. But shorting may be expensive and sometimes impossible to do. Looking at long-only mutual fund performance removes those unrealistic profits.
Performance Shortfalls

Here are AKW’s regression results using 25 years of fund data from January 1991 through December 2016:

We see a 50% shortfall in the performance of the market factor. This is not surprising. For many years, other research has shown this effect. High beta tends to underperform low beta on a risk-adjusted basis going forward in time. 
In the AKW regression, the size factor shows a small but insignificant improvement in actual versus theoretical returns. Value is the most commonly used factor. AKW’s regression shows that value fund managers captured only 60% of the value premium since 1991. This compliments the recent findings of Kok, Ribando & Sloan (2017). They claim that outside the initial evaluation period of 1963 to 1981, the evidence of a value premium is weak to non-existent.

The largest shortfall AKW discovered is with momentum. The realized momentum return of live portfolios was close to zero, compared to a theoretical return of around 6% per year. Stock momentum alpha has not been positive since 2002, according to AKW. This is consistent with research by Battacharya, Li & Sonaer (2016) who find that momentum profits from U.S. stocks have been insignificant since 1999.

AKW say transaction costs play a major role as the source of slippage between theoretical and realized factor returns. In their words, “…higher turnover strategies, such as momentum, have trading costs that may be large enough to wipe out the premium completely if enough money is following the strategy.”

AKW concludes their study by asking if 10,000 quants all pursue the same factor tilts, how likely is it that these factors will add value?

Skepticism and Pushback

Skepticism toward new information is a good thing. More research and analysis can help advance what we know about the world.

Corey Hoffstein offers a critical response to the AKW study in an article he calls “A Simulation Based Rebuttal to Research Affiliates.” Corey points out we should not overlook style drift as a significant source of error. Return estimates can be inaccurate if managers switch investing styles. Most mutual funds have investment philosophies that stay consistent over time. Growth funds do not usually become value funds, for example. But it can occasionally happen.

In support of style drift, Corey shows 3-year rolling betas versus full period betas for the Vanguard Wellington Fund (VWELX). His data is from January 1994 through July 2016.

Corey’s logic is similar to saying one should be suspicious of the 10% average return of the S&P 500 index over the past 50 years because yearly returns have varied from -37% to 38%.  

Research of pension consultants shows that 3-year performance by equity managers is often mean reverting. This may explain some of the difference between full period and 3-year rolling window returns. With 3-year rolling returns, some, and perhaps a lot, of the variation in returns may be random noise.

In addition to the full data set, AKW looks at an expanding window of returns that incorporates all the data available up to that point. An expanding window regression converges to the full sample factor betas toward the end of the sample period. When AKW compares expanding window regressions to full period ones, they get comparable results.

Corey’s second argument is that you can attribute a portion of the AKW identified shortfall to estimation error. Factor loading estimates are noisy. Estimation error in the independent variables creates a pull toward zero in the beta coefficients. That causes a downward biasing of factor premia estimates in the second stage of AKW’s regression. This is a valid point.

But Corey offers no direct evidence of how much estimation bias there is in the AKW regression. Instead, Corey conducts a 1000 hypothetical fund simulation using normally distributed betas.

There are good reasons why simulations are seldom used in financial markets research. Simulations may give a false sense of precision. They are dependent on distributional assumptions that are often unrealistic when applied to financial markets. Market returns are not normally distributed with constant volatility. Underlying distributions may be non-stationary and lack independence. In his simulation, Corey assumes that mutual fund returns are normally distributed with constant volatility.

Academic researchers prefer to use as much real data as they can rather than simulated data. The AKW regression uses 25 years of actual mutual fund data, which should reduce the influence of tracking error on AKW's results.

Corey uses only one fund, VWEIX, with his simulation to estimate how much downward bias there might be in the AKW regression. He looks at the difference in standard deviation between full period and 3-year rolling estimates of VWELX’s beta coefficients. Corey is unable to show that estimation errors have the same distribution scale as the betas themselves.

Corey concludes there may be significant downward bias in the AKW regression estimates. But Corey does not explain the different degrees of slippage for different factors. Even if you accept Corey's simulation, results from 1994 through 2016 of only one fund may be on outlier. Other funds may conform to AKW's results. In the end, Corey says, "our results do not fully refute AKW’s evidence."

AKW does acknowledge downward bias in betas due to estimation error in the independent variables. They conduct six different robustness tests that reinforce their results and help mitigate that error. These robustness test results are consistent with their core findings. Studies here and here also confirm the disappearance of momentum profits since the 1990s.

We Are All Biased

I applaud Corey’s skepticism with regard to unexpected research findings. I also applaud him when he says, “…published research in finance is often like a back test. Rarely do you see any that does not support the firm’s products or existing views.”  We should also keep that in mind regarding critical assessments of new information by those having opposing viewpoints. As the old saying goes, "Never ask a barber if you need a haircut."

April 12, 2017

Lessons Learned from Sports Investing

Wee Willie Keeler was one of the greatest contact hitters in baseball. One year, 30 of Keeler’s 33 home runs were inside the park. Keeler’s motto was, “Keep your eye clear, and hit ‘em where they ain’t.”

I have always tried to do this by focusing on underexploited investment opportunities. In the 1970s that meant stock options. In the 1980s I had great success with managed futures.

Also in the 1980s I had a family member who bet on football games. He knew I invested using quantitative methods, so he asked me to take a look at betting certain NFL home underdogs. I was skeptical and reluctant at first, but then obliged him. I was surprised to discover there was a profit there.

I became intrigued with the possibility of exploiting inefficiencies in the football betting market. There were no sports databases back then and almost no published sports research. So I hired some UC Berkeley students to go through years of the data with me to test betting strategies.

After we had a stable of successful angles, I put one of the students on a bus to Reno each weekend. Encouraged by our early results, I expanded my research to include college and pro football and basketball. We were incredibly successful with football.

I focused on areas where the linesmakers were not paying enough attention, such as game time weather conditions, team mean reversion, public overconfidence, and over inflated betting lines.

We even came up with a player stat-based Monte Carlo simulator that played through entire baseball games. It gave a good edge early in the season before others figured out the impact of off-season trades.

One of my research assistants continued to analyze sports after graduation. He became Vice President of Basketball Operations for an NBA championship team, then VP of Basketball Strategy and Data Analysis with another NBA team.

Our biggest edge came from betting against public biases. For example, teams that showed very poor performance in their last game are often under bet in their next game. As in stock market investing, I found that mean reversion and public myopia could be exploited in sports wagering. (My best indicator of positive future results has always been when investors overreact to short-term losses and close out their accounts.)

Issues with Doing Well

As we continued to do well, some bookmakers would no longer take our action. A smart one became friendly and brought us other bookmakers’ football lines. This way he would know our plays and could bet along with us.

Afternoons we would hang large white marker boards on the walls of my investment office and write down the betting lines from all our sources. Fortunately, we had very few office visitors back then! As others found out about our success, I began managing a successful sports betting syndicate.

I had a 12-foot BUD (Big Ugly Dish) installed at my house and would watch as many games as I could. That was the problem. Sports research and wagering took over my life. It was causing me to neglect my family. I also became concerned with security. As our wagering grew, we would fly to Las Vegas or receive FedEx packages full of cash in order to settle up. So I set sports aside.

Looking back on my sports activities, I realize now that I learned some valuable lessons that helped make me become a better researcher and investor. Here are some of those lessons:

Always Have an Edge

When I went to Nevada with friends, I never played casino games. When they asked why, I replied, “I don’t gamble.” They would laugh knowing I was betting tens of thousands of dollars every week on sporting events. But I have always needed a positive expectation before assuming any risk. To me, this is what distinguished what I was doing from gambling.

My need for a positive expectation also led me to the under exploited niche of dual momentum investing. Most of those who invest have little or no edge. You cannot have an advantage doing what everyone else is doing. You would be better off then investing in low-cost passive index funds.

Herding is a powerful behavioral instinct that can lead to mediocre investment returns.  You should have a healthy dose of skepticism about strategies that differ from the market portfolio. This also means looking beyond academic studies. You need to be aware of how strategies actually perform real time. And you need to consider how they will perform in the future as they attract more capital. [1]. Dual momentum is generally ignored as an investment strategy. I don't expect that to change anytime soon due to strong behavioral biases. These include anchoring, aversion to tactical investing, home country bias, and familiarity biases.

Do Your Homework

Betting lines, like financial markets, are mostly efficient. The only way to be confident you have an edge is through thorough research using plenty of data. Doing this gives you confidence. It helps you stay with your approach despite short-term fluctuations in the value of your bankroll or your investments. Dsciplined bankroll management is important for long-run success with sports and any other investment.

Keep Things Simple

The biggest problem with model development is expecting ex-post results to hold up well out-of-sample. Selection bias, over optimization, and model overfitting are also serious problems in both sports and non-sports research. If you keep tweaking your strategies, it isn’t difficult to find betting angles that give you over 60% winners. But these almost never hold up in real time. What you want is a logical basis for a wager, consistent back test results, and real-time validation of backtested strategies.

Sports research taught me the importance of having simple strategies with intuitive logic behind them and plenty of backtest data. This is what led me to momentum investing. It is simple, logical, and supported by over 200 years of backtest validation across many different markets.

Have Realistic Expectations

If you win a profitable percentage of your sports bets, you are still going to have some serious losing streaks. You have to accept this. Warren Buffett is often quoted as saying the # 1 rule of investing is to not lose money, and the # 2 rule is to never forget rule #1. Yet Buffett’s Berkshire Hathaway was down more than 50% twice during the past 15 years. Despite this, Buffett has done well. Confidence in your approach and emotional discipline are what you need once you have a proven edge.

Expecting to consistently win at sports much more than 60% of the time is unrealistic. Expecting to beat the markets most of the time on a short-term basis is also unrealistic. Here is the percentage of time that Global Equities Momentum (GEM) featured in my book outperformed the S&P 500 index over various periods since 1971:

Time horizon
% of time GEM outperformed the S&P 500
3 months
1 year
3 years
5 years
10 years
Results are hypothetical, 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, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

Over one year or less, GEM didn't do much better than a coin flip. But over five or more years, results are considerably different. Patience is important whether you are a traditional investor or a speculator on sporting events. Warren Buffett was right when he said the stock market is a mechanism for transferring wealth from the impatient to the patient.

Leave Your Opinions at the Door

You need to forget your likes or dislikes and go where the data takes you to be an effective sports bettor.  The same is true with other types of investing. I have seen investors disregard good opportunities that conflicted with their prior beliefs and biases.

To be a good winner over the long run, you need to be a good loser over the short run. You can do this if you have a proven edge, a simple approach, and realistic expectations. Good luck to you!

February 22, 2017

Factor Zoo or Unicorn Ranch?

According to Morningstar, as of June 2016, the assets in smart beta exchange traded products totaled $490 billion. BlackRock forecasts smart beta investing using size, value, quality, momentum, and low-volatility factors will reach $1 trillion by 2020 and $2.4 trillion by 2025. This annual growth rate of 19% is double the growth rate of the entire ETF market. Are factors the cure-all for our investment needs? Or are they more like “active management” that almost everyone wanted instead of passive index funds in the 1970s?

No one wants to be just average. This ironically gave most investors below average returns as they used the same information to compete against one another for the same returns.  Superior performance was usually due more to luck than to skill. Bill McNabb, CEO of Vanguard, pointed out it has been passive index funds that have been in the top quartile of long-term performance.

Factor-based investors and advisors now think they have an advantage. They base this on the results of theoretical asset pricing models. Investors have lost sight of the fact that factors were once called risk factors. If factors offer higher returns because their risks are higher, do they really provide an advantage to investors? Small cap stocks, for example, may offer higher returns. But their volatility and survival risks are also higher. Value stocks may offer higher returns over the long run, but they may have extended periods of under performance. They may fall into a value trap where they stay undervalued or go out of business.

What investors really want is a factor premium that exists after accounting for risk. But Mr Market is not usually disposed toward providing a free lunch.

Asset pricing models often look at long/short returns without taking proper account of the price impact of trading as well as other issues. Factors that looked good on paper may be lacking in robustness, pervasiveness, persistence, or intuitiveness. Let us look at these issues more closely.

Does Size Matter?

The small cap size premium was first identified by Banz in 1981. His results were influenced by extreme outliers from the 1930s.

Looking at more recent history, the oldest small cap index is the Russell 2000. It started in January 1979. Here is the Russell 2000 annual return and volatility over the life of the index compared to the S&P 500 index.

The Russell 2000 underperformed the S&P 500 by 1.3% annually and had a higher standard deviation. The Russell 2000 thus underperformed on both a risk-adjusted and non-risk adjusted basis.[1]

Here is a chart comparing the Sharpe ratios of all small and large cap stocks over a longer period of time. Small cap stocks failed to show significantly higher risk-adjusted profits than large cap stocks.

In the table below long-only small caps slightly outperformed large caps globally since 1982. But small caps have underperformed large caps in the U.S. since 1926. Where is the outperformance that Banz talked about? 
According to Shumway & Warther (1998) in “The Delisting Bias in CRSP's Nasdaq Data and its Implications for the Size Effect”, small caps originally showed a premium because they had an upward bias due to inaccurate returns on delisted stocks. When this bias was removed, the small cap anomaly disappeared. Just 37% of small cap stocks have holding period returns greater than one-month Treasury bills, versus 69% of stocks in the largest decile.

In “Transaction Costs and the Small Firm Effect,” Stoll & Whitney (1983) showed that transaction costs also offset a significant portion of the small cap size premium.

Some construct their own factor pricing models that show a small cap premium if you combine size with other factors. In other words, size matters depending on what you are able to do with it.

Front Running

Some attribute the poor performance of the Russell 2000 index to the actions of front runners. Index replicators follow formulas for trading. They have little control over what and when to trade. Their trades are also known by the public ahead of time.

I pointed out in my last post that front runners cost S&P GSCI index investors 3.6% in annual return. Front running can happen with any index or factor-based strategy having known portfolio rebalancing dates.

Front runners can initiate trades ahead of index replicators or smart beta fund managers. They take profits after the replicators and fund managers finish their trading. Front runners thereby capture part of the factor or index return at the expense of index and fund investors.

If I were still managing hedge funds, I might front run rules-based strategies like value or momentum. These strategies often hold less liquid, more volatile stocks that offer the highest front running profits. Momentum would be a particularly attractive target. Its high portfolio turnover means more opportunities for profit. 

Value - The Price is Right?

We all like bargains. Advisors and fund sponsors play off that desire by promoting the idea of a value premium. This past month I read two investment blogs saying cheap value stocks have outperformed the market by 4% per year.

According to Asness et al. (2015), the only time there seemed to be a significant positive value premium in large-cap stocks was over the in-sample 1963-1981 period. Over a longer 88-year period, there was no significant value premium. They argued that value might still be useful as a diversifier in multi-factor portfolios where they decide how to determine those factors.

Kok, Ribando, & Sloan (2016) showed that strategies using common fundamental metrics of value, such as book-to-market or earnings-to-price, do not deliver superior performance. Instead, these ratios identify firms with temporarily inflated accounting numbers that tend to mean revert. .

Loughran and Hough (2006) looked at the performance of all U.S. equity funds from 1962 through 2001. They used the prior 36 months to sort funds by book-to-market (top versus bottom quartile) and size (top versus bottom half). 

Equal Weighted Mutual Fund Returns 1965 to 2002

Large Cap
Small Cap
Source: Loughran and Hough (2006), “Do Investors Capture the Value Premium?

From 1965 through 2001, the average large cap growth fund returned 11.30% per year, while the average large cap value fund returned 11.41%. The outperformance of 0.11% for
large cap value over growth was insignificant.

With small caps, the authors were expecting different results. They were surprised that small cap value funds earned 14.10%, while small cap growth funds returned 14.52%. Small cap value underperformed small cap growth by 0.42% per year.  

Israel & Moskowitz (2012) show that the value premium is insignificant among the two largest quintiles of stocks and is concentrated among small cap stocks. These results are robust over 86 years of U.S. equity data and almost 40 years of data across four international markets. 

Why then did small cap value funds underperform small cap growth funds? Loughran and Hough said wide bid-ask spreads and the price impact of trading worked against the capture of a value premium in small-cap stocks. For value investing in general, they concluded, “We propose that the value premium is simply beyond reach…investors should harbor no illusion that pursuit of a value style will generate superior long-run performance.”

Some practitioners try to excuse these results by saying there are better valuation metrics than book-to-market (B/M). But the Israel & Moskowitz results were similar using valuation measures other than book-to-market. Kok, Ribando, & Sloan (2017) also found "remarkably consistent results" using different valuation ratios and weightings. Loughran & Wellman (2010) found only a .02% per month difference in performance between book-to-market (HML) and the enterprise multiple (EM), another popular valuation metric.

Some who believe in the superiority of value or small cap investing point to performance of the Dimensional Fund Advisors (DFA) funds. Their U.S. Small Cap Portfolio (DFSTX) began in March 1992 and was the first factor-based small-cap fund. DFA's U.S. Large Cap Value Portfolio (DFLVX) and U.S. Small Cap Value Portfolio (DFSVX) funds began in February and March of 1993. All these funds have positive alphas. But none of the alphas are statistically significant.[2] To the extent that the DFA funds have done reasonably well may not be entirely due to their factor tilts

DFA serves as a market maker in the stocks they hold. This means they can be patient when adjusting portfolio positions. That reduces their costs of trading in exchange for some additional tracking error. Using a buy-sell range also reduces turnover and trading costs. Holding a large number of securities further reduces the price impact of DFA's trading.

DFA has also benefited from not being tied to an index and thereby subject to front running costs. DFA has been aggressive in lending securities for a fee. Additionally, DFA uses momentum to filter their trades. They generally avoid IPOs and stocks with high borrowing costs.

Stocks with high borrowing costs often have a large short interest. This means there is a limited supply of stock available for borrowing. Studies here, here, and here show that heavily shorted stocks have negative abnormal returns, while lightly shorted stocks outperform their benchmarks. DFA has benefited considerably from avoiding stocks with high short interest.

Source: Boehmer et al. (2009), “The Good News in Short Interest”

Risk Factors

People may not remember that factors were once called “risk factors.” Value funds have tracking errors that can persist for 10 or more years. Tracking error is a form of risk. It can cause investors and money managers to liquidate their positions at inopportune times.

Another risk is scalability. It might not be possible for popular strategies like value to always maintain an advantage over the market. This is particularly true of value stocks that are often out-of-favor and ignored. This can make them less liquid and more expensive to trade.

In “A Taxonomy of Anomalies Costs and their Trading Costs” Novy-Marx & Velikov (2015) looked at how capital levels can affect factor trading profits. Their calculations showed that excess profits disappear once the amount in value strategies exceeds $20.7 to $50.6 billion.

The Novy-Marx & Velikov capital levels are based on a turnover reducing approach. It buys value stocks ranked in the top 10th or 30th percentile. But it does not liquidate them until stocks drop out of the top 50th percentile. DFA, MSCI and others use a similar turnover reducing approach. 

Here is a chart showing the amount of capital invested in dedicated U.S. large and mid-cap value funds. It does not include managed accounts, hedge funds, and many of the other 400+ funds having the word “value” in their names.

U.S. Large Cap Value Index Funds
iShares Russell 1000 Value (IWD)
$35.2 b
Vanguard Value (VTV)
$27.6 b
DFA US Large Cap Value I (DFLVX)
$19.7 b
iShares S&P 500 Value (IVE)
$13.1 b
iShares Russell Mid Cap Value (IWS)
$9.4 b
Vanguard Mid Cap Value (VOE)
$6.6 b
TIAA-CREF Large Cap Value Index (TRLCX)
$6.3 b
DFA US Large Cap Value III (DFUVX)
$3.4 b
Schwab US Large Cap Value (SCHV)
$2.9 b
Total Value Assets
$124.3 b

The $124.3 billion in value funds far exceeds the upper bounds where Novy-Marx and Velikov say value profits would disappear.

Momentum – the Premier Anomaly

Momentum is the strongest market anomaly based on academic research. Momentum has been studied now for more than 25 years. It meets all the tests of robustness, pervasiveness, persistence, and intuitiveness.

Momentum performs best in focused, concentrated portfolios. Momentum is a high turnover strategy. Momentum stocks are often volatile with wide bid-ask spreads. Trading billions of dollars around the same time in a modest number of volatile stocks may impact trade execution. It would be like trying to force a dozen people through a small door opening.

Academics have long been concerned about the price impact of momentum trading. One of the first  studies of this was by Lesmond, Schill & Zhou (2002) in their “The Illusive Nature of Momentum Profits.” They found that momentum creates an illusion of profit opportunity when none really exists. Momentum is a high turnover strategy. Momentum stocks are relatively less liquid with disproportionally large trading costs. Two years later, Korajcyzk & Sadka (2004) found that profit opportunities could vanish once the amount invested in momentum-based strategies reaches $5 billion.

Counter to these findings, Frazinni, Israel & Moskowitz (2012), based on 16 years of  actual AQR data, argue that the potential scale for factor trading is more than an order of magnitude greater than previous studies suggested. They said this capacity could increase even further by using optimized trading methods. But they show the actual cost of trading as more than 1/3 of gross historical factor returns. This should increase as factor-based investing continues to gain in popularity. Regarding momentum stocks, AQR has been trading non-focused momentum portfolios (over 400 stocks in their large cap U.S. momentum fund). This may not be truly representative of the impact from momentum trading.

More recently, Ratcliffe, Miranda & Ang (2016) from BlackRock suggested that a greater amount of capital could be traded using momentum.

In contrast to these two studies, Fisher, Shah & Titman (2015), using observed bid-ask spreads, got results much closer to those of Lesmond et al. and Korajcyzk & Sadka than Frazinni et al.

Novy-Marx & Velikov (2015) also determined the capacity for stock momentum before profits would vanish.

This is close to the $5 billion amount where Korajcyzk & Sadka said momentum profits would disappear. Novy-Marx & Velikov used an optimization algorithm to keep them in trades longer, as discussed by Frazzini et al.

Here is a table of the amounts invested in U.S. momentum exchange traded ptoducts:

It does not include mutual funds, managed accounts, or hedge funds. Even so, it exceeds the level of assets where both Novy-Marx & Velikov and Korajcyzk & Sadka say momentum profits should no longer exist.

Here is a table from a recent study of factor capacity. It is by Beck, Hsu, Kalesnik & Kostka (2016) in “Will Your Factor Deliver? An Examination of Factor Robustness and Implementation Costs.” They used a different method than Novy-Marx & Velikov to compute factor capacity.

With $10 billion invested in large cap momentum, the value added by momentum goes from +2.7% per year before transaction costs to -3.4% after transaction costs. This is with monthly portfolio rebalancing. If you rebalance quarterly instead of monthly, your additional annual return goes from +2.0% before trading costs to -1.6% afterwards.

This situation is much like the one I discussed in my last post. Those offering commodity products to the public say passive commodities are still a worthwhile diversification. But independent researchers with no products to promote say the opposite. Who should we believe? Maybe practitioner data is better than academic data.

To help find out, we can look at the performance of the oldest publicly available momentum funds. First is the PowerShares DWA Momentum ETF (PDP) managed by Dorsey Wright. It began on March 1, 2007. The second is the AQR Large Cap Momentum (AMOMX) mutual fund. It began on July 9, 2009.

From its start through January 2017, PDP had an annual return of 6.44%, while its chosen Russell 3000 Growth benchmark returned 8.67%. This is an average annual return shortfall of 2.23%. PDP has a focused portfolio of 100 momentum stocks.

AMOMX had an annual return of 14.55% since its inception, while its chosen Russell 1000 Growth benchmark returned 16.11%. This is an average annual shortfall of 1.56%. Besides managing seven momentum mutual funds, AQR uses momentum with their multi-style funds and large hedge fund. AQR spreads their large-cap U.S. momentum holdings among 496 stocks. This is half the fund’s available universe of 1000 stocks. Research by Alpha Architect shows that momentum works best with focused portfolios of 50 or fewer stocks. Why wouldn't AQR use more focused portfolios if there is little impact from trading momentum stocks?

Ten years of underperformance for PDP and 8.5 years for AMOMX are not long enough to draw meaningful conclusions. But there is another possible explanation for underperformance other than or in addition to trading costs. Momentum itself may have lost its mojo since it became widely known and followed in the 1990s.

Battacharya, Li & Sonaer (2016) found that momentum profits from U.S. stocks have been insignificant since the late 1990s. Robert Arnott of Research Affiliates said their research shows stock momentum has underperformed since 1993 [2]. This was the same year Jegadeesh & Titman published their seminal study on stock momentum. Hwang & Rubesam (2013) showed that the momentum premium for stocks disappeared in the early 1990s.


We can find intuitive reasons why size, value, and momentum might provide a premium based on  risk, investor behavior, or market structure. This becomes more challenging with quality. Why should quality stocks be mispriced by the market? There is no reason to believe that higher quality stocks are riskier than lower quality stocks, which would require them to offer a premium for investors to hold them. It is also hard to find behavioral factors or structural impediments that would explain why one would neglect high quality stocks causing them to command a behavioral premium. It is not surprising then that there are few signs of a premium or premium persistence across multiple definitions of quality.

Cakici (2015) found only marginal evidence that gross profitability (a subset of quality) exists globally. Hsu & Kalesnik (2014) reported in “Finding Smart Beta in the Factor Zoo” that two measures of quality (gross profitability and ROE) in international stocks from 1987 through 2013 showed no significant improvement in Sharpe ratio over lower quality stocks. They also found no evidence of a significant advantage using four measures of quality from 1967 through 2013 in U.S. stocks:

Multi Factor Portfolios

West, Kalesnik & Clements (2016) in “How Not to Get Fired in Smart Beta Investing” included quality in a multi-factor environment.

They determined that quality, value, and momentum are a non-robust combination. Why is this important?

More multi-factor ETFs were created in the last two years than any other category of ETF. In a January 2016 survey by Greenwich Associates, 57% of institutional investors said they used multi-factor funds in some way now. 48% said they plan to increase their use soon.

Multi-factor portfolios have less volatility and tracking error compared to single factor portfolios. In “A Smoother Path to Outperformance with Multi-Factor Smart Beta Investing,” Brightman, Kalesnik, Li & Shim (2017) show that annual volatility drops from 16.4% for an average factor to 15.2-15.6% for a multi-factor portfolio. This reduction is desirable. But those familiar with portfolio theory know that factor portfolio returns are a weighted average of individual factor returns. If factor returns are disappointing due to lack of scalability (value and momentum), data accuracy and persistence (size), or robustness (quality), multi-factor returns may also be disappointing.

On the positive side, a multi-factor approach can cut benchmark tracking error in half. But would it really matter if 10 years of factor-based underperformance were reduced to 5 years? Small cap value once underperformed the market for 42 consecutive months. If that had been 21 months, would it have made much difference? Most investors would have been gone long by then.

Low Volatility

In a Brown Brothers Harriman survey of 175 financial advisors and institutional investors, low volatility was the most popular smart-beta choice. 44% of respondents chose low volatility over other factors. One of the first anomalies that troubled academics was that lower beta or volatility portfolios performed better than should relative to higher beta or volatility portfolios. A case can be made that leverage constraints cause high volatility stocks to be bid up so they are overpriced relative to low-volatility stocks.

However, low volatility is a problematic factor. The first cautionary sign is a chart of pre-1967 performance in the appendix of Novy-Marx’s (2016) paper “Understanding Defensive Equity.” Volatility and beta are estimated using daily data from the prior year when available. Otherwise, Novy-Marx uses 5 years of monthly data.
There is little difference between the lowest and highest volatility quintiles. With respect to beta, low beta is the worst performer, while high beta turns in the second-best performance.

Novy-Marx also pointed out that the vast majority of low volatility profits since 1968 came from the short side. He showed that most of the benefits from low volatility investing could be achieved simply by eliminating small growth stocks from one’s portfolio.

In “The Limits to Arbitrage and the Low-Volatility Anomaly,” Li, Sullivan & Garcia-Feijoo (2014) found that the excess return associated with low volatility was present only in the first month after portfolio formation. Additionally, excess return has been weak since 1990. They also found that the low volatility premium was offset by high transaction costs. It was largely eliminated if you omitted stocks priced under $5 per share.

Garcia-Feijoo, Kochard, Sullivan & Wang (2015) in “Low-Volatility Cycles: The Influence of Valuation and Momentum on Low-Volatility Portfolios,” showed that the excess return from low-volatility is reliably positive only when low-volatility stocks are much cheaper than high volatility stocks as shown by a high book-to-price (B/P) ratio.

Using U.S. stock data from 1929 through 2010, van Vliet (2012) found low-volatility has had time-varying exposure to the value factor. When low-volatility stocks had value exposure, they returned an average of 9.5% annually versus the market’s 7.5%. But when low-volatility stocks had growth exposure, they returned 10.8% annually versus the market’s 12.2%.

Getting back to the idea of short interest, Jordan & Riley (2016) show in “The Long and Short of the Vol Anomaly,” that short interest dominates the low-volatility effect from July 1991 through December 2012.

High volatility stocks with low short interest had extraordinarily positive returns. High volatility stocks with high short interest had extraordinarily poor returns. Low volatility stocks had a similar, but less dramatic, disparity in performance based on short interest. Short interest has had a large impact on low-volatility performance.

Summarized below are the issues associated with the low-volatility premium:

•    Weak since 1990
•    Absent in higher priced stocks
•    Exists mostly on the short side
•    Largely offset by transaction costs
•    Reliably positive only when cheap
•    Not present in equal weight portfolios
•    Present only in the first month after formation

Less Downside Risk

With all these negatives, one might wonder why low-volatility has been the fastest growing factor. This may have to do with investors thinking low-volatility has lower risk exposure than the market.

It is not surprising that investors are more risk-averse now. They have experienced two bear markets over the past 20 years where stocks lost half their value.

How much risk reduction is there really from low-volatility investing? To find out, I accessed the online data provided by van Vliet & De Koning. They used the 1000 largest NYSE, AMEX, and NASDAQ stocks over $1 per share in the CRSP database. Stocks were equal weighted and sorted into deciles based on their volatility over the past 36 months. These portfolios were rebalanced quarterly.

I accessed the data starting in January 1934 to avoid the extreme returns of the late 1920s and early 1930s. I used the top two low-volatility deciles, representing 200 stocks, which is a typical fund-size portfolio. I compared the performance of the low-volatility portfolio to the S&P 500 and to a robust version of trend following absolute momentum that I use in my dual momentum models. Absolute momentum holds the S&P 500 when the model is in stocks and intermediate U.S. Government bonds when the model is out of stocks. Data is from Ibbotson Associates.

Jan 1934 – Dec 2014
S&P 500
Absolute Momentum
Standard Deviation
Sharpe Ratio
Worst Drawdown
Worst U. S. Bear Markets 1934- 2014

S&P 500
Absolute Momentum
Jul 2007 – Feb 2009
Apr 2000 – Sep 2002
Jan 1973 – Sep 1974
Nov 1968 – Jun 1970

Mar 1937 – Mar 1938
Results are hypothetical, 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, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

The low-volatility portfolio outperformed the S&P 500. But absolute momentum was more effective at both reducing drawdown and enhancing return. 

For those who want more evidence on the efficacy of trend following, here are the results from Greyserman and Kaminski’s application of 12-month absolute momentum to stock indices, bonds, commodities, and currencies back to the year 1223. Assets were held long or short depending on the trend of the last 12 months. The sizes of the five largest drawdowns were reduced by an average of one-third.

Source: Greyserman & Kaminski (2014), Trend Following with Managed Futures

The viability of trend-following momentum back to the 13th century is strong evidence that it is not an artifact of data mining.


There are plenty of research papers and articles extolling the virtues of factor based investing. Factors look good in theory and on paper. But whether they provide superior risk-adjusted real world returns is another story [3]. Those promoting factor investing may be taking a page out of the political playbook. If you say something repeatedly, people will start to believe you and ignore contrary evidence. Investors may think they can do better than market by using higher cost factor-based investing. But not everyone can be above average.

[1] For more on the the Russell 2000 index and its issues, see Alpha Architect's "A Better Way to Buy the Russell 2000." Other small cap indices have done better than the Russell 2000, but have still been disappointing versus large cap indices.
[3] When I looked at the 41 factor-based funds with more than 5 years of price history, only three had an alpha that was statistically significant at the 5% confidence level.