November 26, 2017

Factor Investing: Implementation 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.

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 too 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.

Fund sponsors who jumped on the factor bandwagon were not happy to see these results. Like 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 proprietary data ending in 2013. They showed scalable results over this period. But the number of funds using momentum has increased substantially since then.

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.

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 prior 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.

The main drawback of all these studies, whether academic or industry based, is that they depend on assumptions about future transaction costs and market liquidity. Assessing implementation costs using parametric transaction cost models may be incomplete or misguided. No one can say with any degree of certainty what the future will bring. Ratcliffe et al. acknowledge this when they say, “The exercise we conduct in this paper is hypothetical and involves several unrealistic assumptions.”

Real World Results

It is not uncommon for academic finance theories to not hold up in the real world. The capital asset pricing model (CAPM) is a good example of that. In past blog posts here, here, and here, we highlight some factor research using actual fund results. One study we cite by Loughran & Hough (2006) compares the past performance of value versus growth funds. After examining mutual fund performance from 1965 to 2001, they concluded that superior long-run performance from value is an “illusion.”

A second study is by Arnott, Kalesnik & Wu (2017). They 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 whatever.

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.” Their work reviews prior studies of real world factor capacity and corrects some shortcomings of the Arnott et al. study.

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 approach differs from the Arnott et al. one by focusing more explicitly on implementation costs. They make improvements in the way Fama-Macbeth regression is used. 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 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.

Their Fama-Macbeth approach shows that implementation costs erode almost all the return to value and momentum strategies of mutual funds.  But there is little impact on market and size strategies. Matched pairs analysis shows comparable performance attrition for value and momentum strategies. But 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 examine. None of the factor strategies earn returns after real-world costs during the 1970 to 2016 period.

In future research, the authors say they will apply these same tools to other residents of the factor zoo (such as low volatility and quality) and see how they survive in the wild.


I wrote my first momentum paper in 2011. It was called “Optimal Momentum: A Global Cross Asset Approach.” [1] I looked at momentum applied to stocks, industries, investment styles, and geographic equity markets. I found that momentum worked best when used with geographically diversified stock indices.

In 2015, Geczy & Samonov (2015) applied momentum to U.S. stocks, global sectors, country equity indices, government bonds, currencies, and commodities. Looking at the past 215 years of data, they came to the same conclusion as I did. Momentum works best when applied to geographically diversified stock indices.

Neither my study nor Geczy & Samonov’s study took into account implementation costs, which would have made our equity index results even stronger compared to stocks. Implementation costs are substantially lower when momentum is applied to stock indices rather than to individual stocks.
Yet almost every momentum fund applies momentum to individual stocks rather than to country or regional stock indices.

Studies such as those by Arnott et al. and Patton & Weller may eventually get fund sponsors to pay attention to the implementation cost evidence with stock-based factor investing. But I would not count on it anytime soon. The growth of factor- based investing has been explosive and is expected to continue that way.

Continued growth in factor-based investing could very well aggravate the scalability problem associated with high implementation costs. Ignoring implementation costs, there is still widespread belief that factors can enhance return or decrease risk. Financial advisors and fund sponsors still promote research based on theoretical rather than actual factor returns.

The same behavioral biases that make momentum effective may prevent financial professionals and investors from recognizing important information regarding implementation costs. These biases include anchoring, slow diffusion of information, and herding. This situation may not change until years later when investors compare the actual performance of factor-based funds to their appropriate benchmarks.

[1]  Second place winner of the 2011 Wagner Award for Advances in Active Investment Management given annually by the National Association of Active Investment Managers (NAAIM).

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. Everyone should benefit from reading this book.

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 some 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.

John von Neumann said that with four parameters he can fit an elephant, and with five he can make it wiggle its trunk.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 much 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 duing 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 very well be the strongest factor. Yet it is also the most ignored factor. This is good news for those of us using it.

There are serious questions about the real-time efficacy of factor-based investing, especially in the future as it continues to grow in popularity. This may be at least partially due to the over exploitation and capacity constraints of some factors, as explained here and here. Based on its general non-acceptance, trend followers should have nothing there to worry about.

[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 or 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 serious 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. Very little 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 rather than theoretical results of a popular investment factor. But now there is another study. 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 covariances 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. Value is suspect now on both a theoretical and actual basis.

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 the late 1990s.

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 may be 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 one 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 constant over time. Growth funds do not often 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 like 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 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. This 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 bias there is in the AKW regression because fo this. Instead, Corey conducts a 1000 hypothetical fund simulation using normally distributed betas.

There are good reasons why simulations are rarely used in financial markets research. Simulations are dependent on distributional assumptions that are often unrealistic with financial markets. Market returns are not independent, and their underlying distributions may be non-stationary.

In his simulation, Corey assumes that returns are normally distributed, which is not the case for mutual fund returns. Nor does Corey show that estimation errors have the same distribution scale as the betas themselves. If  one is going to use simulated data, it would be better to use simulations with other distributions.

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 be enough to minimize 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 differences in standard deviation between full period and 3 year rolling estimates of VWELX’s beta coefficients.

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

AKW acknowledges this downward bias in betas due to estimation error in the independent variables. They conduct six different robustness tests that reinforce their results and may help mitigate that error. Their robustness test results are consistent with AKW’s core findings.

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 see that with many advisors and fund managers, as well as throughout the blogsphere. 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 the same thing by focusing on underexploited investment opportunities. In the 1970s that meant stock options. In the 1980s I had success with managed futures.

Also in the 1980s I had a family member who bet on football games. He knew I invested using data-driven quantitative methods, so he asked me to take a look at betting NFL home underdogs. I was 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 the inefficiencies in this market. There were no computer-based sports databases back then and almost no published sports research. So I hired some UC Berkeley students to go through the data and help me test logical betting strategies.

After we had a stable of successful angles, I put one of these students on a bus to Reno each weekend. Encouraged by our early results, I expanded this research to include all sports, both pro and college.

I focused on areas where the linemakers were not paying enough attention, such as game time weather conditions, team mean reversion, and bettor over confidence.

We even came up with a player stat-based Monte Carlo simulator that predicted the outcome of every baseball game. It gave us a good edge early in the season before others figured out the impact of the off-season player trades.

One of my research assistants continued to analyze sports after graduation. He became Vice President of Basketball Operations for an NBA championship team. He is now 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 with stock market investing, mean reversion and public myopia are rampant 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. One let us bet early so he could use that information to move his lines. Another became a friend and would bring us other bookmakers’ lines as soon as they were available. This way he would know all our plays and could bet right along with us.

Afternoons we would hang large marking boards on the walls of our investment office and write down the betting lines from all our outs. We often found exploitable disparities in the lines. Fortunately, we had very few office visitors back then!

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 wagering was causing me to neglect my family. So I eventually set it aside. (I may take it back up again now that I no longer have family responsibilities.)

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

Always Have an Edge

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

Most of those who invest actively have little or no edge. You cannot have an advantage doing what everyone is doing. You would be better off investing in low-cost passive index funds. As I indicated in my last blog post, factor-based investing may soon pose the same problem. My need for a positive expectation led me instead to the little exploited niche of dual momentum investing.

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 your homework gives you confidence. It helps you stay with your approach despite short-term fluctuations in the value of your investments.

For investors, this can mean not doing what everyone else is doing. Herding is a powerful behavioral instinct, but it can lead to mediocre or worse investment returns.  You need to 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 in light of scalability and liquidity issues. And you need to consider how they will perform in the future as they attract more capital. [1]

Keep Things Simple

Selection bias, over optimization, and model overfitting are serious problems in both sports and non-sports research. If you keep tweaking a strategy, it isn’t difficult to find betting angles that look like they have over 60% winners. But these almost never hold up in real time. What we wanted to see was a logical basis for the wager, consistent back test results, and real-time validation going forward.

Sports research taught me the importance of having a simple strategy with intuitive logic behind it. You also need plenty of backtest data across different markets. This is what led me to momentum investing. It is simple, logical, and supported by over 200 years of backtest validation across nearly all markets.

Have Realistic Expectations

If you win a proftable percentage of your sports bets, you are still going to have some serious losing streaks. You just 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 still 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 for most people. 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 did not do much better than a coin flip. But over 5 or more years, those results change considerably. Patience is important whether you are a traditional investor or a speculator on sporting events. Warren Buffett had the right idea 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 for investing. I have seen many investors disregard or override their strategies when these conflicted with their hopes or cherished beliefs. Some close their accounts or decline to open new accounts because of their behavioral biases or fears. To be a 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 with a simple approach, have done your homework, and have realistic expectations.

[1] For more on this, see my blog post "Factor Zoo or Unicorn Ranch" and Research Affiliates' "The Incredible Shrinking Factor Return".