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 using size, value, quality, momentum, and low-volatility 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 like “active management” that everyone wanted to have instead of holding passive index funds in the 1970s?

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

Factor-based investors and advisors now think they have an advantage. They base this belief on the results of theoretical asset pricing models, many of which have failed empirically.

Asset pricing models look at long-term long/short returns without taking into account the price impact of trading. Factors that looked good on paper may be lacking in robustness, pervasiveness, persistence, or intuitiveness. So let's look at this 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 substantially 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 and 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.

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

Some researchers say a small cap premium still exists if you combine size with other factors. In other words, size can be important depending on what you 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 then 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. This may be a case of theoretical results differing from actual ones. Or it may be a case of the value premium never existing in the first place. According to Asness et al., the only period where there seemed to be a significant positive 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.

A few months back, I referenced a study by Loughran and Hough that is worth mentioning again. These authors looked at the performance of all U.S. equity funds from 1962 through 2001. They used the prior 36 months to sort funds by style (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%. This large cap outperformance of 0.11% of value over growth was insignificant.

With small caps, the authors were very surprised at the results. 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 and Moskowitz (2012) showed that the value premium is insignificant among the two largest quintiles of stocks and is concentrated among small cap stocks. [2] So, why 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 who want to 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) that began in March 1992 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 with respect to the market. But none of the alphas are statistically significant.[3] To the extent that the DFA funds have done reasonably well may not be due only 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. This 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 very large number of securities 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, as well. Additionally, DFA has avoided IPOs and stocks with high borrowing costs, and they use a momentum to filter their trades. 

Stocks with high borrowing costs usually 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.

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 are known for tracking error that can persist for 10 or more years. Value trap induced 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. That can make them less liquid and more expensive to trade.

In “A Taxonomy of Anomalies Costs and their Trading Costs” Novy-Marx and 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 and 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 now 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 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. It is with investability that momentum falls short.[4]

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 in a modest number of volatile stocks is bound to 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 and Zhou (2002) in their “The Illusive Nature of Momentum Profits.” They found that momentum creates an illusion of profit opportunity when none really exists. Two years later, Korajcyzk and Sadka (2004) determined that profit opportunities could vanish once the amount invested in momentum-based strategies reaches $5 billion.

Counter to these findings, Frazinni, Israel and Moskowitz (2012) from AQR, based on 16 years of proprietary data, argued that the potential scale of momentum 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.

More recently, Ratcliffe, Miranda and Ang (2016) from BlackRock also suggested that a greater amount of capital could be traded using momentum. But they also made this disclaimer, “The exercise we conduct in this paper is hypothetical and involves several unrealistic assumptions.”

In contrast to these two studies, Fisher, Shah and 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 and Velikov (2015) also determined the capacity for stock momentum before profits would vanish.

This is close to the $5 billion amount where Korajcyzk and Sadka said momentum profits would disappear. Novy-Marx and 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:

This is a conservative listing. It does not include mutual funds, managed accounts, or hedge funds. Even so, it exceeds the level of assets where both Novy-Marx and Velikov and Korajcyzk and 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 and Kostka (2016) in “Will Your Factor Deliver? An Examination of Factor Robustness and Implementation Costs.” They used a different method than Novy-Marx and 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. Expected high future growth in factor-based investing should make this worse.

This situation is much like the one I discussed in my last post. Those offering commodity products to the public said passive commodities are still a worthwhile diversification. But a larger number of independent researchers, with no products to promote, said the opposite. Who should we believe?

To help us answr that question, let us 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 had 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%. These are short periods of time to evaluate performance. But it does suggest some caution.

Besides managing seven momentum mutual funds, AQR uses momentum with their multi-style funds and large hedge fund. Even though the Frazinni et al. paper said stock momentum could handle considerably more capital, AQR now spreads their large-cap U.S. momentum holdings among 496 stocks. This is half that fund’s available universe of 1000 stocks.

Eight and ten years is not a long time to draw meaningful conclusions from fund data. But these results are consistent with research by Battacharya, Li & Sonaer (2016) who find that momentum profits from U.S. stocks have been insignificant since the late 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. 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 and 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 and 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 reduced tracking error compared to single factor portfolios. In “A Smoother Path to Outperformance with Multi-Factor Smart Beta Investing,” Brightman, Kalesnik, Li and 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 will also be disappointing. In addition, multi-factor portfolios can face greater uncertainty due to selection bias and increased data mining.

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 before 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. There is no risk-based reason why low-volatility/low beta stocks should outperform their counterparts. But a case can be made that leverage constraints can cause high volatility stocks to be bid up so they are overpriced relative to low-volatility stocks.

However, low volatility is the most 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. These results contradict those found by Novy-Marx and others since 1968.

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 and 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. It also was not present in equal weight portfolios.

Garcia-Feijoo, Kochard, Sullivan and 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 and 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 here 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 less 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 and 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 proprietary 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. Trend following absolute momentum was much more effective than buy-and-hold. The sizes of the five largest drawdowns were also reduced by an average of one-third.

Source: Greyserman and 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 research papers and articles almost every day extolling the virtues of factor investing based on studies of historical stock data. Factors may look good in theory and on paper. But whether they can provide superior risk-adjusted real world returns after costs is another story. Too many people may be thinking they can do better than market by using higher cost factor-based investing. Not everyone can be above average. There is a good chance many of these strategies will underperform, especially as the amount of capital invested in them continues to growth.

Even  now, each factor that I looked at failed to hold up under one or more of these tests: robustness, persistence, pervasiveness, intuitiveness, and investabilty. Those who are prudent and truly interested in evidence-based investing will be cautious. Others will continue to accept what they have been told by product sponsors and a small number of academic theorists.

[1] For more on the the Russell 2000 index and its issues, see Alpha Architect's "A Better Way to Buy the Russell 2000".
[2] Results were similar using valuation measures other than book-to-price. Kok, Ribando, and Sloan (2017) also found "remarkably consistent results" using different valuation ratios and weightings.
[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.
[4] This applies to stock momentum. Research shows that momentum works best when applied to geographically diversified stock indices. See "Momentum for Buy-and-Hold Investors".