Is there reason to believe cross-sectional patterns in returns will persist, even after they’re known? Larry Swedroe reviews a study that explores this question using more than 100 years of factor data from around the world.

Factor-based investing seeks to capture the long-term premiums highlighted by academic researchers. Factors are the security-related traits/characteristics that give rise to common patterns of return across broad sets of securities.

To identify factors, researchers typically construct long/short portfolios that are long the preferred exposure and short the unwanted exposure. Most mutual funds employing factor-based strategies are long only. Funds that are long/short typically are referred to as style premium funds (i.e., AQR’s Style Premia Alternative Fund (QSPRX)). They offer a “pure play” on the premium by eliminating (or by minimizing) exposure to market beta that comes with long-only strategies. Thus, they provide additional diversification benefits. (Full disclosure: My firm, Buckingham Strategic Wealth, recommends AQR funds in constructing client portfolios.)

Unfortunately, the financial media and some practitioners refer to factor-based investing as “smart-beta” investing. When asked about the term “smart beta,” Nobel Prize-winner William Sharpe’s response was that it made him sick. While much, if not the vast majority, of what Wall Street will call smart beta makes me sick as well, one can make the mistake of throwing out the proverbial baby with the bathwater. That’s what I believe Bill Sharpe and many others may be doing.

I’ve explained before why I think most of what is called smart beta is really nothing more than a marketing gimmick — the result of loading on factors (such as size, value, momentum and profitability/quality) other than market beta. Most smart beta products are not delivering alpha (which is what is often implied by the term “smart”), just beta on other factors.

However, as I’ve also pointed out, pure indexing strategies possess certain weaknesses that can be minimized, if not eliminated. Creating fund construction and implementation rules that do so could be described as smart beta.

Long-Term View On Factors

Elroy Dimson, Paul Marsh and Mike Staunton contribute to the literature with their study, “Factor-Based Investing: The Long-Term Evidence,” which was published in a special 2017 issue of The Journal of Portfolio Management. Their objective was to look back in time across more than 100 years of data and 23 countries to determine if there are reasons to believe cross-sectional patterns in returns will persist, or whether they are just anomalies that tend to disappear after publication.

The authors’ study examined the size, value, income (or yield), momentum and volatility factors. They noted that these are far from new phenomena; Dimson described all of them three decades ago in his 1988 book, “Stock Market Anomalies.” In other words, we now have decades of out-of-sample evidence, not only in the U.S., but also from many other countries.

Dimson, Marsh and Staunton begin by noting: “The returns to factor exposures vary across risk factors, they can be quite divergent, they differ between countries, and they fluctuate over time. These factors matter a great deal because small companies will continue to perform differently from large stocks — even if they fail on average to outperform — and similarly, value stocks, high yielders, and past winners will continue to show different performance characteristics from growth stocks, low yielders, and past losers, regardless of whether they generate a premium.”

I’ll review their findings, as well as add a few of my own thoughts and observations through other data.

Size Factor

Viewed in an international context, smaller companies perform very differently (that is, the size effect is a unique/independent factor) from larger companies, and have provided, the authors found, an annual premium of 3.8%. We can also see the size effect in terms of absolute returns to long-only portfolios.

From 1926 through 2016, a dollar invested in larger U.S. companies grew in value to $4,690, while a similar investment in U.S. small-cap stocks gave a terminal value of $33,879, more than seven times greater. U.S. micro-cap stocks did best of all, with an ending value of $53,263. The returns on U.S. large-cap stocks were an annualized 9.7%, while small-cap and micro-cap stocks achieved 12.1% and 12.7%, respectively.

Dimson, Marsh and Staunton noted the size premium has been larger since the turn of the century, a period of relatively poor performance for equities. From 2000 through 2016, the size premium was positive in every country except Norway, and averaged 5.6% per year.

Unfortunately, I would add, many investors may have missed out on earning the premium because it had performed poorly over the prior 16 years, with the world size premium being an average annual loss of approximately 2.7% per year from 1984 through 1999 as calculated by Dimensional Fund Advisors, a period that followed shortly on the heels of the publication of the first research by Rolf Banz documenting the size effect. Many may have concluded that the size premium had disappeared.

Dimson, Marsh and Staunton concluded: “There is no doubt that portfolios tilted toward or away from the market’s average size exposure are taking on significant risk relative to the market as a whole. Prudent long-horizon investors should plan on no more than a normal reward for the risk, illiquidity, and management costs associated with running a portfolio of low-capitalization stocks.”

Value Factor

Dimson, Marsh and Staunton found the value premium was positive in 20 countries, negative in three and on a worldwide basis, 2.1% per year. In terms of absolute returns to long-only investors, the authors present out-of-sample results from the U.K. A £1 investment in the growth index in 1955 would have grown in nominal terms to £419 by the end of 2016, an annualized return of 10.3%. The same initial investment allocated to the value index would have generated £9,173, more than 21 times as much, and equivalent to an annualized return of 16.0%.

As with the size premium, the value premium was earned erratically, with large year-to-year variations. In particular, it performed poorly in the 1990s, when it was negative.

I would note that the global value premium, as calculated by Dimensional, was an average annual loss of approximately 3.1% per year in that decade. Similar to what occurred with the size premium, this period shortly followed the publication of research identifying a value premium — Murphy’s Law at work.

Since 2000, Dimson, Marsh and Staunton found that positive value premiums have existed in all but four countries, and the annualized value premium on the world index was 2.5%. Of course, as I’ve often discussed, only those investors, like Warren Buffett, who had the discipline to stay the course, earned that premium.

The authors also noted there is substantial global evidence that the value premium is larger among small companies than it is among big companies. In the U.S., from 1926 through 2016, big growth stocks generated an annualized return of 9.6%, small growth stocks returned 8.7% per year, big value stocks returned 12.2% per year, and small value stocks returned 15.1% per year.

Income Factor

Research has documented a return premium from stocks with an above-average dividend yield. As Dimson, Marsh and Staunton note, the income factor is a manifestation of the value factor, as stocks with high dividend yields tend to be value stocks (meaning they sell for a low multiple of fundamental factors such as earnings, sales, dividends and cash flow). The authors found high-yielding stocks outperformed low-yielders in every country except New Zealand and Ireland.

Across all 21 countries they examined in this case, the average premium was 3.9% per year.

In terms of absolute returns to a long-only strategy, the authors offer this out-of-sample evidence: An investment of £1 in the low-yield strategy at the start of 1900 would have grown to £6,810 by the end of 2016, an annualized return of 7.8%. The same initial investment allocated to high-yield stocks would have generated £158,727 (or 23 times greater), equivalent to a return of 10.8% per year.

The yield premium over the first 17 years of the 21st century was positive in 19 of the 21 countries Dimson, Marsh and Staunton analyzed and averaged 6.2%, far above the level of the longer-term period. They also found that higher-yield strategies were less volatile than lower-yield and zero-yield portfolios, had somewhat lower betas (0.89 versus 1.0), and earned a higher Sharpe ratio (almost twice that of the low-yielding strategy).

They concluded: “It is thus hard to explain the superior performance of higher yielders in terms of risk, when, on conventional measures, they have lower volatility and betas.”


Dimson, Marsh and Staunton note that, in theory, any premium related to relative strength strategies should be arbitrated away, as there is not a risk-based explanation for it. In addition, they note that published research on the momentum premium dates back at least to the 1960s. Yet they found the premium is persistent, pervasive, robust to different definitions and survives transaction costs.

They also observe that, as with the other premiums, the returns from momentum strategies are volatile, with the occasional very bad year in which markets sharply reverse direction. Dimson, Marsh and Staunton found the momentum premium was positive and quite large for all countries except China, Japan, Portugal and Sweden, and averaged 8.5% per year over the 22 countries they studied.

They also found that, after 2000, momentum investing was profitable in 21 of the 23 markets (Japan and the U.S. being the two exceptions). I think this highlights the importance of having a globally diversified momentum strategy, as is the case for all factors.

In terms of absolute returns, following a 6/1/6* momentum strategy, an investment in U.S. loser stocks would have appreciated from $1 in 1926 to $3,634 by the end of 2016, while an equal initial investment in winner stocks would have appreciated to $2.1 million — an annualized return of 17.5%. At the end of the period, the winner portfolio would have been worth 586 times as much as the loser portfolio, which earned the equivalent of 7.4% per year.

Similarly, in an out-of-sample test from a universe of the top 100 U.K. stocks at the start of each year from 1900 to 2016, winners outperformed losers by 10.2% per year.

Volatility Factor

It has long been known the return from low-beta securities was higher than the classic Capital Asset Pricing Model (CAPM) implied, and that the return from high-beta securities was lower than the CAPM predicted. The low-beta anomaly has been persistent and pervasive around the globe, with the highest-beta stocks underperforming dramatically. The results hold up over a wide range of markets.

However, Dimson, Marsh and Staunton note that volatile stocks tend to have relatively low market capitalizations, creating an implementation challenge in that a long/short strategy aiming to take advantage of the underperformance of risky stocks would be shorting the highest-risk companies. For the U.S. and the U.K., low-risk companies represent an average 40% and 54% of the equity market’s value, respectively, whereas high-risk companies represent an average of just 8% of the market in both countries. The cost of transacting small-cap and micro-cap securities is large.

In my view, investors can take advantage of this information simply by screening out high-risk stocks, rather than shorting them.

Other Factors

In a brief discussion of other factors, Dimson, Marsh and Staunton note that publication can lead to popularity, with the ensuing cash flows causing the valuations of the long and the short sides of factors to converge — reducing or even eliminating a premium as trades become crowded. This is true whether a factor has a risk-based or behavioral-based explanation.

Specifically, they write: “The hunger for income may have elevated the prices of some stocks to an unsustainable level. That would be because many asset owners, not limited to factor investors, want to enhance the income they feel they can draw down from their portfolios.”

In their concluding remarks, Dimson, Marsh and Staunton note the factors they analyzed do perform differently, thus affecting portfolio performance.

They further write: “In addition to co-movement, there may also be a premium in expected returns for exposure to these factors. While cogent rationales can be advanced for small-cap and value premiums, the fact is that both effects fluctuate and the small-firm premium has been negative for protracted periods.” They add: “Just like predictions of the equity risk premium, it can be dangerous to extrapolate past performance into the future.”


Unfortunately, when it comes to investing, all crystal balls are cloudy. Thus, the best investors can do is to make judgments based on the historical evidence and logic. As Dimson, Marsh and Staunton note, we must recognize that all factors have experienced, and almost certainly will continue to experience, long periods of underperformance.

This fact isn’t a reason to avoid factors and miss out on their diversification benefits and expected premiums. However, it does mean investors must be prepared to endure those long periods and stay disciplined, which I have learned requires a strong belief system. If you are not convinced you have that strong belief system, a necessary condition for having the discipline and patience you will need to maintain your exposure to a factor through those inevitable bad times, you should not invest in that factor, and that includes market beta.

As Dimson, Marsh and Staunton mention in their study, in our book, “Your Complete Guide to Factor-Based Investing,” my co-author Andrew Berkin and I established criteria investors should use before considering an investment in a factor. For a factor to be considered, it must meet all of the following tests. To start, it must provide explanatory power to portfolio returns and have delivered a premium (higher returns). Additionally, the factor must be:

  • Persistent: It holds across long periods of time and different economic regimes
  • Pervasive: It holds across countries, regions, sectors and even asset classes
  • Robust: It holds for various definitions (e.g., there is a value premium whether it is measured by price-to-book, earnings, cash flow or sales)
  • Investable: It holds up not just on paper, but also after considering actual implementation issues, such as trading costs
  • Intuitive: There are logical risk-based or behavioral-based explanations for its premium and why it should continue to exist.

John Cochrane famously noted that, today, with more than 600 factors identified in the literature, we now have a “zoo” of factors covering many different categories. Some are related to macroeconomic variables; others are related to asset characteristics. Some factors have risk-related explanations, others are attributed to behavioral considerations, and many have arguments for both.

The good news is that from among all these factors from which to choose, the evidence led Andy and I to conclude there are just eight that meet our criteria. We present the evidence to support our conclusions, citing more than 100 academic papers, and to enable you to draw your own. The eight factors that meet all of our criteria are market beta, size, value, momentum, profitability and quality, term and carry.

What about all those other factors? Some have not passed the test of time, fading away after their discovery, perhaps because of data mining or random outcomes. Or, perhaps a factor worked only for a special period, regime or narrow band of securities. Finally, many factors have explanatory power already well captured by the factors we recommend. (In other words, they are variations on a common theme, such as the many definitions of value).


* A 6/1/6 strategy ranks stocks by their returns over six months, waits for one month, and then buys the winners and shorts the losers over the next six months; the strategy is then repeated.

This commentary originally appeared June 25 on

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