Fact, Fiction, and the Size Effect

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
User avatar
Robert T
Posts: 2524
Joined: Tue Feb 27, 2007 9:40 pm
Location: 1, 0.2, 0.4, 0.5
Contact:

Fact, Fiction, and the Size Effect

Post by Robert T » Tue May 22, 2018 6:56 pm

.
Interesting read from AQR - https://papers.ssrn.com/sol3/papers.cfm ... id=3177539
The facts we present include: that the size effect diminished shortly after its discovery and publication; that it is dominated by a January seasonal effect; that it is not applicable or does not work for other asset classes outside of individual equities; that it can be made much stronger when looked at in conjunction with other factors (namely, quality or defensive factors); that the size premium mostly comes from microcap stocks and is difficult to implement in practice; and, finally, that the size effect continues to receive a disproportionate amount of attention relative to other factors with similar or stronger evidence behind them. The fictions we attempt to clarify include: that the size effect is one of the strongest anomalies; that other factors performing better among small stocks is evidence of a size effect; that the size effect is robust to how you measure it; that it works in other markets and settings; and that it seems to be more than just an illiquidity premium.

User avatar
nisiprius
Advisory Board
Posts: 36637
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Tue May 22, 2018 9:02 pm

Another interesting read from AQR, from 2015: The Small-Firm Effect is Real, and it's Spectacular, and the 2015 paper it references, Size Matters, if you Control Your Junk by five authors including two of the authors of the 2018 paper.

(As a general skeptic I like the 2018 paper better. That's just my confirmation bias, of course.)

I've boldfaced some sentences below:

Asness, Frazzini, Israel, Moskowitz, and Pedersen, 2015:
The size premium has been challenged along many fronts: it has a weak historical record, varies significantly over time, in particular weakening after its discovery in the early 1980s, is concentrated among microcap stocks, predominantly resides in January, is not present for measures of size that do not rely on market prices, is weak internationally, and is subsumed by proxies for illiquidity. We find, however, that these challenges are dismantled when controlling for the quality, or the inverse “junk”, of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk also explains interactions between size and other return characteristics such as value and momentum.
Alquist, Israel, and Moskowitz, 2018:
Fiction: Many anomalies being stronger among small stocks is evidence of a size effect.

The first part of this statement is true, but the latter part is false. The size effect – that small stocks outperform large stocks – is often confused with other factors, such as value, being stronger among small stocks than among large stocks. Many anomalies (though not all) are indeed stronger among small stocks, but this has nothing to do with the “size effect” or more precisely a return premium for size per se. This statement is about other return premia being stronger (at least gross of trading costs) among smaller cap stocks. This could be due to illiquidity, more limited arbitrage, higher volatility, or more retail investors associated with small stocks, all of which may exacerbate any return premium associated with other factors, but none of which necessarily have anything to do with a premium associated with small firms themselves.
The second article says it is "fiction" that "Many anomalies being stronger among small stocks is evidence of a size effect." The first one says the existence of a size factor--a "spectacular" one, according to Asness' essay--is proved by its showing up when combined with quality. It almost sounds as if the second paper is calling the first paper fiction.
Last edited by nisiprius on Tue May 22, 2018 9:21 pm, edited 5 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

golfCaddy
Posts: 701
Joined: Wed Jan 10, 2018 10:02 pm

Re: Fact, Fiction, and the Size Effect

Post by golfCaddy » Tue May 22, 2018 9:09 pm

This is a great find.
As the graph clearly shows, there is a substantial return to the size factor in January, but absolutely no evidence of any size premium outside of January. The returns to size are completely flat throughout most of the year. Whatever premium the size factor has seems to be generated almost exclusively in January.

User avatar
nisiprius
Advisory Board
Posts: 36637
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Tue May 22, 2018 9:16 pm

golfCaddy wrote:
Tue May 22, 2018 9:09 pm
This is a great find.
As the graph clearly shows, there is a substantial return to the size factor in January, but absolutely no evidence of any size premium outside of January. The returns to size are completely flat throughout most of the year. Whatever premium the size factor has seems to be generated almost exclusively in January.
Similarly, Jeremy Siegel had noted long ago that the size effect is completely attributable to the single time period 1975 through 1983. Throw out that time period and the whole small-cap premium disappears.

Image
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
Epsilon Delta
Posts: 7430
Joined: Thu Apr 28, 2011 7:00 pm

Re: Fact, Fiction, and the Size Effect

Post by Epsilon Delta » Tue May 22, 2018 9:25 pm

nisiprius wrote:
Tue May 22, 2018 9:02 pm

Asness, Frazzini, Israel, Moskowitz, and Pedersen, 2015:

Alquist, Israel, and Moskowitz, 2018:

The first one says the existence of a size factor--a "spectacular" one, according to Asness' essay--is proved by its showing up when combined with quality. It almost sounds as if the second paper is calling the first paper fiction.
Any papers by Frazzini and Pedersen? :shock:

User avatar
matjen
Posts: 1938
Joined: Sun Nov 20, 2011 11:30 pm

Re: Fact, Fiction, and the Size Effect

Post by matjen » Tue May 22, 2018 9:29 pm

Thanks for the heads up on this Robert T.
A man is rich in proportion to the number of things he can afford to let alone.

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Tue May 22, 2018 9:57 pm

nisiprius wrote:
Tue May 22, 2018 9:02 pm
Another interesting read from AQR, from 2015: The Small-Firm Effect is Real, and it's Spectacular, and the 2015 paper it references, Size Matters, if you Control Your Junk by five authors including two of the authors of the 2018 paper.

(As a general skeptic I like the 2018 paper better. That's just my confirmation bias, of course.)

I've boldfaced some sentences below:

Asness, Frazzini, Israel, Moskowitz, and Pedersen, 2015:
The size premium has been challenged along many fronts: it has a weak historical record, varies significantly over time, in particular weakening after its discovery in the early 1980s, is concentrated among microcap stocks, predominantly resides in January, is not present for measures of size that do not rely on market prices, is weak internationally, and is subsumed by proxies for illiquidity. We find, however, that these challenges are dismantled when controlling for the quality, or the inverse “junk”, of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk also explains interactions between size and other return characteristics such as value and momentum.
Alquist, Israel, and Moskowitz, 2018:
Fiction: Many anomalies being stronger among small stocks is evidence of a size effect.

The first part of this statement is true, but the latter part is false. The size effect – that small stocks outperform large stocks – is often confused with other factors, such as value, being stronger among small stocks than among large stocks. Many anomalies (though not all) are indeed stronger among small stocks, but this has nothing to do with the “size effect” or more precisely a return premium for size per se. This statement is about other return premia being stronger (at least gross of trading costs) among smaller cap stocks. This could be due to illiquidity, more limited arbitrage, higher volatility, or more retail investors associated with small stocks, all of which may exacerbate any return premium associated with other factors, but none of which necessarily have anything to do with a premium associated with small firms themselves.
The second article says it is "fiction" that "Many anomalies being stronger among small stocks is evidence of a size effect." The first one says the existence of a size factor--a "spectacular" one, according to Asness' essay--is proved by its showing up when combined with quality. It almost sounds as if the second paper is calling the first paper fiction.
That's not contradictory, though.

The first paper uses junk (negative quality) to show more robust results for junk-controlled size. Junk-controlled size is not the same thing as the regular size factor. Regular small cap indexes and most understandings of small cap portfolios would have market and size exposure, but negative quality. The conclusions about size being more robust are only in the context of a multi-factor model that controls for junk. Not the regular size factor that you'd see in the Fama-French 3-factor model.

The second paper makes a different point about different effects, that some anomalies (effect sizes) are larger in small caps. That's not about the size factor directly but potentially interactions between factors, if you want to think of it that way.

In fact, they have this to say about the size factor in the second paper, which basically repeats the kinds of points and supports what the first paper was about:
The interaction between size and quality/junk is far stronger than size’s interaction with other factors (beta, value, momentum) and accounting for it produces a more significant size premium. Regardless of the quality metric used, metrics that vary substantially both qualitatively and in terms of measured correlation, we find a much stronger and more stable size effect when controlling for a firm’s quality. This is why the Fama and French five factor model also helps resurrect size, as the RMW factor based on profitability is one measure of quality.

Firm size is highly confounded with firm quality, which distorts the relation between size and expected returns. Large firms tend to be high quality firms, while small firms tend to be “junky.” Since high quality stocks outperform junk stocks on average, the basic size effect is fighting a
strong quality effect. Going long small stocks and short large stocks, a size-based strategy is long a potential size premium but also short a quality premium, which both understates the actual size effect and introduces additional variation from the quality factor.

In addition to resurrecting the size premium, controlling for quality also reconciles many of the empirical irregularities associated with the size effect that we (and the literature) have documented. For instance, controlling for quality resurrects the size effect after the 1980s and explains its time variation, restores a linear relationship between size and average returns that is no longer concentrated among the tiniest firms, revives the returns to size outside of January and simultaneously diminishes the returns to size in January – making it more uniform across months of the year, and uncovers a larger size effect in almost two dozen international equity markets, where size has been notably weak. These results are robust to using non-market based size measures, making the size premium a much stronger and more reliable effect after controlling for quality (Asness, Frazzini, Israel, Moskowitz, and Pedersen [2017]).
I also like the second paper more. It covers more topics, among other things. It does not, however, call the first one fiction.

jbranx
Posts: 258
Joined: Thu Feb 09, 2017 6:57 pm

Re: Fact, Fiction, and the Size Effect

Post by jbranx » Tue May 22, 2018 10:00 pm

One of the first papers I remember reading challenging the small cap effect was by Bill Fouse, who created the first index fund at Wells Fargo back in 1969 and managed an allocation fund at Mellon Capital for Vanguard at one time. It was titled "The Small Stocks Hoax" and was published in the Financial Analysts Journal, Vol. 45, No. 4 (Jul. - Aug., 1989), pp. 12-15. Here was his concluding paragraph:

"What should one conclude from all
of the above? There is no mysterious
return to smallness. There is no free
lunch. The moral of the story is: Beware
of quasi-academics bearing
anomalies."

User avatar
willthrill81
Posts: 5717
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: Fact, Fiction, and the Size Effect

Post by willthrill81 » Tue May 22, 2018 10:27 pm

nisiprius wrote:
Tue May 22, 2018 9:16 pm
Similarly, Jeremy Siegel had noted long ago that the size effect is completely attributable to the single time period 1975 through 1983. Throw out that time period and the whole small-cap premium disappears.
I verified this in Portfolio Visualizer and was amazed to see that from 1984 until now, the TSM return was 10.61%, and the small-cap return was 10.63%. TSM outperformed in the 1990s, SC outperformed in the 2000s, and they've been neck and neck since 2010. SC has had higher volatility, though, and a lower Sharpe.

That being said, a decade of outperformance by either of these asset classes over the other makes me wonder whether an even split might be an effective means of hedging one's bet. Or perhaps throw in Mel's mid-caps and have a three-way split?
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

heyyou
Posts: 3126
Joined: Tue Feb 20, 2007 4:58 pm

Re: Fact, Fiction, and the Size Effect

Post by heyyou » Tue May 22, 2018 10:45 pm

Thus AQR funds with their deeper insight, will immediately start to outperform all of the other fund companies, since no other fund companies will understand or adapt to this knowledge? So this is a stock picker's market, right? Let me know how that works out, after the next decade. Seems like the market often forgets to track whatever patterns have been discerned by humans and their computers.

User avatar
JoMoney
Posts: 5821
Joined: Tue Jul 23, 2013 5:31 am

Re: Fact, Fiction, and the Size Effect

Post by JoMoney » Tue May 22, 2018 11:09 pm

Image
Link


... or here's a different one with the Wilshire Small, Mid, Large, Total Market. Not what one would expect under the premise of a "size premium" especially given the results of larger Mid-cap stocks.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

User avatar
privatefarmer
Posts: 339
Joined: Mon Sep 08, 2014 2:45 pm

Re: Fact, Fiction, and the Size Effect

Post by privatefarmer » Wed May 23, 2018 2:54 am

all I know is, if you compare small value vs the total market over the last 48 years, according to portfoliovisualizer, small value has killed it. I looked at '72-81, '82-91, '92-'01, '02-'11, and '12-present and small value beat total market in every single case except '12-present they are tied. Overall, there has been ~3% premium in the 46 year period.

I then compared the funds I own, DFSVX (domestic small value) and DISVX (international small value) to the total market/international market over the last 20 years and DFA has won in every single 5-year period that I looked at ('98-'02, '03-07, '08-'12, '13-present), and beat the total market by about 4% over the 20-year period.

It does seem that the small value premium has not been as strong since the early 90s, presumable bc of publication, but it has still definitely been present.

I realize that I am comparing small VALUE to total market and not just small vs large but I figure if you buy the fama French data might as well look at it holistically.

User avatar
nisiprius
Advisory Board
Posts: 36637
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Wed May 23, 2018 5:53 am

lack_ey wrote:
Tue May 22, 2018 9:57 pm
...That's not contradictory, though... The conclusions about size being more robust are only in the context of a multi-factor model that controls for junk. Not the regular size factor that you'd see in the Fama-French 3-factor model.

The second paper makes a different point about different effects, that some anomalies (effect sizes) are larger in small caps. That's not about the size factor directly but potentially interactions between factors, if you want to think of it that way.

In fact, they have this to say about the size factor in the second paper, which basically repeats the kinds of points and supports what the first paper was about:
The interaction between size and quality/junk is far stronger than size’s interaction with other factors (beta, value, momentum) and accounting for it produces a more significant size premium. Regardless of the quality metric used, metrics that vary substantially both qualitatively and in terms of measured correlation, we find a much stronger and more stable size effect when controlling for a firm’s quality. This is why the Fama and French five factor model also helps resurrect size, as the RMW factor based on profitability is one measure of quality.
It still sounds as if they are using a private definition of the "size factor," or two different definitions, and it still sounds to me as if they are saying in one place that the size factor exists ("has been resurrected") because it exists in combination with quality, and in another place that it is incorrect to say there is a size factor if it is only seen in combination with another factor, such as momentum.

To put it another way, in the past when I've made posts that were generally skeptical about the value of small caps, the invariable response was "yes, but have you looked at small-cap value?" (Oddly, the traditional slice-and-dice portfolios (e.g. the Coffeehouse portfolio) generally called for specific allocations to large value, small blend, and small value, even though most of the magic was in the small value style box. I've wondered why.)

So are these papers saying yes, the small-cap premium is dead, and small-cap-with-value is also dead, but small-cap-with-quality is huge? Are the papers very complicated stalking-horses for "small-cap quality?"
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
Rick Ferri
Posts: 8530
Joined: Mon Feb 26, 2007 11:40 am
Location: Georgetown, TX. Twitter: @Rick_Ferri
Contact:

Re: Fact, Fiction, and the Size Effect

Post by Rick Ferri » Wed May 23, 2018 6:23 am

I believe the conclusion we can draw from the evidence is that small size alone has not outperformed on a risk-adjusted basis, and that a higher allocation to small cap over its market cap weight should be done using a multi-factor approach.
The Education of an Index Investor: born in darkness, finds indexing enlightenment, overcomplicates everything, embraces simplicity.

ignition
Posts: 182
Joined: Sun Dec 11, 2016 11:28 am

Re: Fact, Fiction, and the Size Effect

Post by ignition » Wed May 23, 2018 7:51 am

Rick Ferri wrote:
Wed May 23, 2018 6:23 am
I believe the conclusion we can draw from the evidence is that small size alone has not outperformed on a risk-adjusted basis, and that a higher allocation to small cap over its market cap weight should be done using a multi-factor approach.
There might be some diversification benefits to holding both small caps and large caps in equal weights (at least over the last 40 years): http://awealthofcommonsense.com/2015/04 ... p-premium/. Not sure how that will play out in the future though...

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Wed May 23, 2018 10:36 am

Rick Ferri wrote:
Wed May 23, 2018 6:23 am
I believe the conclusion we can draw from the evidence is that small size alone has not outperformed on a risk-adjusted basis, and that a higher allocation to small cap over its market cap weight should be done using a multi-factor approach.
Holding a 100% SC portfolio has not outperformed a 100% LC portfolio on a risk-adjusted basis, though it has on a an absolute basis.

Holding a 50% SC/50% LC portfolio, on the other hand, HAS outperformed a 100% LC portfolio on BOTH a risk-adjusted basis AND an absolute basis.

Manage for the portfolio, not the assets.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Wed May 23, 2018 10:58 am

nisiprius wrote:
Wed May 23, 2018 5:53 am
It still sounds as if they are using a private definition of the "size factor," or two different definitions, and it still sounds to me as if they are saying in one place that the size factor exists ("has been resurrected") because it exists in combination with quality, and in another place that it is incorrect to say there is a size factor if it is only seen in combination with another factor, such as momentum.
I think the 2015 paper makes it clear that "has been resurrected" is in the context of a multi-factor model controlling for junk. The title itself is "Size Matters, If You Control Your Junk." Likewise in the conclusion, "Size matters – and, in a much bigger way than previously thought – but only when controlling for junk." It's a conditional. That carries a different meaning than your phrasing, which states that size exists because of quality.
nisiprius wrote:
Wed May 23, 2018 5:53 am
To put it another way, in the past when I've made posts that were generally skeptical about the value of small caps, the invariable response was "yes, but have you looked at small-cap value?" (Oddly, the traditional slice-and-dice portfolios (e.g. the Coffeehouse portfolio) generally called for specific allocations to large value, small blend, and small value, even though most of the magic was in the small value style box. I've wondered why.)
In my view you have to rate everything along a scale of belief. Size (the usual definition, not in a model controlling for junk) is basically the least robust factor anybody cares about, in terms of delivering excess returns. In practical terms, it does it with nontrivially more risk, not particularly great Sharpe ratios, where in long-only land, small cap stocks may well have worse risk-return than the market. I think many of its defenders go a bit too far.

Nevertheless, the evidence in support is not that bad if you consider daily rather than just monthly data, and also look at different breakpoints. Each size decile has had more or less greater returns than the next. But it also gets worse if you look internationally. In the end, it's nothing robust but I would tend to want to bet with it than against it.

All that is in the context of determining long-term excess returns. As a model for explaining performance, the 3-factor model is fine, and it doesn't matter that much if the average size factor return is not particularly distinguishable statistically from 0 in that context. If two diversified, non-overlapping portfolios of small caps with similar 3-factor exposures have similar returns, that means the factor model is doing fine, even if maybe it's not as ideal as other potential formulations.

Small cap value can be understood just in terms of factor exposures, or treated as its own category (or perhaps also including some interaction term). That's a bit of a different conversation, one involving value, that doesn't in of itself reflect on the size factor.
nisiprius wrote:
Wed May 23, 2018 5:53 am
So are these papers saying yes, the small-cap premium is dead, and small-cap-with-value is also dead, but small-cap-with-quality is huge? Are the papers very complicated stalking-horses for "small-cap quality?"
They're not even saying that the small cap premium or size premium is dead. They're saying it hasn't been and is not robust, and may never have existed. That's not the same thing as saying it doesn't exist. There may be something real there.

Raw results for small cap with value are relatively strong. Where are you getting the impression from this that it's dead? Look at page 26 of the new paper, for example.

If the papers are stalking-horses for small cap quality, they're not doing a fantastic job. They don't show great results for that relative to other factors and factor combinations.

It does call into question investing in small caps for the sake of small caps or the size factor, when you could be investing in something else instead. Given the costs of implementing micro caps, the relatively smaller historical excess return in non-micro cap small stocks, and the known higher risk in small caps, this doesn't look like a strong bet. That said, if theoretically given the option of costlessly and with zero capital investing in the SMB factor as an optional add-on, okay, I'd take a bit of that. In the real world, focus on other things, or use multifactor approaches. Most multifactor small cap funds include quality, so there you go.

User avatar
nisiprius
Advisory Board
Posts: 36637
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Wed May 23, 2018 3:45 pm

Thanks, lack_ey.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
Lauretta
Posts: 796
Joined: Wed Jul 05, 2017 6:27 am

Re: Fact, Fiction, and the Size Effect

Post by Lauretta » Wed May 23, 2018 4:26 pm

If I remember correctly I saw an argument according to which one of the reasons the S&P600 beats the Russell 2000 is that it tend to avoid the junk stocks.
When everyone is thinking the same, no one is thinking at all

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Wed May 23, 2018 4:34 pm

Lauretta wrote:
Wed May 23, 2018 4:26 pm
If I remember correctly I saw an argument according to which one of the reasons the S&P600 beats the Russell 2000 is that it tend to avoid the junk stocks.
Also it suffered less from frontrunning, but yes, the effective quality screen (earnings requirement) does filter out some junk and that should have contributed positively.

golfCaddy
Posts: 701
Joined: Wed Jan 10, 2018 10:02 pm

Re: Fact, Fiction, and the Size Effect

Post by golfCaddy » Wed May 23, 2018 6:15 pm

vineviz wrote:
Wed May 23, 2018 10:36 am
Rick Ferri wrote:
Wed May 23, 2018 6:23 am
I believe the conclusion we can draw from the evidence is that small size alone has not outperformed on a risk-adjusted basis, and that a higher allocation to small cap over its market cap weight should be done using a multi-factor approach.
Holding a 100% SC portfolio has not outperformed a 100% LC portfolio on a risk-adjusted basis, though it has on a an absolute basis.
Excluding the January effect, it didn't even outperform on an absolute basis.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 6:28 am

golfCaddy wrote:
Wed May 23, 2018 6:15 pm

Excluding the January effect, it didn't even outperform on an absolute basis.
Yeah, that's not true.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

User avatar
JoMoney
Posts: 5821
Joined: Tue Jul 23, 2013 5:31 am

Re: Fact, Fiction, and the Size Effect

Post by JoMoney » Thu May 24, 2018 7:16 am

vineviz wrote:
Thu May 24, 2018 6:28 am
golfCaddy wrote:
Wed May 23, 2018 6:15 pm

Excluding the January effect, it didn't even outperform on an absolute basis.
Yeah, that's not true.
It is according to Prof. Siegel's look at the January effect, from "Stocks for the Long Run":
Jeremy Siegel in Stocks for the Long Run wrote:..The 4.36-percentage-point excess return of small stocks in January far exceeds the difference in annual returns between large and small stocks. In other words, from February through December, the average returns on small stocks have fallen short of the returns on large stocks. On the basis of history, the only advantageous time to hold small stocks is the month of January...
Image
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 7:43 am

JoMoney wrote:
Thu May 24, 2018 7:16 am

It is according to Prof. Siegel's look at the January effect, from "Stocks for the Long Run":
For one thing, Siegel was only looking at small cap stocks in general and not small cap value in particular.

I don't have easy access to data covering the same time period that Siegel used, but here's what a $10,000 investment in each of VFINX and VSIVX would look like going back to June 1998 replacing every January return with 0.00%.

Image

Over that period of time, SCV outperformed LC in 50% of the Januaries and underperformed in 50% but the arithmetic mean of January returns for SCV was slightly higher.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

User avatar
nisiprius
Advisory Board
Posts: 36637
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Thu May 24, 2018 8:00 am

vineviz wrote:
Thu May 24, 2018 7:43 am
JoMoney wrote:
Thu May 24, 2018 7:16 am

It is according to Prof. Siegel's look at the January effect, from "Stocks for the Long Run":
For one thing, Siegel was only looking at small cap stocks in general and not small cap value in particular.
Yes, and the topic of this thread is "the size effect." It is specifically about one factor, the "size factor" or the "small firm effect," "discovered" and published about by Banz in 1981. The paper is about (rather complicated) relationships between factors, and trying to disentangle how much of effects seen in combinations (like small-cap value) are actually attributable some predictable economic or financial characteristic of small companies.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 9:05 am

nisiprius wrote:
Thu May 24, 2018 8:00 am
Yes, and the topic of this thread is "the size effect." It is specifically about one factor, the "size factor" or the "small firm effect," "discovered" and published about by Banz in 1981. The paper is about (rather complicated) relationships between factors, and trying to disentangle how much of effects seen in combinations (like small-cap value) are actually attributable some predictable economic or financial characteristic of small companies.
You're right: using the SCV data was my mistake due to confusion. I apologize for muddying the discussion.

That said, the so-called 'January Size Effect' is only an anomaly to the extent that it can be arbitraged away by investors, and the evidence on that is decidedly mixed.

The SMB factor premium is, indeed, concentrated on the months of December, January, and February. The last long-term research I can recall reading suggested that it was only statistically significant and positive for those months. What is interesting is that since the "January Effect" was first documented, it has shrunk but not completely disappeared. Thus, over the past 15 years or so, small stocks outperformed large ones pretty dramatically in December, January, and February but also outperformed marginally during the other 9 months of the year. IMO, this makes the case that it can be dismissed as an anomaly (and unlikely to persist) pretty weak.

The size factor is, it's true, one of the weakest risk factors we observe but the size premium is still positive.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

Random Walker
Posts: 3063
Joined: Fri Feb 23, 2007 8:21 pm

Re: Fact, Fiction, and the Size Effect

Post by Random Walker » Thu May 24, 2018 9:36 am

I think Larry Swedroe’s 5 criteria for a factor provide an excellent framework for evaluating whether to incorporate a source of return into a portfolio. They are persistent, pervasive, robust, investable, intuitive. Perhaps I’m a bit naive, optimistic, or devoid the brains to actually look at data. But compared to many people here, I think I put relatively more weight on intuitive and relatively less on historical persistence. Note I really mean just relatively less, not totally ignore :-).
Somebody got a Nobel prize for showing that a firm’s cost of capital is equal to it's expected return. Intuitively it makes sense to me that a small firm should have to pay a higher interest rate on borrowed money than a large firm: it’s a riskier loan. So I’m a fan of a small cap premium. The reason I bring this up is that all factors will have long periods of underperformance and we can only invest looking forward. When one is looking forward in the midst of a period of underperformance, he really needs that intuitive belief to stick to his plan. The cost of capital story provides me with that intuitive belief.

Dave

marcopolo
Posts: 1115
Joined: Sat Dec 03, 2016 10:22 am

Re: Fact, Fiction, and the Size Effect

Post by marcopolo » Thu May 24, 2018 12:00 pm

Random Walker wrote:
Thu May 24, 2018 9:36 am
I think Larry Swedroe’s 5 criteria for a factor provide an excellent framework for evaluating whether to incorporate a source of return into a portfolio. They are persistent, pervasive, robust, investable, intuitive. Perhaps I’m a bit naive, optimistic, or devoid the brains to actually look at data. But compared to many people here, I think I put relatively more weight on intuitive and relatively less on historical persistence. Note I really mean just relatively less, not totally ignore :-).
Somebody got a Nobel prize for showing that a firm’s cost of capital is equal to it's expected return. Intuitively it makes sense to me that a small firm should have to pay a higher interest rate on borrowed money than a large firm: it’s a riskier loan. So I’m a fan of a small cap premium. The reason I bring this up is that all factors will have long periods of underperformance and we can only invest looking forward. When one is looking forward in the midst of a period of underperformance, he really needs that intuitive belief to stick to his plan. The cost of capital story provides me with that intuitive belief.

Dave
I know past performance of a "source of income" is not very predictive of its future returns. I do wonder if intuition about future performance is any better? I would imagine many mutual funds pick their investments on such intuition, their track record to date has not been very promising. Maybe that will change in the future. Maybe your intuition is better than all those professional that have been trying it for years. I, for one, have no such faith in my own intuition.
Once in a while you get shown the light, in the strangest of places if you look at it right.

Random Walker
Posts: 3063
Joined: Fri Feb 23, 2007 8:21 pm

Re: Fact, Fiction, and the Size Effect

Post by Random Walker » Thu May 24, 2018 12:46 pm

Marcopolo,
Not really talking about intuition in the gut feel / psychic sort of mode. More talking about believing in a rational risk based or behavioral based reason for a premium to exist. In the case of size, I do think that smaller companies should be riskier and I believe I have learned that the cost of capital story supports that.
That being said, I also have greater faith in value than small, and believe in the lottery effect for small growth. So all of my small holdings are small value.

Dave

marcopolo
Posts: 1115
Joined: Sat Dec 03, 2016 10:22 am

Re: Fact, Fiction, and the Size Effect

Post by marcopolo » Thu May 24, 2018 12:56 pm

Random Walker wrote:
Thu May 24, 2018 12:46 pm
Marcopolo,
Not really talking about intuition in the gut feel / psychic sort of mode. More talking about believing in a rational risk based or behavioral based reason for a premium to exist. In the case of size, I do think that smaller companies should be riskier and I believe I have learned that the cost of capital story supports that.
That being said, I also have greater faith in value than small, and believe in the lottery effect for small growth. So all of my small holdings are small value.

Dave
I can certainly understand your rationale, and do sincerely hope your reasoning pays off for you. I would simply point out that many (most?) of the active fund managers that have tried various strategies and failed to deliver also had what they believed to be rational or behavioral reasons to think their particular tilt/strategy/hedge/etc. was going to be the one that was going to deliver a premium. Again, I do hope your tilts end up paying off for you.
Once in a while you get shown the light, in the strangest of places if you look at it right.

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 1:11 pm

The theory of factor models is that equity returns may be accurately modeled as a linear combination of independent factors (that is, as a linear model).

We have clear evidence that size and value are not independent. The cited work shows/claims that size and quality are not independent.

Draw your own conclusions.
Risk is not a guarantor of return.

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Thu May 24, 2018 1:20 pm

Non-exhaustive potential reasons for small caps returning more:
  • Lower liquidity and illiquidity premium
  • Informational uncertainty about prospects
  • Greater sensitivity to financial distress and negative economic activity
  • Higher cost of capital and default risk
You might say that in some of the above, it's not really the size that's the risk factor, but small companies being a proxy for some other actual risk. But that's the case for some other factors as well.

There are also some potential mispricing arguments rather than risk-based explanations. Some of the greater risk can actually just be captured by market beta overall, or of course in the first point by say just looking for liquidity instead. This paper makes the argument that higher cost of capital doesn't make sense because if it were true, small companies would just merge together to get around that. But I think it could make sense with respect to larger companies being more likely to have established brands and business lines, more consistency, and some other advantages that a thrown-together fused mass of small companies wouldn't have.

Some other arguments made in the paper I don't quite buy. Nevertheless, the evidence is what it is, and size hasn't been as consistent as other factors by a decent margin. It's also undeniable that small caps are riskier.

The interesting thing to me is the implication of the quality factor on size. If quality factor returns are at least significantly a result of mispricing, then the conclusion is that small caps are riskier and do return significantly more as some might expect, except that the mispricing of junk has in practice reduced the impact and effectively masked the result. It's counting on a behavioral effect or mispricing to show and enlarge the risk story of the size effect.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 1:22 pm

jalbert wrote:
Thu May 24, 2018 1:11 pm
The theory of factor models is that equity returns may be accurately modeled as a linear combination of independent factors (that is, as a linear model).

We have clear evidence that size and value are not independent. The cited work shows/claims that size and quality are not independent.
Size and value may appear related in a colloquial sense but in an econometric sense the factors you mentioned (size, value, quality) can be isolated and quantified independently. I spent many hours doing it in grad school.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 1:28 pm

Quantified independently is different from being uncorrelated, independent variables, which is what the “independent” means when independent variables are defined for statistical linear models. That the magnitude of effect of the value factor is dependent on size would be an example of a violation of independence between the variables.
Risk is not a guarantor of return.

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Thu May 24, 2018 1:37 pm

jalbert wrote:
Thu May 24, 2018 1:28 pm
Quantified independently is different from being uncorrelated, independent variables, which is what the “independent” means when independent variables are defined for statistical linear models.
Linear models don't require independence of the explanatory variables with each other.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 1:59 pm

jalbert wrote:
Thu May 24, 2018 1:28 pm
That the magnitude of effect of the value factor is dependent on size would be an example of a violation of independence between the variables.
Although any given asset may load on both size and value factors, the factors themselves are independent.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 2:02 pm

Certaibly you can do a regression with explanatory variables that are not independent, and the result is weaker statistically.

The factor models attempted to explain equity returns with independent factors. This is embodied in statements like value stocks have a higher expected return than growth stocks, small stocks have a higher return than large stocks etc.
Risk is not a guarantor of return.

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 2:09 pm

vineviz wrote:
Thu May 24, 2018 1:59 pm
jalbert wrote:
Thu May 24, 2018 1:28 pm
That the magnitude of effect of the value factor is dependent on size would be an example of a violation of independence between the variables.
Although any given asset may load on both size and value factors, the factors themselves are independent.
Their effect on return is not independent.
Risk is not a guarantor of return.

dcabler
Posts: 613
Joined: Wed Feb 19, 2014 11:30 am

Re: Fact, Fiction, and the Size Effect

Post by dcabler » Thu May 24, 2018 2:17 pm

We will finally know when we've reached the end of the world when BH'ers finally all agree on whether to include small caps and whether/how much international to include in a portfolio! :sharebeer

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 2:18 pm

jalbert wrote:
Thu May 24, 2018 2:09 pm
Their effect on return is not independent.
You keep using that word. I don’t think it means what you think it means.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

User avatar
triceratop
Moderator
Posts: 5638
Joined: Tue Aug 04, 2015 8:20 pm
Location: la la land

Re: Fact, Fiction, and the Size Effect

Post by triceratop » Thu May 24, 2018 2:21 pm

jalbert wrote:
Thu May 24, 2018 1:11 pm
The theory of factor models is that equity returns may be accurately modeled as a linear combination of independent factors (that is, as a linear model).

We have clear evidence that size and value are not independent. The cited work shows/claims that size and quality are not independent.

Draw your own conclusions.
I thought the theory was that factor models better model ex-post equity returns than does CAPM beta?
"To play the stock market is to play musical chairs under the chord progression of a bid-ask spread."

lack_ey
Posts: 6612
Joined: Wed Nov 19, 2014 11:55 pm

Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Thu May 24, 2018 2:26 pm

Related to the independence question, here's a modeled market beta of the SMB factor over time, assuming the linear coefficient is basically a Gaussian random walk over time (which is probably not how the relationship actually evolves over time, but is simple enough and illustrative), showing the credible interval for the estimate given the model:

Image

As noted in a number of places, SMB regresses a bit on the market factor, though I demonstrate here that the relationship may be variable. In any case, they're not credibly independent, generally speaking.


I think the point jalbert is making is that returns in some cases are not specified well by factor models because of interactions between explanatory variables. For example, long-run historical small cap value performance shows factor loadings on market, size, and value, but then additional alpha on top of that because a 3-factor model can only capture direct linear relations with the three factors and not the interaction between size and value in the small cap value part of the market, assuming that's true. Over some periods, large value may show negative alpha owing to the loading on value but the smaller premium in large value relative to small value.

The issue with making models more complicated by adding additional terms or restructuring them is that even the simple models have issues with wide levels of uncertainty about model parameters. It can get even worse if we try to model relations as time varying, which they probably are.

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 2:37 pm

vineviz wrote:
Thu May 24, 2018 2:18 pm
jalbert wrote:
Thu May 24, 2018 2:09 pm
Their effect on return is not independent.
You keep using that word. I don’t think it means what you think it means.
I do know quite well what it means, but I agree that I’ve not been wording my objection with much precision or accuracy.

The original theory was that the more a stock is a value stock the greater it’s expected return. The smaller a stock the greater it’s expected return. The research results invalidated that theory.
Risk is not a guarantor of return.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 2:42 pm

jalbert wrote:
Thu May 24, 2018 2:37 pm
The original theory was that the more a stock is a value stock the greater it’s expected return. The smaller a stock the greater it’s expected return. The research results invalidated that theory.
To which I can only point out two things: that wasn’t the origal theory and, even if it were, its never been invalidated.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 2:49 pm

Small-cap Growth seems to underperform large-cap Growth for instance.
Risk is not a guarantor of return.

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 3:00 pm

lack_ey wrote:
Thu May 24, 2018 2:26 pm
I think the point jalbert is making is that returns in some cases are not specified well by factor models because of interactions between explanatory variables.
Maybe that is the point he’s trying to make: I can’t tell.

From my point of view, no pricing model is ever expected to be 100% explanatory. Certainly a model doesn’t need to be to be useful.

I’ve never encountered any equity assets where FF3 didn’t explain returns better, even adjusting for the extra explanatory variables, than CAPM. I don’t think anyone imagines that there are not additional factors that can be integrated (as indeed FF, AWR, Frazzini, etc have done). But even with those additions, SMB holds broad explanatory power even during cycles where it is negative.
Last edited by vineviz on Thu May 24, 2018 3:10 pm, edited 1 time in total.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

User avatar
vineviz
Posts: 1665
Joined: Tue May 15, 2018 1:55 pm

Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 3:09 pm

jalbert wrote:
Thu May 24, 2018 2:49 pm
Small-cap Growth seems to underperform large-cap Growth for instance.
Over the past 48 years, that hasn’t been the case: they’ve got almost identical CAGRs.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

User avatar
Kevin M
Posts: 10079
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Fact, Fiction, and the Size Effect

Post by Kevin M » Thu May 24, 2018 3:13 pm

So, Robert T, are you making any changes to your investment policy based on this research, and why or why not?

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

jalbert
Posts: 3656
Joined: Fri Apr 10, 2015 12:29 am

Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 3:28 pm

Over the past 48 years, that hasn’t been the case: they’ve got almost identical CAGRs.
SCV vs SCG since 1972:

https://www.portfoliovisualizer.com/bac ... rowth2=100

For value stocks the size factor has contributed to increased returns:

https://www.portfoliovisualizer.com/bac ... Value1=100

For growth stocks, the size factor has contributed to slightly decreased returns. The recent run up in SCG has restored it to closer to LCG, but certainly not contributing to excess return:

https://www.portfoliovisualizer.com/bac ... Value1=100

If controlling for quality addresses the issue, it still means that the 3-factor model is wrong.
Risk is not a guarantor of return.

User avatar
triceratop
Moderator
Posts: 5638
Joined: Tue Aug 04, 2015 8:20 pm
Location: la la land

Re: Fact, Fiction, and the Size Effect

Post by triceratop » Thu May 24, 2018 3:37 pm

jalbert wrote:
Thu May 24, 2018 3:28 pm
If controlling for quality addresses the issue, it still means that the 3-factor model is wrong.
As I pointed out above the 3-factor model attempts to explain ex-post returns better than CAPM. Please explain how it is "wrong". How much of the data does beta explain? Note that this has nothing to do with whether SmB or HmL is positive or negative.
"To play the stock market is to play musical chairs under the chord progression of a bid-ask spread."

Post Reply