Fact, Fiction, and the Size Effect

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jalbert
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Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 3:49 pm

Given the anomaly with how size has worked for Value stocks and growth stocks, I struggle to see it as an improvement on CAPM. I think adding in the value factor improves on CAPM, but incorporating the size factors regresses from that.

You may be looking at CAPM through today’s lens. CAPM never attempted to explain more than the market factor and security-specific effects, whereas the 3-factor model has to rely on alpha as a fudge factor for the anomaly of the size factor being inverted for growth stocks.

This is in contrast to writings that say the 3-factor model is strongly explanatory and pervasive across all markets.
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Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Thu May 24, 2018 3:54 pm

So if we look at let's say 100 randomly selected U.S. equity mutual funds, adjusted R^2 for a 3-factor model you think would be worse than adjusted R^2 for a 2-factor model of market and value?

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Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 4:09 pm

I don’t know. There are all sorts of factors laden in active management of mutual funds.

I wasn’t trying to make a definitive claim about a 2-factor model of market factor and value. But backtests of the value factor conform to what the model predicts. It explains some of the alpha in CAPM.

Backtests of the 3-factor model are problematic on account of size effects being inverted for growth and value. This seems to push some of the explanation of return back into alpha to compensate for the size anomaly in the 3-factor model.

The statistical test you propose would also be measuring things like value funds with heavier or milder size tilts, where the size factor worked as advertised.
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Re: Fact, Fiction, and the Size Effect

Post by Jags4186 » Thu May 24, 2018 4:43 pm

nisiprius wrote:
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
I guess I do not understand the point of this chart. If you take out the best performing period of an asset class of course it will bring the overall returns down. If we hack out the 8 year period of Large Cap returns from 1984-1991 Small Cap obliterates Large Cap. Have I made the size premium return with a vengeance?

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Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Thu May 24, 2018 5:05 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.
I don't believe they are. I'm confused about this myself, because I used to be familiar with "principal component analysis" in which a swarm of points in N-space is modeled by first finding the axis with the highest loading, then finding the axis perpendicular to that that has the second highest loading, and so forth. In this form of analysis, the components, the axes, emerge mathematically from the positions of the points and are guaranteed to be independent (orthogonal, uncorrelated).

I'm afraid I emailed Kenneth French asking him what I was doing wrong:
The correlation between Rm-Rf and SMB came out 0.337, the correlation between Rm-Rf and HML came out 0.2364, and the correlation between SMB and HML came out 0.118.

I expected them all to be zero, because I thought factors were specifically constructed so as to have zero cross-correlations.

What am I misunderstanding?
And he sent me a one-sentence reply:
They are not constructed to have zero correlation.
Apparently the factors are defined based on financial economics and investing intuition, and then are discovered to have low (but not zero) correlation with each other.
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Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Thu May 24, 2018 5:10 pm

Jags4186 wrote:
Thu May 24, 2018 4:43 pm
...I guess I do not understand the point of this chart. If you take out the best performing period of an asset class of course it will bring the overall returns down. If we hack out the 8 year period of Large Cap returns from 1984-1991 Small Cap obliterates Large Cap. Have I made the size premium return with a vengeance?
It's a badly drawn chart. I suspect it of being a diagram that was originally rendered in color and then published in black-and-white.

Ignore the two top curves, which are S&P 500 and small stock, unmodified, with small outperforming the S&P 500.

Look at the two (not one, two) lower curves, which represent the S&P 500 and small stocks with 1975-1983 removed from both of them, apples to apples. Look at the solid black horizontal line going across the grey band and the dotted line above it going across the grey band. Then look at the dotted greyish line and the solid black line, right of the grey band and also left of the grey band.

When you remove 1975-1983 the two curves almost overlay each other.

With 1975-1983 included, the final values are about $15,368 for small and $3,616 for S&P 500. Wow. With them excluded from both sequences, the final values are $1,011 for small and $963 for the S&P 500, almost the same.

So what it boils down to is that the entire outperformance of small-caps over about 87 years is the result of one brief shining movement from 1975-1983. And the question is: even if small-caps are everything the advocates say they are, how long are you going to need to hold to have a good chance of catching the next shining moment?
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Re: Fact, Fiction, and the Size Effect

Post by triceratop » Thu May 24, 2018 5:18 pm

nisiprius wrote:
Thu May 24, 2018 5:05 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.
I don't believe they are. I'm confused about this myself, because I used to be familiar with "principal component analysis" in which a swarm of points in N-space is modeled by first finding the axis with the highest loading, then finding the axis perpendicular to that that has the second highest loading, and so forth. In this form of analysis, the components, the axes, emerge mathematically from the positions of the points and are guaranteed to be independent (orthogonal, uncorrelated).

I'm afraid I emailed Kenneth French asking him what I was doing wrong:
The correlation between Rm-Rf and SMB came out 0.337, the correlation between Rm-Rf and HML came out 0.2364, and the correlation between SMB and HML came out 0.118.

I expected them all to be zero, because I thought factors were specifically constructed so as to have zero cross-correlations.

What am I misunderstanding?
And he sent me a one-sentence reply:
They are not constructed to have zero correlation.
Apparently the factors are defined based on financial economics and investing intuition, and then are discovered to have low (but not zero) correlation with each other.
Why did you expect there to be perfectly zero correlation in noisy data, with factor definitions applied into the future? Why would you expect that? Who told you that factors have something to do with PCA? I'm not surprised you received a one-sentence response; I'm surprised you received a response at all. Anyway, I look at this directionality as a good thing: wouldn't they be more suspicious if they were constructed to be perfectly decorrelated?
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Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Thu May 24, 2018 5:48 pm

If you look at the way the factor series are defined, there's nothing there that would force the (true, or sample) correlations down to zero, and so they're not. I don't think ti's that surprising intuitively that for example small stocks might have higher equity beta on average than large stocks (let's say, maybe more sensitive to good vs. bad times, not being able to truck through any circumstance like some of the megacaps), and as such in many situations the size factor as small minus big ends up with some equity market beta exposure.

With equity market neutral funds we see a distinction between strategies that are gross balanced by dollars invested in terms of the long and short side being equal, and other strategies that attempt to be beta neutral. These are not the same. Likewise, a factor defined as one portfolio minus another may have some net exposures to certain other things like market beta. Expanding on this, there's no particular reason why the correlations between two different non-market factors should be zero. Value and momentum structurally make sense to be negatively correlated because stocks that have fallen sharply have a depressed price and could well have higher fundamental-to-price ratios (higher value), and those that have gained have higher prices and could have lower fundamental-to-price ratios.

PCA is a useful tool for a number of things but not really relevant here. For one, we want consistent definitions that make some kind of economic sense and furthermore are not data dependent.

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Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Thu May 24, 2018 6:06 pm

triceratop wrote:
Thu May 24, 2018 5:18 pm
...Who told you that factors have something to do with PCA?...
Nobody, but I did think they had something to do with factor analysis. I was wrong.

(Factor analysis is somewhat similar to principal component analysis. I only mentioned principal component analysis because I actually did it once, and I never have done factor analysis).
Last edited by nisiprius on Thu May 24, 2018 6:19 pm, edited 1 time in total.
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Re: Fact, Fiction, and the Size Effect

Post by Jags4186 » Thu May 24, 2018 6:07 pm

nisiprius wrote:
Thu May 24, 2018 5:10 pm
Jags4186 wrote:
Thu May 24, 2018 4:43 pm
...I guess I do not understand the point of this chart. If you take out the best performing period of an asset class of course it will bring the overall returns down. If we hack out the 8 year period of Large Cap returns from 1984-1991 Small Cap obliterates Large Cap. Have I made the size premium return with a vengeance?
It's a badly drawn chart. I suspect it of being a diagram that was originally rendered in color and then published in black-and-white.

Ignore the two top curves, which are S&P 500 and small stock, unmodified, with small outperforming the S&P 500.

Look at the two (not one, two) lower curves, which represent the S&P 500 and small stocks with 1975-1983 removed from both of them, apples to apples. Look at the solid black horizontal line going across the grey band and the dotted line above it going across the grey band. Then look at the dotted greyish line and the solid black line, right of the grey band and also left of the grey band.

When you remove 1975-1983 the two curves almost overlay each other.

With 1975-1983 included, the final values are about $15,368 for small and $3,616 for S&P 500. Wow. With them excluded from both sequences, the final values are $1,011 for small and $963 for the S&P 500, almost the same.

So what it boils down to is that the entire outperformance of small-caps over about 87 years is the result of one brief shining movement from 1975-1983. And the question is: even if small-caps are everything the advocates say they are, how long are you going to need to hold to have a good chance of catching the next shining moment?
Yes after posting I realized what the chart was showing. From 1926-1975 and from 1984-2012 Small Caps performed identically. But what makes that the arbiter of the premium? What is special about 1926? What is special about 1984? It seems to me that the premium only didn’t show itself when you start at those dates, but you could easily manipulate the dates within the time periods exclusive of 1975-1983 and still find the premium. If you start at 1991 the premium certainly showed up. If you start in 1937 or 1931 the premium certainly showed up. You only marginally outperformed if you invested in 1926 or 1984.

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Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Thu May 24, 2018 6:39 pm

Jags4186 wrote:
Thu May 24, 2018 6:07 pm
...Yes after posting I realized what the chart was showing. From 1926-1975 and from 1984-2012 Small Caps performed identically. But what makes that the arbiter of the premium? What is special about 1926? What is special about 1984? It seems to me that the premium only didn’t show itself when you start at those dates, but you could easily manipulate the dates within the time periods exclusive of 1975-1983 and still find the premium. If you start at 1991 the premium certainly showed up. If you start in 1937 or 1931 the premium certainly showed up. You only marginally outperformed if you invested in 1926 or 1984...
Oh, well. That's why I have a pretty thick layer of skepticism about all of this. The question to my mind isn't so much "is there a small firm effect," there is the big overarching question which is that financial data shows such huge fluctuations that just about all the differences people claim to have found, between one strategy and another, are smaller than the differences that happen if you make even a small changes in endpoints.

I posted about this a while ago: Endpoint sensitivity on "historic" data. The point I made was that even perhaps the most basic of all financial statistics, the "historic return of the US stock market," even over a period as long as eighty years, can come out anywhere from 9% to 11% if you move the endpoints by a few years. So, forget the future: we don't really know the past performance of "the stock market" to better than ±1%.

But how often do you see any asset returns stated with any kind of range or error bound on them? Never, that's how often.

The idea of security in long-term data is deceptive. First of all, because of the fractal-like, fat tails, "misbehavior of markets" (Mandelbrot), "Extremistan" (Taleb) nature of financial data, 90 years isn't really a lot of data. It's not as bad as the Cauchy distribution in which the mean never settles down at all, but it's not tame, either. Events like 1929 are so huge that affect the mean of a 90 year period that includes them.

Then throw in the question of whether you can seriously believe that the pre-electronic, pre-SEC stock market is really "the same thing" as the modern stock market. That is, do you really believe that they both follow the same quantitative model, with the same parameters plugged into it? The standard deviation of stocks is going to be the same whether it is being done by computers trading in milliseconds, or by human beings who have (literally) heard inside information from Edward Francis Hutton?

I have decided that I personally will not even bother to pay attention to anything if the author does not state a reason for the choice of endpoints.

However, "what is special about 1926," that at least has an explanation.

There are two common endpoints that can be considered to be somewhat "fair" (i.e. not cherry-picked). 1926 is the starting point for the CRSP data, which I wrote about Origins of the CRSP; what about that 1926 starting point? The Center for Research in Securities Prices, CRSP, was originally sponsored by Merrill Lynch for the purpose of getting data they could use in advertising, to back up a claim that common stocks, if held for a long time, were prudent investments for retail investors. 1926 was apparently an arbitrary but tasteful choice.

Anyway, there is now a large corpus of data, collected and curated by the CRSP, beginning at 1926, with nothing comparable before it.

A second frequently-used starting point for stock market data is 1871, the beginning of the stock data collected by the Cowles Commission and published in 1938 and updated in 1939... IIRC.
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Re: Fact, Fiction, and the Size Effect

Post by Jags4186 » Thu May 24, 2018 7:11 pm

nisiprius wrote:
Thu May 24, 2018 6:39 pm
I posted about this a while ago: Endpoint sensitivity on "historic" data. ... published in 1938 and updated in 1939... IIRC.
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Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 9:58 pm

nisiprius wrote:
Thu May 24, 2018 5:10 pm
So what it boils down to is that the entire outperformance of small-caps over about 87 years is the result of one brief shining movement from 1975-1983. And the question is: even if small-caps are everything the advocates say they are, how long are you going to need to hold to have a good chance of catching the next shining moment?
This is, again, factually inaccurate.

$10,000 invested in small cap stocks at the end of 1926 would have been worth $838,000 dollars in 1974. The same investment in large cap stocks would have been worth $359,000.

It's true that 1984 to 1998 was a long period in which large cap outperformed small cap stocks, but also true that from 1999 to 2017 small cap dramatically outperformed large cap. In other words, large cap outperformance is the exception and not the rule.

Even more relevant to the typically investor experience, if you look at the 72 different rolling twenty years periods since 1927 small caps have outperformed large caps in 60 of them. While an 83% success rate isn't nearly a 'sure thing', it's definitely not a losing record or a single 'shining moment'.
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Re: Fact, Fiction, and the Size Effect

Post by jalbert » Thu May 24, 2018 10:22 pm

jalbert wrote:
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.
What I’ve been doing a poor job of articulating can be described in a more straightforward manner. That the size factor is inverted for growth relative to value in large samples since the early 70’s seems to falsify that the return of a stock is a linear function of size, value, and market beta.
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Re: Fact, Fiction, and the Size Effect

Post by vineviz » Thu May 24, 2018 11:33 pm

jalbert wrote:
Thu May 24, 2018 10:22 pm
That the size factor is inverted for growth relative to value in large samples since the early 70’s seems to falsify that the return of a stock is a linear function of size, value, and market beta.
It might seem that way to you, but I see no logical reason why such an inversion (even if it were true) would support such a conclusion.
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Re: Fact, Fiction, and the Size Effect

Post by jalbert » Fri May 25, 2018 1:53 am

Level sets for at least two different numeric values of the value parameter on the surface of the graph of return (as a function of market beta, value, and size), holding market beta fixed, must have slopes with different signs to generate sample data where return decreases as size increases for value but return increases as size increases for growth. That is not the behavior of a linear function.

But the inversion of the size parameter is clearly shown in the backtest data I offered above from portfoliovisualizer.com.

I listened to a youtube video of an interview of Gene Fama at a DFA advisors conference where he clearly demonstrated awareness of the issue by describing small-cap growth as a terrible asset class. This is not a secret. Most proponents of factor investing describe small-cap growth as the black hole of investing.

In fact the whole point of RobertT's original posting was to post a link to research showing that by controlling for quality, this inversion of the size effect is remedied.

I think Rick Ferri partially answered KevinM's question-- if you invest in small-caps, they either should be value-tilted or quality-screened or both. That would be the implication of the work if you subscribe to factor investing. Once quality is introduced it is a 4-factor model.

I would consider the failure of the 3-factor model to model return as a linear model of market beta, value and size as an indicator that one should proceed with caution using 3-factor regressions as a portfolio construction or analysis technique.
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Re: Fact, Fiction, and the Size Effect

Post by Robert T » Fri May 25, 2018 3:28 am

Kevin M wrote:
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
No need to make any changes.

Historical evidence (over multiple time frames) and actual returns indicate that my allocation/combination of factor load targets are not simply leveraged beta (the point made in the paper about small caps re: “the size premium on its own is significant, but adjusting for market beta renders it insignificant”). My factor load targets are not simply to beta and size, but also value – and as the paper indicates “other premia are larger when implemented among small cap stocks.”

The point in the paper that “the returns to size are far less stable, less persistent, and less robust than these other factors” is not a new finding. It was one of the reasons my target load for value is double that for size, and for market beta is five times that for size. Another point highlighted in the paper that “the size effect mostly comes from microcap stocks” is also not new – hence the earlier discussion on the Bridgeway fund that since inception 21 years ago has trailed CRSP10 by 0.1%.

Even if higher returns are simply the equivalent of leveraged beta (the first point on small caps in the paper) doesn’t mean there is no reason to hold these types of assets. As Swensen indicated in his book re: leverage – you can either borrow funds to invest in the market (explicit leverage) or you can hold riskier than market assets with no borrowing (implicit leverage). In this context an investor has a choice – obviously no guarantees.

I am also not convinced that ‘quality’ beats all other factor tilts in small caps.
  • 1964-2017: Annualized return/ SD / Sharpe Ratio

    10.2% / 17.2 / 0.40 = Market (CRSP1-10)
    14.7% / 24.4 / 0.52 = FF Small Cap Quality (High operating profitability)
    15.0% / 22.1 / 0.56 = AQR Small Cap Quality*
    16.2% / 24.0 / 0.58 = FF Small Cap Value
    17.9% / 25.6 / 0.62 = FF Small Cap Momentum
* Derived from the ‘quality minus junk’ data set.

Will a multifactor tilt in small caps outperform single factor tilts (on after cost basis)? DFA seems to show little/no difference in returns (e.g. if you compare the Dimensional US Targeted Value Index Series without a profitability screen (from the 2013 DFA Matrix Book) 1928-2012 annualized returns = 13.0%, adding a profitability screen (from the 2018 DFA Matrix book) yields that same return of 13.0% for the same time period. AQR shows higher returns in its ‘new core equity paradigm paper. Time will tell.

Robert
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Re: Fact, Fiction, and the Size Effect

Post by Snowjob » Fri May 25, 2018 8:08 am

willthrill81 wrote:
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?
Just as the entire out-performance of the S&P small 600 was due to the avoidance of the junk internet companies in the late 1990's by requiring 4 quarters of profitability before inclusion. I will maintain a small tilt to of about 5-8% of my portfolio to small and small value just in case I'm wrong but other than two distinct periods I don't see any difference. HOWEVER, they do seem to run at different times, so as part of an overall equity allocation I believe there can be a re-balancing bonus between large and small, which would be a true benefit as your not giving up expected returns as you do when you re-balance between equity and bond.

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Re: Fact, Fiction, and the Size Effect

Post by vineviz » Fri May 25, 2018 9:11 am

jalbert wrote:
Fri May 25, 2018 1:53 am
Level sets for at least two different numeric values of the value parameter on the surface of the graph of return (as a function of market beta, value, and size), holding market beta fixed, must have slopes with different signs to generate sample data where return decreases as size increases for value but return increases as size increases for growth. That is not the behavior of a linear function.
None of the arguments for any asset pricing model (CAPM, FF3, Carhart, AQR, FF5) have anything to do with these supposed qualities of a linear function that you are proposing as laws..

As triceratop has pointed out more than once, the full extent of any claim that Fama & French made on this front is that their three factor pricing model explains asset returns better than the single factor CAPM. This is, in fact, easy to verify.

From 1972 to present, CAPM explains about 75.4% of the monthly return variance of the small cap growth portfolio whereas FF3 explains 97.7%. That's a huge improvement, one that is robust across other time periods and assets.

It is true that even under FF3, the small cap growth portfolio has a significant negative alpha but the large cap growth portfolio has a significant positive alpha. This is easy to understand, though, if you understand that those two portfolios differ in their loadings on other factors besides the ones specified in the FF3 model. If you add in other common risk factors (especially, but not only, QMJ) to the model you can reduce the alpha (which really is only the residual) of both portfolios to near zero.

In other words, the large cap growth and small cap growth portfolios you are looking at are not – and were never meant to be – constructed such that they hold market beta fixed. Or, indeed, ANY factor fixed. Although it is theoretically possible to build a portfolio that loads on one factor with zero weights on all other factors (some so-called single factor 'Smart Beta' funds attempt to do this, with mixed success) no common stock index does this.

From 1972 to present, the small cap growth portfolio had 21.49 bps of OUTPERFORMANCE over large cap growth each month due to the size effect. It had 27.09 bps of UNDERPERFORMANCE due to other factors. The single biggest factor was QMJ but HML, STREV, LTREV, and BAB were also significant.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Fact, Fiction, and the Size Effect

Post by Random Walker » Fri May 25, 2018 9:18 am

Snowjob wrote:
Fri May 25, 2018 8:08 am
I will maintain a small tilt to of about 5-8% of my portfolio to small and small value just in case I'm wrong but other than two distinct periods I don't see any difference. HOWEVER, they do seem to run at different times, so as part of an overall equity allocation I believe there can be a re-balancing bonus between large and small, which would be a true benefit as your not giving up expected returns as you do when you re-balance between equity and bond.
Sounds to me like you’re starting down the path towards diversifying across factors and sources of return. It starts with just a little tilt to size or value. Then you start looking at diversification differently: not number of stocks but across factors and sources of return. Next you’ll add more international, then CS and TS Momentum, profitability. After that comes the dive into alternatives. Next thing you know, you’ll be bragging about risk parity when talking investing :-)
Diversifying across factors has excellent potential, especially since each factor has an expected premium and they all can underperform for long periods. A naive 1/n portfolio diversified across factors looks pretty solid. Take a peek at the tables in Chapter 9 of Larry Swedroe’s Factor Book.

Dave

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Re: Fact, Fiction, and the Size Effect

Post by nisiprius » Fri May 25, 2018 9:56 am

vineviz wrote:
Fri May 25, 2018 9:11 am
...As triceratop has pointed out more than once, the full extent of any claim that Fama & French made on this front is that their three factor pricing model explains asset returns better than the single factor CAPM. This is, in fact, easy to verify.

From 1972 to present, CAPM explains about 75.4% of the monthly return variance of the small cap growth portfolio whereas FF3 explains 97.7%. That's a huge improvement, one that is robust across other time periods and assets...
I'm sorry, I'm going to ask you to try to explain that in plain layman's terms.

Because on the face of it, what that appears to be saying is that the 1993 work was 97.7% complete, and that all of the factor work that's been done since 1993, including the Fama-French five-factor model has been devoted to trying to find tiny refinements within the minute unexplained 2.3% residuum.

Add to this that it is a completely separate question how much benefit you get from basing your personal investing strategy on a 97.7%-complete model rather than a 75.4%-complete. In this thread and others it has been seriously challenged whether you see any benefit at all, or any benefit that is robust and reliable enough to have much conviction that you personally will see a meaningful benefit within your investing lifetime.
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Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Fri May 25, 2018 10:25 am

nisiprius wrote:
Fri May 25, 2018 9:56 am
vineviz wrote:
Fri May 25, 2018 9:11 am
...As triceratop has pointed out more than once, the full extent of any claim that Fama & French made on this front is that their three factor pricing model explains asset returns better than the single factor CAPM. This is, in fact, easy to verify.

From 1972 to present, CAPM explains about 75.4% of the monthly return variance of the small cap growth portfolio whereas FF3 explains 97.7%. That's a huge improvement, one that is robust across other time periods and assets...
I'm sorry, I'm going to ask you to try to explain that in plain layman's terms.

Because on the face of it, what that appears to be saying is that the 1993 work was 97.7% complete, and that all of the factor work that's been done since 1993, including the Fama-French five-factor model has been devoted to trying to find tiny refinements within the minute unexplained 2.3% residuum.

Add to this that it is a completely separate question how much benefit you get from basing your personal investing strategy on a 97.7%-complete model rather than a 75.4%-complete. In this thread and others it has been seriously challenged whether you see any benefit at all, or any benefit that is robust and reliable enough to have much conviction that you personally will see a meaningful benefit within your investing lifetime.
I didn't write that, but I think I can respond. (I'm going to assume the figures are correct here without double-checking myself or any further verification.)

The R^2 cited is for a specific small growth portfolio, not for random or more general allocations of stocks, where FF3 may not be as good. The size and value factors are constructed in a way that help them explain a portfolio such as this. By construction a small growth portfolio is selected based on stock value and size, so the result really should not be terribly surprising. We'd hope that groupings based on value and size would be explained by a model that uses value and size factors. This mostly just challenges jalbert's reservations about the usefulness of the model in describing portfolios tilted significantly on both value and size, where we'd expect some interaction between the two. Here we see just the (linear, no interactions) factor model doing decently well, though of course with some unaccounted alpha.

This example highlights one area where CAPM leaves a good deal unexplained, but FF3 can do a lot better. But there are allocations where just the market factor of CAPM can do well on its own. For example, we get over 97% using CAPM on Vanguard's S&P 500 fund for the last 40 years. Adding size would make it better, but it's not a huge deal there.

The reason we have other factor models is because some allocations are explained less well by market, size, and value, and particularly in the cases where these show significant negative or positive alpha, there may be something worthwhile to investigate. We might even call some of these things... anomalies. In other cases we can just have mediocre model fit on the basis of idiosyncratic and sector risks not being captured by the factors. A simple example is a sector fund. For the last 20 years or so (check the sector SPDR ETFs on PortfolioVisualizer for an easy approximation), the energy sector ETF XLE has had FF3, FF5, Carhart, etc. of under 50% R^2.

Then we need to make a distinction between model explanatory power and then investing strategies. In some contexts we're interested in using a model to understand what happened; in others we want to project forward; one application with a lot of attention is for portfolio construction. These are not the same things. A factor model could be good at explaining monthly variance in returns without all factors necessarily having positive average return. It's just that those seeking higher return (perhaps with higher risk) are interested in loading on factors that may result in higher return. In general a model doesn't have to be good at explaining a lot of the variance to be able to implicitly suggest a portfolio with significantly higher past return.

For investing in the future, there's the question of how to estimate distributions for factor returns (including that of the market), which may be different from historical observed distributions. Standard procedure seems to be to mostly wave your arms and hope that the sign doesn't flip for the means, and that even if you don't actually know what's going to happen, maybe you have a better shot counting on certain things to persist to some degree based on economic theory, data across time and markets, and so on. It's inevitably significantly subjective.

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Re: Fact, Fiction, and the Size Effect

Post by vineviz » Fri May 25, 2018 11:11 am

nisiprius wrote:
Fri May 25, 2018 9:56 am
. . . .on the face of it, what that appears to be saying is that the 1993 work was 97.7% complete,
That's not really how you should look at it. For one thing, that R-sq number applies only to that one particular asset. It's not a measure of the OVERALL effectiveness of the pricing model.

Plus, no asset pricing model will EVER be able to explain returns with 100% accuracy so it's not really accurate to say that the pricing models are complete or not.
nisiprius wrote:
Fri May 25, 2018 9:56 am
. . . . all of the factor work that's been done since 1993, including the Fama-French five-factor model has been devoted to trying to find tiny refinements within the minute unexplained 2.3% residuum.
That 2.3% might seem minute to you, but it potentially represents HUGE spreads in asset returns especially when compounded over long periods of time.

Even if you aren't building a portfolio to maximize returns, knowing what risks you are exposed to and which you are not is still highly important to most investors.
nisiprius wrote:
Fri May 25, 2018 9:56 am
Add to this that it is a completely separate question how much benefit you get from basing your personal investing strategy on a 97.7%-complete model rather than a 75.4%-complete. In this thread and others it has been seriously challenged whether you see any benefit at all, or any benefit that is robust and reliable enough to have much conviction that you personally will see a meaningful benefit within your investing lifetime.
Apart from reiterating that approaching this from a completeness perspective will mislead you, I can assure you that the difference between pricing assets using the CAPM and using FF5 (or some other more robust model) has huge implications for investors. It's analogous in some ways between the experience of driving a 1965 Ford Fairlane versus driving a Tesla Model S.

By way of example, the single factor CAPM model has no capacity to predict whether three particular ETFs (SPYG, SPYV, ITOT) should have the same returns or different returns: they all have the same five-year market factor (i.e. beta) of 0.98. But even a Boglehead investor can intuit that those three funds are not interchangeable and that they expose the investor to different risk factors. Whereas the CAPM lacks the ability to describe that, the FF3 or FF5 models do not.

I view that as a benefit.
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Re: Fact, Fiction, and the Size Effect

Post by Snowjob » Fri May 25, 2018 1:05 pm

Random Walker wrote:
Fri May 25, 2018 9:18 am
Snowjob wrote:
Fri May 25, 2018 8:08 am
I will maintain a small tilt to of about 5-8% of my portfolio to small and small value just in case I'm wrong but other than two distinct periods I don't see any difference. HOWEVER, they do seem to run at different times, so as part of an overall equity allocation I believe there can be a re-balancing bonus between large and small, which would be a true benefit as your not giving up expected returns as you do when you re-balance between equity and bond.
Sounds to me like you’re starting down the path towards diversifying across factors and sources of return. It starts with just a little tilt to size or value. Then you start looking at diversification differently: not number of stocks but across factors and sources of return. Next you’ll add more international, then CS and TS Momentum, profitability. After that comes the dive into alternatives. Next thing you know, you’ll be bragging about risk parity when talking investing :-)
Diversifying across factors has excellent potential, especially since each factor has an expected premium and they all can underperform for long periods. A naive 1/n portfolio diversified across factors looks pretty solid. Take a peek at the tables in Chapter 9 of Larry Swedroe’s Factor Book.

Dave
God I hope not, its taken my years to change from individual stocks, bonds, leverage etc. I'm just starting to enjoy simplicity just a few index funds, don't tell me this is only a transition point to more complications haha

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Re: Fact, Fiction, and the Size Effect

Post by jalbert » Fri May 25, 2018 1:43 pm

one of the arguments for any asset pricing model (CAPM, FF3, Carhart, AQR, FF5) have anything to do with these supposed qualities of a linear function that you are proposing as laws..
I hope you are not suggesting we should ignore the mathematical properties of a linear function when evaluating how well such a function models stock returns. If return is a linear function of market beta, value, and size, then if you take the partial derivative of return with respect to size you get a constant (the coefficient of the size parameter). This means that if you fix market beta and value at any particular values the resulting return curve always has the same slope with respect to size. This level set curve is a straight line, and all such straight lines have the same slope. This is a provable property of linear functions.

Returns over the last 46 years are a large out of sample validation of the model that failed. The 3-factor model predicted the behavior of the size factor for value stocks quite well: as you reduce size of value stocks, returns improved in the sample. The model failed for growth stocks because small-cap growth has been worse than large and mid-cap growth, in opposition to what the model would predict. When you look at all small-caps in aggregate, the effect for value stocks is robust enough to make up for the failure for growth stocks and show a size effect for the market in aggregate.

The success of the model for value stocks is legitimately exploited by setting small-cap value tilts by those willing to take more risk and take the risk of long periods of market tracking error.

But I would not describe the 3-factor model as persistent and pervasive across all markets when it failed for growth stocks in the market for which it was developed.
Index fund investor since 1987.

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Re: Fact, Fiction, and the Size Effect

Post by vineviz » Fri May 25, 2018 2:56 pm

jalbert wrote:
Fri May 25, 2018 1:43 pm
If return is a linear function of market beta, value, and size, then if you take the partial derivative of return with respect to size you get a constant (the coefficient of the size parameter). This means that if you fix market beta and value at any particular values the resulting return curve always has the same slope with respect to size. This level set curve is a straight line, and all such straight lines have the same slope. This is a provable property of linear functions. Returns over the last 46 years are a large out of sample validation of the model that failed.
Even if I were to grant the last sentence (I do not), please remember that testing the validity of multilinear equation – after all, a vector of three different slopes – requires a lot more than just eyeballing one chart online. At the very least, those LCG and SCG portfolios do NOT have the property you claim to desire which is to hold both beta and value constant.
jalbert wrote:
Fri May 25, 2018 1:43 pm
But I would not describe the 3-factor model as persistent and pervasive across all markets when it failed for growth stocks in the market for which it was developed.
It getting tiresome to be forced to repeatedly point out that it DIDN'T fail, but to that repetition I'll add only that whatever issues you have with the three factor model it absolutely is superior both theoretically and empirically to the single factor model (CAPM) that preceded it.
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Re: Fact, Fiction, and the Size Effect

Post by lack_ey » Fri May 25, 2018 4:30 pm

To some extent the perspective of how good a model is depends on what you want to learn from it and how you're evaluating it. If you focus on explaining the variability of returns, FF3 seems to hold well for evaluating small growth or some other Morningstar style box. Statistics such as R^2 are related to this.

On the other hand, if what you want to do is explain or predict mean long-term returns, this is about a 1st order (mean) rather than a 2nd order (variance) stat, and the results seem maybe less satisfactory.

After all, the sample means for Mkt-RF, SMB, and HML for the U.S. monthly data are 0.66%, 0.21%, and 0.38%. That's small relative to the sample standard deviations of 5.34%, 3.20%, and 3.49%. There's a lot of variability relative to the mean size of the effect even in the historical costless data, which also among other things makes estimating the mean hard (the "true" value could fall in a wider range, though the actual true value is probably not constant and none of these models are correct anyway). It's possible to capture a lot of the variability of a portfolio using a linear combination of factors while providing a significantly biased estimate.

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Re: Fact, Fiction, and the Size Effect

Post by Portfolio7 » Fri May 25, 2018 5:55 pm

Snowjob wrote:
Fri May 25, 2018 1:05 pm
Random Walker wrote:
Fri May 25, 2018 9:18 am
Snowjob wrote:
Fri May 25, 2018 8:08 am
I will maintain a small tilt to of about 5-8% of my portfolio to small and small value just in case I'm wrong but other than two distinct periods I don't see any difference. HOWEVER, they do seem to run at different times, so as part of an overall equity allocation I believe there can be a re-balancing bonus between large and small, which would be a true benefit as your not giving up expected returns as you do when you re-balance between equity and bond.
Sounds to me like you’re starting down the path towards diversifying across factors and sources of return. It starts with just a little tilt to size or value. Then you start looking at diversification differently: not number of stocks but across factors and sources of return. Next you’ll add more international, then CS and TS Momentum, profitability. After that comes the dive into alternatives. Next thing you know, you’ll be bragging about risk parity when talking investing :-)
Diversifying across factors has excellent potential, especially since each factor has an expected premium and they all can underperform for long periods. A naive 1/n portfolio diversified across factors looks pretty solid. Take a peek at the tables in Chapter 9 of Larry Swedroe’s Factor Book.

Dave
God I hope not, its taken my years to change from individual stocks, bonds, leverage etc. I'm just starting to enjoy simplicity just a few index funds, don't tell me this is only a transition point to more complications haha
I first built a portfolio with a size tilt, then threw in a value tilt, and I just bought a very little MTUM (which seems to serve as a decent diversifier), but I can only buy it in our little IRAs. I'm also looking at FVAL, but have the same restrictions. I seem to have the bug. :o
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Re: Fact, Fiction, and the Size Effect

Post by Random Walker » Fri May 25, 2018 9:53 pm

I definitely have the above mentioned bug. From 96-2001 I had individual stocks through a broker friend. Read a lot and became a hard core ultra low ER TSM Boglehead 2001-9. Started with in interest in tilting to value in taxable account. In 2009 switched to advisor DFA route. Since then have tilted more and more heavily, added alternatives, and converted from bond fund to individual muni bonds.
I really do believe, as Larry Swedroe has written, in “looking at diversification differently”:diversifying across factors and sources of return. I’m not really surprised that I tilted to the size and value risk factors. I am surprised that my belief in the behavioral anomalies of CS Momentum and TS Momentum has strengthened. I’m a big believer in value because it has both risk based and behavioral based explanations. The more I learn, the more faith I put in the behavioral component of value.
Larry has shown that when a portfolio diversified across factors underperforms, it’s not by much at all. When it outperforms, it’s significant. As I’ve progressed in investing, and now have more to lose, I see risk as putting all my bets on the single factor, market beta.

Dave

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Re: Fact, Fiction, and the Size Effect

Post by Rick Ferri » Mon May 28, 2018 11:55 am

Random Walker wrote:
Fri May 25, 2018 9:53 pm
I definitely have the above mentioned bug....As I’ve progressed in investing, and now have more to lose, I see risk as putting all my bets on the single factor, market beta.

Dave
Hmm. We disagree on what progress in investing is. I see progress as getting beyond complexity, buying a few total-market index funds and fugetaboutit!

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Re: Fact, Fiction, and the Size Effect

Post by JoMoney » Mon May 28, 2018 12:06 pm

Rick Ferri wrote:
Mon May 28, 2018 11:55 am
... and fugetaboutit!
Good advice.
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Re: Fact, Fiction, and the Size Effect

Post by stlutz » Mon May 28, 2018 1:02 pm

As an aside, nobody has ever actually been able to find that Fidelity "study".

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Re: Fact, Fiction, and the Size Effect

Post by livesoft » Mon May 28, 2018 1:24 pm

The Fidelity thing as reported is an Urban Myth. The true study (also never published for obvious reasons) was the accounts that had done the best were the ones where the Fidelity advisor had died.
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Re: Fact, Fiction, and the Size Effect

Post by Random Walker » Mon May 28, 2018 1:27 pm

:arrow:
Rick Ferri wrote:
Mon May 28, 2018 11:55 am
Random Walker wrote:
Fri May 25, 2018 9:53 pm
I definitely have the above mentioned bug....As I’ve progressed in investing, and now have more to lose, I see risk as putting all my bets on the single factor, market beta.

Dave
Hmm. We disagree on what progress in investing is. I see progress as getting beyond complexity, buying a few total-market index funds and fugetaboutit!

Rick Ferri
I’ve definitely taken note! You’re one of my biggest early influences and market efficiency fits so neatly with my world view. Seeing you evolve in the opposite direction definitely makes me think twice!

Dave

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Re: Fact, Fiction, and the Size Effect

Post by Rick Ferri » Mon May 28, 2018 2:10 pm

On paper, a more complex strategy should outperform a simple one, but I don't believe it does in real life for most people. The outcome of simplicity is actually greater in real life than the outcome for complexity, even if in theory complexity outperforms.

We know complexity will cost more and that it takes up more of our time. But that's not all. Complexity changes. What will be new that we'll have to include in a portfolio 5 or 10 years from now?

There's also tracking error in any portfolio that's not a market portfolio, but we can't know how negative tracking error will affect us if it goes on for a long time.

These issues lead to cognitive errors. How many times will we change a complex strategy? Probably several. How will these changes affect our long-term return? Probably not much. What's the next thing I'll have to add? Complexity will require adding the next "evidence-based" asset class, factor or strategy.

All of the above have lead to an advancement in my investment views. The more I know, the more I realized how little I know, and how little anyone knows. Yet we must invest. So, how do we do it?

Simpler is better. Less is more.

Rick Ferri
The Education of an Index Investor: flounders in darkness, finds enlightenment, overcomplicates strategy, embraces simplicity.

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