FA article "Rethinking Small Caps"

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FA article "Rethinking Small Caps"

Post by CaliJim »

In a recent article in Financial Advisor Magazine titled "Rethinking Small Caps, Challenging long-held beliefs, new research shows large caps have the advantage", Scott Mackillop presents data that questions the validity of the idea that small beats large on a risk adjusted return basis.

See:
http://www.fa-mag.com/component/content ... &Itemid=73

"We set out to learn what had happened to the small-beats-large anomaly in the days since it was first revealed by Rolf Banz and discovered that it may never have existed at all. If anything, it appears that large stocks beat small. Our findings are counter to those of earlier researchers.

Four factors that may explain the difference in our findings:...." [paraphrased here]:

1) Represented small with CRSP 9-10, and large with S&P500
2) CRSP data is constantly revised and improved (?)
3) Used annualized returns, not average monthly returns
4) Used lag-adjusted returns

But.. golly gee whiz and yikes.

Um .. why is it, again, that one should tilt towards small (and value)?

What say you about this article?

[edit: fixed typo:"CRSP 9-1" -> "CRSP 9-10"]
Last edited by CaliJim on Mon Sep 12, 2011 11:23 pm, edited 1 time in total.
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Post by Lbill »

Thanks for the link. I'll be interested in what some of the experts like Larry Swedroe have to say about this.
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Post by Jay69 »

Im in to see how this one plays out.

I know I have read somthing close to this before around here,
We believe that often an anomaly disappears or is diminished once its existence is widely known. The original purpose of our research was to explore what happened to the small-beats-large anomaly after it was revealed by Banz in 1981.
Thanks for the link, a lot of information to digest, my quote above is just the start of this paper.
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Post by asset_chaos »

On a risk adjusted basis small and large should have the same---or similar depending on time period studied---returns. Small has more risk and a higher expected return than the total market portfolio. Large has less risk and a lower expected return than the total market portfolio. That's what theory says. Is that more or less what they found? One takes on small (or value) risk in one's equities because one can stand the extra risk and wants the extra return over the total market portfolio.

On a technical note, why would they represent small by CRSP 1-9. That includes the largest companies in the definition of small and excludes the smallest companies in CRSP 10 from the definition of small. I don't see how that makes sense.
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Post by staythecourse »

I looked at the article when it first was posted and was unimpressed.

It slickly mentions on a risk adjusted basis large cap is better. Their own data shows in all the time intervals the return is more with small vs. big.

I don't think folks invest in small for better risk adjusted return, but for a larger returns overall (albeit at a higher risk then the general market).

Good luck.
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Post by CaliJim »

asset_chaos wrote:why would they represent small by CRSP 1-9.
typo. fixed. thanks.
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Post by yobria »

Thanks for the link. My thoughts never vary when I see these things:

1. You can tweak time periods, data sets, and other parameters to prove anything you want.

2. Going forward, you should expect no free lunches, ie the risk adjusted return of small caps will be exactly the same as large caps.

Of course, due to #1, you can never prove #2 definitively.

Note that we're talking risk adjusted return. I expect (investable) small caps to outperform large caps going forward modestly, because they're modestly riskier.

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Post by A Devout Indexer »

The research on small stocks showed them to have higher returns than you'd expect based on their market beta, which ultimately led researchers to fashion a more complete model of return behavior (the CAPM 1 factor model became the Fama/French 3 factor model).

I am not sure why the findings that small is riskier than large is particularly newsworthy. That's where the higher returns come from. As to the disappointing results of the CRSP 9-10 index in the post 1981 period, it has a lot to do with the devastating '84-'90 period where small < large by ~10% per year. Of course, this was preceded by a 7 year period even more favorable for small v large. Starting your view of small/large in 1929 or 1982 will force you to wait a long time to see the advantage.

Ultimately, the case for adding small to a large portfolio was never about reducing risk, it was about potentially enhancing risk adjusted returns through improved diversification. And as we've seen over the last 10 years, that diversification benefit is still alive and well, especially if we include MSCI EAFE Small.
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Post by Noobvestor »

Since the founding of the Vanguard Small Cap Value fund it looks (eyeballing it here) 50 to 100% more return than Total Market (which is cheating in the opposition's favor, since TSM contains some small - sorry, guess I should have done large!) So ... what's the debate here exactly?

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Post by A Devout Indexer »

By the way, this highlights an important concept in investing: sometimes you have to wait a long time for risk to be rewarded. The equity risk premium has gone negative for 15+ year periods, small v large even longer. LT Bond investors once had to wait 50 years to surpass inflation!

If you are like the rest of us and don't know for sure which risks will be rewarded (and by how much) in the future, you are best served diversifying modestly across all of them. For example, favor equities over bonds depending on your goals and risk tolerance, diversify w/i the equity market across small and value stocks, and w/i the bond market across interest rate and credit risk.

And go global as best you can. The difficult '84-'90 period for US small stocks was more than offset by the +28% per year results for Int'l small over this same period.
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Post by A Devout Indexer »

For anyone interested in the history of small v large stocks, I made this comment in another thread:

Here is the history of the small cap effect as best I can measure:

1927-1932: small cap loses -16.9% per year vs -5.6% per year for the S&P 500 as the Great Depression is devastating on all stocks, small in particular
(total annualized return = -16.9% for small/-5.6% for large)

1933-1945: the recovery is much stronger for small and the '37 bear market not as bad, small cap doubles up large +26.1% to +13.2%
(total annualized return = +10.6% for small/+6.9% for large)

1946-1957: Both did well, large did better, +9.5% for small, +13.2% for large
(total annualized return = +10.2% for small/+9.3% for large)

1958-1968: Both did really well, small did outstanding, +22.4% for small, +12.7% for large
(total annualized return = +13.3% for small/+10.2%for large)

1969-1974: Two brutal bears w/i a few years of each other hit small worse than large, -14.3% for small, -3.4% for large
(total annualized return = +9.4% for small/+8.4% for large)

1975-1983: A playback of the 30s recovery, small +30.6%, Large +15.7%
(total annualized return = +12.5% for small/+9.6% for large)

1984-1990: the risk of small shows up, SC earnings never recover from the devastating early '80s recession, Small +5.4%, Large +14.7%
(total annualized return = +11.7% for small/+10.1% for large)

1991-1993: small shows signs of life, Small +28.8%, Large +15.6%
(total annualized return = +12.4% for small/+10.3% for large)

1994-1998: Tech boom helps all but favors large over small, Small +13.0%, Large =+24.1%
(total annualized return = +12.4% for small/+11.2% for large)

1999-2010: in almost a mirror image of the early 80s, small declines less than large and recovers more quickly, Small +9.0%, Large +2.0%
(total annualized return = +12.0% for small/+9.9% for large)

This is why you hear people say they expect to earn 1% or 2% per year for taking the additional risk of small cap stocks
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Post by grayfox »

A Devout Indexer wrote: Here is the history of the small cap effect as best I can measure:
That is interesting data. But it would be a lot easier to visualize if you were able to present it in a chart like Mr Bogle's Telltale chart.

Also, some of the runs of small or large are very long, as much as a decade. Maybe it's best to switch to small after it has had a bad run. Otherwise, you might be disappointed for quite a few years. Like right now, small has had an 11-year run. Time for large?
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Post by MossySF »

grayfox wrote:Also, some of the runs of small or large are very long, as much as a decade. Maybe it's best to switch to small after it has had a bad run. Otherwise, you might be disappointed for quite a few years. Like right now, small has had an 11-year run. Time for large?
"After" is very hard to time. You'd have to switch to it "during" a bad run. Got guts?
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Post by larryswedroe »

Just got back from long trip enjoying NE Canada, and don't have much time but noted this post and did very quick read of the paper to try to provide some perspective. I did not even have to get very far to see the many problems in this paper

First, as others have pointed out, the theory on small is not that it has provided higher risk adjusted returns, just higher returns for the extra risk. And I don't think anyone would debate that small stocks are riskier and should be thus priced to provide higher expected returns. There certainly is no debate in the academic community

Second, the selection of the post Banz period to analyze things is really data mining because it begins right at the tale end of a bubble in small stocks. This would be like saying we look at the equity risk premium beginning in 2000 because everyone has discovered that stocks have provided higher returns so it should go away. Well valuations matter. And valuations of small stocks had reached absurd levels and could not only not be sustained but inevitably had to lead to underperformance

Third, the use of alpha to show higher risk adjusted returns makes no sense to me. That is what is left over after you account for the exposure to small and value.

Fourth, FF never set out to ask if investors were adequately compensated for the risks of small stocks. They simply made that up, which one would have to question then much of the rest of what they say---which IMO is also wrong headed.

Fifth, DFA did not set out to "capitalize" on the small outperformance. What they set out to do was to provide investors who wanted exposure to small stocks the best vehicle to do that. Which even the authors admit they accomplished, outperforming their own benchmark which passive funds are NOT SUPPOSED to be able to do. They generated alpha by intelligent design (screens that eliminated the anomolies that academics had found) and also intelligent trading, being provider instead of taker of liquidity.

Sixth, even if you accepted the idea that small has underperformed since Banz, does that tell you that small stocks are not riskier and thus do not have higher expected returns? That would be like drawing this conclusion:

From 1968 through 2008 (a much longer period than they looked at) US Large Growth stocks returned 8.3% and UNDERPERFORMED LT US Treasuries by 0.4%. Now what conclusion do you draw here? That stocks are safer and thus have lower expected returns?

And that is just some of the problems

Note the small premium has been since 1926 2.3% and that is the small vs large (top half vs bottom half). If we look at say deciles 1-2 and 9-10) then we get much larger difference--the monthly premium has been roughly 50-bp. The annualized returns are 2.8% difference and as they admit one can add alpha to that difference even after expenses as DFA has demonstrated in past.

Here is some further data to show that they are wrong
If they are right then one should see similar patterns internationally
Well since 1970 international small stocks returned annualized 15.1 percent vs 10.1 for EAFE (through July.
And if we begin in 82 there is still a 2.1% outperformance for small

And we also know that in EM the small premium has been huge, and realizable in live data. Since inception in 98 the DFA EMS fund returned, through July, 15.7% vs 11.4% for the EM Index.

FWIW IMO you'll never see this in any academic journal as it would never get past the peer review process. Simply bad paper IMO.
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Post by CaliJim »

Thanks for all the great comments.

Perhaps it is time to cancel my free subscription to FA. :wink:
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If it doesn't provide higher risk-adjusted return...

Post by nisiprius »

larryswedroe wrote:JFirst, as others have pointed out, the theory on small is not that it has provided higher risk adjusted returns, just higher returns for the extra risk.
The obvious question, then, is why one would include small-cap stocks at all? Why not just boost allocation to the total stock market?

Yet the Coffeehouse Portfolio includes a "small blend" slice, and the second step in portfolio construction illustrated in The Quest for Alpha, is to add "Fama-French Small Cap Index." (Which has the effect of increasing both return and standard deviation of the portfolio).

It's hard to believe that the correlation between small-cap and the total market is low enough to offer much diversification benefit. I don't know where to look for long-term results, but assetcorrelation.com shows this for Vanguard Total Stock Market (VTSMX), and DFA Small Cap Portfolio (DFSTX), on the supposition that DFA's might be better or purer than Vanguard's. Do correlations ever get higher than that?

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Post by nisiprius »

This is the SBBI Yearbook data for 1926-2004. Inflation-adjusted, total return (with dividends). (Haven't found a later used copy at a price I can afford, darn it). Endpoint selection is always a problem, but since I'm assuming not very many people would have been in a position to load up on small-company stocks in 1931, to my eyeball it looks as if 1926-1970 they did about the same; from 1980 (the publication of Dr. Rolf W. Banz's paper) to the present they did about the same; essentially all the action happened from 1970-1980 when small-company stocks almost tripled in real value while the S&P 500 was going nowhere.

But then, one of the things I never can quite get my head around is that so often outperformance does occur in concentrated bursts. The question is, for small-company stocks how often are you going to get a fabulous decade? It looks like there was only one of them in about eighty years. Is the theory that you just hang in there, hoping for another, and shrugging if off philosophically if you don't?

The SBBI "large company" data is the S&P 500, and before that, the S&P 90. Their "small company" data is the Rolf W. Banz "fifth quintile of the NYSE" up to 1980, an extension of that methodology up to 1981, and then the DFA Small Company Fund 9/10 Fund thereafter.

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Re: If it doesn't provide higher risk-adjusted return...

Post by yobria »

nisiprius wrote:The obvious question, then, is why one would include small-cap stocks at all? Why not just boost your total stock allocation allocation to the total stock market?
And the obvious answer is that you don't.

Investment books and advisors have to create complex portfolios to get any notice - but that doesn't mean you have to.

Same in many fields - while the human mind craves complexity, there's nothing wrong with simple.

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Re: If it doesn't provide higher risk-adjusted return...

Post by nisiprius »

yobria wrote:
nisiprius wrote:The obvious question, then, is why one would include small-cap stocks at all? Why not just boost your total stock allocation allocation to the total stock market?
And the obvious answer is that you don't.

Investment books and advisors have to create complex portfolios to get any notice - but that doesn't mean you have to.

Same in many fields - while the human mind craves complexity, there's nothing wrong with simple.

Nick
Well, I'm with you, but including just-plain-small-cap (as well as small-cap value) seems to be standard practice for the multi-asset experts. Bill Schultheis' "Coffeehouse Portfolio" includes a 10% slice of "small blend" and the example Larry Swedroe gives in "The Quest for Alpha" shows adding small-cap, as represented by the "Fama/French Small Cap Index," as the second modification to the original 60/40 portfolio--just after adding international.
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Post by Beagler »

Well, to paraphrase Pele, "small-cap stocks have been very, very good to me." YMMV

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Post by Jay69 »

nisiprius wrote:But then, one of the things I never can quite get my head around is that so often outperformance does occur in concentrated bursts. The question is, for small-company stocks how often are you going to get a fabulous decade? It looks like there was only one of them in about eighty years. Is the theory that you just hang in there, hoping for another, and shrugging if off philosophically if you don't?
nisiprius, I have not looked at this nearly as much as you and I admit I'm not smart enough to fiqure out why it does what it does but from my overall high flyover of the subject this is my issue as well. By the time I have enough skin in the game for it to make a difference I'm not going to have enough time left to hope it works. This has been somthing I just cant grasp very well.

Whats one of the Bogleheads rules, dont invest into what you dont understand, I cant get past this point.
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Post by A Devout Indexer »

But then, one of the things I never can quite get my head around is that so often outperformance does occur in concentrated bursts. The question is, for small-company stocks how often are you going to get a fabulous decade? It looks like there was only one of them in about eighty years. Is the theory that you just hang in there, hoping for another, and shrugging if off philosophically if you don't?
Mountain charts are painfully imprecise. My data above shows about what you'd expect from a risk/return relationship: periods of short to intermediate underperformance, but higher returns over time. Of course the timing of the observation matters (starting at the tail end of a small cap "run" leads to smaller subsequent outperformance over the next cycle, say 0.5% to 1.5%, starting at the beginning of a small cap "run" leads to smaller subsequent outperformance over the next cycle, say 3% to 4%).

Why would someone include small cap? As the last decade, or the '66-'82 period shows, a poor run for equities is often aided by above average small cap returns. We know this because beta is not a sufficient proxy for small cap returns: small beats large by more than beta would suggest. This is evidence of a unique risk/return relationship that by definition has a low correlation with other risk/return behaviors (such as stock/bond or long term bond/short term bond). Real returns:

2000-2010
S&P 500 = -2.0%
Small = +4.9%

1966-1982
S&P 500 = 0%
Small = +5.2%

Because the equity risk premium and the size premium have low correlations over medium/long periods, a small tilted allocation has the opportunity for more consistent positive real returns. Of course, adding a value tilt, diversifying globally, and holding a balanced portfolio improves the consistency even further.

Of course, none of this works if you opt for active management, or give up on certain diversification decisions after a poor short/intermediate outcome.
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Re: If it doesn't provide higher risk-adjusted return...

Post by yobria »

nisiprius wrote:Well, I'm with you, but including just-plain-small-cap (as well as small-cap value) seems to be standard practice for the multi-asset experts. Bill Schultheis' "Coffeehouse Portfolio" includes a 10% slice of "small blend" and the example Larry Swedroe gives in "The Quest for Alpha" shows adding small-cap, as represented by the "Fama/French Small Cap Index," as the second modification to the original 60/40 portfolio--just after adding international.
Well all the TSM experts...oh wait, you can't *be* a TSM expert. No writing a book around such a simple strategy.

In seriousness, there's nothing wrong with modestly overweighting small caps:

-Might outperform (look at last 10 years)

-You're still getting 100s of stocks and eliminating some unique risk (better than a single stock).

You might also get some rebalancing benefit. The question is: if you clutter your portfolio with this class, are you really going to rebalance consistently? Did you during the last downturn?

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Post by A Devout Indexer »

If we go back to 1966, we find one raging bull market ('82-'99) where everyone with any equity exposure became fabulously wealthy, bookended by a 17 and 11 year period where a total stock index had 0 and negative real returns, and bonds were flat to mildly positive net of inflation, but global small and value premiums were about double their long term average, likely lifting a balanced portfolio's returns above inflation.

What is the game plan for CAPM/1 factor proponents during the 60% of the time you are losing to inflation? Work forever? Stop spending money? I shudder to think...
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Post by Beagler »

How about microcaps? Rick, among others, has written how microcap stocks appear to exhibit different behavior than large- and small-caps.

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Post by nisiprius »

A Devout Indexer wrote:This is evidence of a unique risk/return relationship that by definition has a low correlation with other risk/return behaviors
Did you look at the assetcorrelations chart? That's not a low correlation, that's close to a perfect correlation.
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Post by yobria »

A Devout Indexer wrote:If we go back to 1966, we find one raging bull market ('82-'99) where everyone with any equity exposure became fabulously wealthy, bookended by a 17 and 11 year period where a total stock index had 0 and negative real returns, and bonds were flat to mildly positive net of inflation, but global small and value premiums were about double their long term average, likely lifting a balanced portfolio's returns above inflation.

What is the game plan for CAPM/1 factor proponents during the 60% of the time you are losing to inflation? Work forever? Stop spending money? I shudder to think...
Note how you switched from past tense in the first paragraph to future in second, as if they were the same.

One of my favorite financial advisor sales techniques. Works with anything: active funds, commodities...smooth and effective.

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Re: If it doesn't provide higher risk-adjusted return...

Post by ObliviousInvestor »

yobria wrote:Well all the TSM experts...oh wait, you can't *be* a TSM expert. No writing a book around such a simple strategy.
I can think of at least two such books I've enjoyed:

http://www.amazon.com/Bogleheads-Guide- ... ads.org-20

http://www.amazon.com/Second-Grader-Bea ... ads.org-20
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Post by A Devout Indexer »

nisiprius wrote:
A Devout Indexer wrote:This is evidence of a unique risk/return relationship that by definition has a low correlation with other risk/return behaviors
Did you look at the assetcorrelations chart? That's not a low correlation, that's close to a perfect correlation.
Your chart shows monthly correlation figures, which are far less meaningful for a long term investor than the intermediate/long term behavior between the market and the separate risk/return behavior of small minus large, which shows the additional return above the market (more or less) for tilting to small--which is all we care about. Does a small tilt add anything beyond adjusting the stock/bond mix?

For example, you see 0.9 monthly correlations, I see $1 growing to $1.01 in the total stock index and $1.42 in the small cap fund when adjusted for inflation. If that looks like identical or similar results to you, then we will agree to see it differently.

If small cap diversification was not a separate risk/return behavior, but instead an extension of the equity premium, you would expect to be able to just lever up a market portfolio and get the same risk and return, but clearly this is not the case.
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Re: If it doesn't provide higher risk-adjusted return...

Post by yobria »

ObliviousInvestor wrote:
yobria wrote:Well all the TSM experts...oh wait, you can't *be* a TSM expert. No writing a book around such a simple strategy.
I can think of at least two such books I've enjoyed:

http://www.amazon.com/Bogleheads-Guide- ... ads.org-20

http://www.amazon.com/Second-Grader-Bea ... ads.org-20
Ok ok, it can be done :)

You just aren't going to make much money without the complexity/free lunch framework.

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Post by nisiprius »

OK, long-term. Here are the SBBI data again, 1926-2004. There are the annual percentage returns for their "small stocks" versus their "large stocks." The correlation coefficient is 0.76. So, for the multi-asset mavens, what's the rule of thumb on what's considered low enough to contribute an important amount of diversification?

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Post by Jay69 »

nisiprius

Could you help me with your chart? I understand what the correlation coefficient of 0.76 is but not how we got there with the chart.

I assume each dot/diamond is one year where do we go from there?
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Post by ObliviousInvestor »

Jay69 wrote:nisiprius

Could you help me with your chart? I understand what the correlation coefficient of 0.76 is but not how we got there with the chart.

I assume each dot/diamond is one year where do we go from there?
The fact that it kinda-sorta looks like an upward sloping line tells us there's positive correlation. (But the fact that it is still somewhat scattered tells us that correlation isn't perfect.)

If there was no correlation, it'd be a completely scattered mess.

If there was negative correlation, it'd be downward sloping.
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Re: If it doesn't provide higher risk-adjusted return...

Post by asset_chaos »

nisiprius wrote:
larryswedroe wrote:JFirst, as others have pointed out, the theory on small is not that it has provided higher risk adjusted returns, just higher returns for the extra risk.
The obvious question, then, is why one would include small-cap stocks at all? Why not just boost allocation to the total stock market?
Perhaps a couple of reasons. Higher absolute returns, if you're willing to stand the extra risk. And risk here is measured as higher standard deviation. As I recall Bogle writing (but can't specify a reference so am paraphrasing) on standard deviation as risk, one percent extra of annual standard deviation is meaningless in the long run but one percent extra of annual return is priceless.
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Post by DetroitRed »

Isn't there a big "data availability" problem with looking at small cap returns before mid-1962? Namely, that CRSP didn't include AMEX stocks until 7/2/62.

That seems to me to be a huge gap. Back then AMEX was known for having lots of small cap stocks (NASDAQ didn't exist and NYSE had very stringent listing requirements).

Here's an example of well-known companies that were on AMEX as of 7/2/62, which means that prior to that time their stock return data was not included in CRSP:

SHERWIN WILLIAMS
BROWN FORMAN DISTILLERS (Jack Daniel’s)
NORFOLK SOUTHERN RAILWAY CO
OCCIDENTAL PETROLEUM
PEP BOYS MANNY MOE & JACK
PARKER PEN CO
STOP & SHOP INC
ZALE JEWELRY CO
Last edited by DetroitRed on Tue Sep 13, 2011 4:11 pm, edited 2 times in total.
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Post by nisiprius »

Jay69 wrote:nisiprius

Could you help me with your chart? I understand what the correlation coefficient of 0.76 is but not how we got there with the chart.

I assume each dot/diamond is one year where do we go from there?
The chart doesn't actually show that. I used Excel to calculate the correlation coefficient and typed that in on the chart. I know what I calculated, by the way, but I don't really know whether it's precisely the same number the financial mavens calculate.

Mike Piper has explained it well. The only thing to be added is that in this posting you'll see what a similar chart looks like when the correlation is close to zero--a round, stippled blob, what Mike called a "completely scattered mess." And a Google search turns up this chart which shows what a very high correlation, 0.97, looks like:

Image
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Re: wow

Post by jeffyscott »

larryswedroe wrote:Second, the selection of the post Banz period to analyze things is really data mining because it begins right at the tale end of a bubble in small stocks.
But their purpose is to determine whether the "anomaly" disappeared after being discovered, so it makes sense to look at that period.

From 1926-1981 they have S&P 500 at 12.46% annualized and CRSP 9-10 at 9.15%. Then from 1982-2010 S&P 500 is 11.3% and CRSP 9-10 is 11.6%, so small barely beat large and one had to endure a SD of about 35% for small vs. about 20% for large to get that tiny increment of additional return.

The small difference in returns can be seen by looking at the maximum period for DFSCX here:

http://quote.morningstar.com/fund/chart ... %2C0%22%7D

However, it does look like the S&P 500 had one big bubble in the 1990s that small avoided, while small had more shorter term volatility throughout the period
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Post by larryswedroe »

Yes I understand that BUT as I said it is like examining the equity risk premium after 1999. STARTING VALUATIONS matter. It made no difference whatsoever that BANZ's paper was published, the fact is small caps were doomed to underperform for while after that because valuations were so high---same way growth stocks were doomed to underperform from 2000 on because valuations were too high.

So starting from that point is POINTLESS, demonstrates nothing really.

And as I said, you have 40 years of stocks underperforming Treasuries--what did that tell you? That risks showed up, not that stocks have lower expected returns--at least I would hope so.

And for Japanese investors over last 20+ years, do you think that shows that Japanese stocks have lower expected returns and must therefore be safer investments?

Best
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Multi factor Considerations

Post by A Devout Indexer »

nisiprius wrote:OK, long-term. Here are the SBBI data again, 1926-2004. There are the annual percentage returns for their "small stocks" versus their "large stocks." The correlation coefficient is 0.76. So, for the multi-asset mavens, what's the rule of thumb on what's considered low enough to contribute an important amount of diversification?

Image
Well, here is how I look at it:

#1 = determine the source(s) of returns for stocks and bonds

Fama/French and others make a compelling case for 5 distinct factors in securities returns (stock/bond; within the stock market small/large and value/growth, within the bond market corporate/government and long-term/short-term)

#2 = observe how those return sources covary with one another

Over 1 year periods the stock/bond factor has a 0.39 correlation with the small premium, 0.11 with the value premium, 0.32 with the credit factor and 0.02 with the interest rate factor.
Over 5 year periods the stock/bond factor has a 0.04 correlation with the small premium, 0.08 with the value premium, -0.01 with the credit factor and 0.06 with the interest rate factor.
Over 10 year periods the stock/bond factor has a -0.35 correlation with the small premium, -0.08 with the value premium, -0.15 with the credit factor and 0.11 with the interest rate factor.

So we see over very short periods, a good (bad) year for stocks signals a positive (negative) return for small over large and corporates over government bonds, and a coin-flip for value/growth and long-term/short-term.

Over long periods a good (bad) stretch for stocks signals a negative (positive) return for small over large, value over growth, corporates over government bonds, and long-term over short-term.

Of course, over time we'd expect (but aren't assured) that all return/risk factors will be positive, so a multi factor portfolio should have the highest returns over time. But because the payoffs have low to negative correlations over sufficiently long periods, we will see a smoothing effect as some risks payoff in a big way to offset some risks producing negative returns. You can think of this as a multi-factor Modern Portfolio Theory.

For example, based on a post I made last night, I found that despite a negative return to the stock/bond factor for the last decade (Russell 3000 minus 1-3 yr t-notes), we have seen a 1% additional value premium, a 4% size premium, a 1% credit premium, and a 4% interest rate premium (source: MSCI indexes for stocks, Barclays for bonds).

Is a portfolio that is diversified across stock/bond + the additional 4 risk/return factors "riskier" than a 1 factor portfolio? Well, it has exposure to more risks, so yes. But to the extent that each risk has low to negative correlations with one another, I'd expect a multi factor allocation to have less portfolio risk than the weighted average of the individual risks with a portfolio return as high as the total exposure to each risk/return.

#3 = determine which of those sources you want to gain exposure to (just because they exist, doesn't mean you should exposure yourself to them), and find the best vehicles to capture the desired effects

Here you should use index funds exclusively where possible, with Vanguard funds/ETFs the primary option with iShares providing a good secondary option.
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Post by A Devout Indexer »

To provide some clarity using a portfolio example, lets use two 60/40 balanced allocations.

(a) is a traditional "CAPM" 1 factor allocation that is 30% Russell 3000, 30% MSCI EAFE, and 40% 1mo t-bills. No additional size/value exposure on the equity side, no additional term/credit risk on the bond side.

(b) is a multifactor portfolio that is 10% Russell 3000, 10% Russell 3000 Value, 10% Russell 2000, 15% EAFE Value, 15% Int'l Small Cap, and 40% Barclays 1-10yr Government/Credit Index

From 1979 through 2010, (a) has generated a real return of 5.2% per year with an annual standard deviation of 10.8. (b) has returned 7.0% per year with an annual standard deviation of 10.9.

Portfolio (a) saw 2 different 10 year periods of negative returns, portfolio (b) saw no negative 10 year periods, and only 2 periods with real returns of less than 4% per year.
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Post by SVariance1 »

I agree with those that say this article is seriously flawed. What stands out to me is the author stating there is a theory that small cap stocks have higher risk adjusted returns compared to large cap stocks. Not sure where they got this from. I think they are mixing up two different concepts: small cap stocks having higher absolute returns and small cap value stocks having higher risk adjusted returns.
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Post by larryswedroe »

to my knowledge NO ONE has ever claimed that small has had higher risk adjusted returns, never. These guys IMO have simply made up things, and more than just this one, as I pointed out.
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Post by nisiprius »

larryswedroe wrote:to my knowledge NO ONE has ever claimed that small has had higher risk adjusted returns, never.
So, if small-cap stocks don't have better risk-adjusted return, why add them, rather than simply increasing overall equity allocation?
Last edited by nisiprius on Tue Sep 13, 2011 8:41 pm, edited 1 time in total.
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Re: Multi factor Considerations

Post by nisiprius »

A Devout Indexer wrote:But to the extent that each risk has low to negative correlations with one another...
Does an 0.76 correlation, as shown in the chart I presented, count as "low to negative correlation?"
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Post by natureexplorer »

There is no true measure of risk, not even in hindsight.
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Re: Mike

Post by grok87 »

larryswedroe wrote:to my knowledge NO ONE has ever claimed that small has had higher risk adjusted returns, never. These guys IMO have simply made up things, and more than just this one, as I pointed out.
On the other hand, perhaps small value stocks do have better risk adjusted returns? i.e. is the small value premium not fully explained by risk?
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Post by ftobin »

nisiprius wrote:
larryswedroe wrote:to my knowledge NO ONE has ever claimed that small has had higher risk adjusted returns, never.
So, if small-cap stocks don't have better risk-adjusted return, why add them, rather than simply increasing overall equity allocation?
I think Larry is going say something like this:

You need to look at the entire portfolio. Two asset classes that have lower risk-adjusted return combined can have greater risk-adjusted return than either one individually. Think of a roulette table whose odds are actually in favor of the player, and numbers are different asset classes. Randomly putting chips on half the numbers has the same expected return as putting all your bets on just one, but with lower risk/volatility. Random chip placement is kind of like lower-correlated assets.

It's hard to stretch the analogy to allow that you allow that some numbers have better return but their odds don't fully reflect the greater risk, but hopefully this paints the picture.
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nisprius

Post by larryswedroe »

First, as I have explained several times, when one owns TSM one only has exposure to one unique or independent risk factor. While owning small stocks there is no exposure to the small risk factor, because the exposure you get from those stocks is offset exactly by the negative exposure large caps have to that risk factor

Second, by adding small caps you add a unique/independent risk factor, one with low correlation to beta risk. That provides a diversification benefit. Markowitz showed that when you add unique risk factors the portfolio can be more efficient if the correlations are less than one. Also one simply may want to have exposure to higher expected returning asset class than TSM is, and it is more efficient to raise expected returns that way than via using leverage, which has costs and risk of margin calls.

For Grok, here again we have the debate about value, is it risk, behavioral or some of both. IMO the evidence comes down pretty strongly that there is risk story (if there wasn't then why would value due much worse in this crisis as one good example). But there is also some good evidence on behavioral story. So IMO it seems likely it is some of both.
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Post by pauliec84 »

I think Larry is going say something like this:

You need to look at the entire portfolio. Two asset classes that have lower risk-adjusted return combined can have greater risk-adjusted return than either one individually. Think of a roulette table whose odds are actually in favor of the player, and numbers are different asset classes. Randomly putting chips on half the numbers has the same expected return as putting all your bets on just one, but with lower risk/volatility. Random chip placement is kind of like lower-correlated assets.

It's hard to stretch the analogy to allow that you allow that some numbers have better return but their odds don't fully reflect the greater risk, but hopefully this paints the picture.
This is the idea that we measure risk not by the asset-specific risk, but the risk it adds to the portfolio. This is the basic idea of beta, and the covariance models. CAPM, APT/Fama French.
Per Larry:
to my knowledge NO ONE has ever claimed that small has had higher risk adjusted returns, never. These guys IMO have simply made up things, and more than just this one, as I pointed out.
Small-Cap does add more return then the at least its CAPM Beta implies. This is the small-cap puzzle. So I think at least a few people, who believe contribution to a portfolio's variance is the definition of risk, would say that small cap provides positive risk adjusted returns.
There is obviously a camp saying that there are risks other then portfolio variance, that small-cap captures (ie recession or human capital risk), but that is not EVERYBODY.
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Re: nisprius

Post by yobria »

larryswedroe wrote:First, as I have explained several times, when one owns TSM one only has exposure to one unique or independent risk factor. While owning small stocks there is no exposure to the small risk factor, because the exposure you get from those stocks is offset exactly by the negative exposure large caps have to that risk factor
This, again is combining a real risk factor (equity risk) with a couple of historical patterns as if they were on the same terms.

We can play this game an infinite number of ways: I'm sure utility stocks (U), and stocks with women CEOs (W) have had unique risk/return properties over some historical period.

I am therefore declaring that there are three risk factors: equity, utility, and women. My three factor model: Rf+Eq+U+W

If you're not overweighting utility and women run companies, you're only capturing one factor! I mean, you might as well give your money to charity.

Anybody know of a good EM UW fund?

Nick
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