Do Small Caps Outperform?

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nisiprius
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Re: Do Small Caps Outperform?

Post by nisiprius » Tue Jun 12, 2018 10:11 pm

nisiprius wrote:
Tue Jun 12, 2018 10:09 pm
vineviz wrote:
Tue Jun 12, 2018 8:49 pm
nisiprius wrote:
Tue Jun 12, 2018 8:29 pm
vineviz wrote:
Tue Jun 12, 2018 8:09 pm
nisiprius wrote:
Tue Jun 12, 2018 4:41 pm
So?
The probability of success is one of the most important pieces of information you need when evaluating uncertain events (like stock market returns). Payoff and costs are the other two big ones.
But, by your own chosen metric, leveraged large-caps would have been superior to small-caps. If "success" is defined as "outperforming (unleveraged) large caps over rolling 20-year periods," small-caps succeeded 64/73 = 88% of the time, but leveraged large-caps succeeded 73/73 = 100% of the time.
What does that have to do with anything? It's the answer to a question no one asked.

The title of this thread isn't "imagine some investment strategy that will outperform small cap stocks".
My point is that we have to begin by deciding whether we are interested in risk-adjusted return or just return. Banz originally said that small-caps had had higher risk-adjusted return, and I think that's what we should be discussing. If small-cap advocates now concede that small-caps longer seem to have had higher risk-adjusted return, and are falling back on saying "but they have had higher return," all I can say is that is not an interesting fact. If we do not care about risk, then we should all be using leverage. By your own chosen metric (percentage of times small caps outperformed large-caps over rolling 20-year periods) leverage is better than using small-caps. That throws into doubt the idea that small-caps have any special virtue beyond simply being riskier.

Maybe I should make it clear that I am not, not, not suggesting that anyone should be using leveraged large caps. My point is that if you ignore risk, that's where logic takes you.

Perhaps the most valid argument for small-caps applies to those who are at 100% stocks and still want more risk. In that case, it certainly seems as if going to 100% small-caps is a way of approximating the effects of leverage without the costs or the downside risks.
Last edited by nisiprius on Wed Jun 13, 2018 7:27 am, edited 2 times in total.
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David Jay
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Re: Do Small Caps Outperform?

Post by David Jay » Tue Jun 12, 2018 10:16 pm

vineviz wrote:
Tue Jun 12, 2018 8:09 pm
nisiprius wrote:
Tue Jun 12, 2018 4:41 pm
But even the small-cap premium itself has been challenged. I admit to leaning on authority, and we could certainly find authorities on the other side... but the existence of a small-cap premium has been challenged by some authorities.
There are people who think the earth is flat, too, but I prefer not to pay them any more attention than I must.
First it was “Mount Everest isn’t an Ocean” strawman for those who were engaging you on the diversification thread. Now those who are engaging you here are flat-earthers. You show serious disrespect for those with whom you have choosen to engage. No one forced you to come on BH and bestow your wisdom on us.
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius

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Re: Do Small Caps Outperform?

Post by JoMoney » Wed Jun 13, 2018 12:03 am

vineviz wrote:
Tue Jun 12, 2018 8:22 pm
JoMoney wrote:
Tue Jun 12, 2018 1:42 pm
FWIW, Prof. Siegel's small-cap stock data set is different then what Ibbotson or Fama-French small-cap use (I believe his is something like the bottom 20% of the NYSE spliced to the Russell 2000)...
Regardless, these were not investable portfolios / funds and the longest time period is retroactively reconstructed. We do have the DFA fund DFSCX since 1981, and it's portfolio (which has more nuances then a strict percentage of the market) and over the 36.5 years since it's been around it managed to eek out an extra 0.55% annualized over Vanguard's 500 index fund.
That's not nothing, especially after expenses.

Besides, today we have dozens of choices that are entirely investable besides DFSCX many of which have much lower expenses. Look at $10,000 put into any number of ETFs since their inception versus the same money put into VFINX on the same date:

IJR $60,858 vs VFINX $25,539
IWM $43,334 vs VFINX $26,539
VB $38,688 vs VFINX $31,635
JKL $35,571 vs VFINX $32,227
SLY $$35,167 vs $27,768
... the past 18 years was a good period for small-caps, add in a roughly similar period before that and it's a net zero (or worse)!
Chart
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Culbretd
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Re: Do Small Caps Outperform?

Post by Culbretd » Wed Jun 13, 2018 1:23 am

nisiprius wrote:
Tue Jun 12, 2018 9:50 pm
Culbretd wrote:
Tue Jun 12, 2018 9:27 pm
nisiprius wrote:(things)
...You still haven’t answered why you compared the Russell 2000 index to the S&P 500 index...
That wasn't me. I never made any such comparison.
Whoops... sorry. Got confused trying to type the response out on my phone. Thought you were OP? My eyes are getting bad and I’m getting old... either way my fault I got really confused for a minute there.

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Re: Do Small Caps Outperform?

Post by nisiprius » Wed Jun 13, 2018 7:18 am

Culbretd wrote:
Tue Jun 12, 2018 9:27 pm
...You still haven’t answered why you compared the Russell 2000 index to the S&P 500 index...
That wasn't me. I never made any such comparison.
Whoops... sorry. Got confused trying to type the response out on my phone. Thought you were OP? My eyes are getting bad and I’m getting old... either way my fault I got really confused for a minute there.
No offense taken, just thought I should mention it.
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Re: Do Small Caps Outperform?

Post by JohnDindex » Wed Jun 13, 2018 7:44 am

nisiprius wrote:
Tue Jun 12, 2018 10:09 pm
vineviz wrote:
Tue Jun 12, 2018 8:49 pm
nisiprius wrote:
Tue Jun 12, 2018 8:29 pm
vineviz wrote:
Tue Jun 12, 2018 8:09 pm
nisiprius wrote:
Tue Jun 12, 2018 4:41 pm
So?
The probability of success is one of the most important pieces of information you need when evaluating uncertain events (like stock market returns). Payoff and costs are the other two big ones.
But, by your own chosen metric, leveraged large-caps would have been superior to small-caps. If "success" is defined as "outperforming (unleveraged) large caps over rolling 20-year periods," small-caps succeeded 64/73 = 88% of the time, but leveraged large-caps succeeded 73/73 = 100% of the time.
What does that have to do with anything? It's the answer to a question no one asked.

The title of this thread isn't "imagine some investment strategy that will outperform small cap stocks".
My point is that we have to begin by deciding whether we are interested in risk-adjusted return or just return. Banz originally said that small-caps had had higher risk-adjusted return, and I think that's what we should be discussing. If we now concede that no longer seem to have had higher risk-adjusted return, and are falling back on saying "but they have had high return," all I can say is that is not an interesting fact. If we do not care about risk, then we should all be using leverage. By your own chosen metric (percentage of times small caps outperformed large-caps over rolling 20-year periods) leverage is better than using small-caps. That throws into doubt the idea that small-caps have any special virtue beyond simply being riskier.

Could you elaborate on why using leverage would be more favorable than over weighting small? Do you consider leverage to be actual margin/gearing your account, or having a 30 year mortgage on a home and pushing extra money into stocks that otherwise would have reduced debt?

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Re: Do Small Caps Outperform?

Post by vineviz » Wed Jun 13, 2018 7:58 am

nisiprius wrote:
Tue Jun 12, 2018 10:09 pm
My point is that we have to begin by deciding whether we are interested in risk-adjusted return or just return. Banz originally said that small-caps had had higher risk-adjusted return, and I think that's what we should be discussing.
I'll address this by expanding on something I said earlier: we should NOT be interested in the risk-adjusted returns of individual assets (or asset classes) unless we intend to hold them in a single-asset portfolio.

No one (here) does that: we own diversified portfolios comprised (we hope) of different assets which are not perfectly correlated. Therefore, the point at which we measure and evaluate risk-adjusted return is at the PORTFOLIO level and not at the asset level.

What matters is the portfolio performance, which is driven by both the volatility and return of the individual assets AND their correlation.

Here's an example to make it as clear as I can. From 1979 to 2018, according to Portfolio Visualizer, here are the Sharpe Ratios for each of the Ibbotson asset indexes ranked from lowest to highest:
  • (0.16) IA SBBI US 30 Day TBill
  • (0.40) IA SBBI US LT Government
  • (0.46) IA SBBI US LT Corporate
  • (0.47) IA SBBI US IT Government TR
  • (0.52) IA SBBI US Small Stock
  • (0.54) IA SBBI US Large Stock
None of these has a higher risk-adjusted return than large stocks, but we all know better than to infer from that we should have portfolios that are 100% large cap stocks.

We hold a mix of different types of bonds and money market funds as part of a diversified portfolio, and I'm sure the reason is already obvious to you: mixing uncorrelated assets that have lower risk-adjusted returns than large caps with those large caps can IMPROVE the risk-adjusted returns of the overall portfolio. In fact, in this example, a naive (equal-weighted) portfolio of those six assets had a Sharpe ratio of 0.71.. Even if you left the large caps out altogether, the other five assets combined in equal weights had a Sharpe ratio of 0.68.

And to go one step further, something we know about asset prices is that their volatilities and correlations have been a lot more stable across time than their returns have been. For all intents and purposes, if small caps are outperforming large caps in a particular time period on an absolute basis, they probably are doing so on a risk-adjusted basis as well. Maybe not always, but usually.

This is critically important, because if we start demanding that EACH holding in our portfolio have the highest Sharpe ratio among all available assets, we end up with a portfolio full of recent winners instead of a Bogleheaded portfolio built with a diverse and sensible array of asset classes.
Last edited by vineviz on Wed Jun 13, 2018 8:25 am, edited 1 time in total.
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Re: Do Small Caps Outperform?

Post by SimpleGift » Wed Jun 13, 2018 8:11 am

vineviz wrote:
Wed Jun 13, 2018 7:58 am
Therefore, the point at which we measure and evaluate risk-adjusted return is at the PORTFOLIO level and not at the asset level.
:thumbsup Excellent post, with a very cogent explanation. Thanks.
Cordially, Todd

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Re: Do Small Caps Outperform?

Post by nisiprius » Wed Jun 13, 2018 10:45 am

Vineviz, how did you access the Ibbotson Associates data in PortfolioVisualizer?

I'm going to present some data that partly supports, partly contradicts my point of view.

Here's the thing. Yes, of course it is true that under some circumstances, and using the MPT/CAPM framework, you can get portfolios with higher Sharpe ratios than any of the portfolio constituents. I get that.

The big question to my mind is this. For the special case of "stocks and bonds," we have robust behavior, due to the fact that they derive their return from fundamentally different sources. It is not just a case of extrapolating from past data. In particular, stocks and bonds have had close to zero correlation--not just imperfect correlation, but seriously low correlation--over just about any time period you look at... while bonds have had an decent positive return over just about any time period you look at. For stocks versus bonds, the diversification benefit virtually always exists and we have high conviction that it will persist going forward. (Indeed, one of the debates is whether we should expect bonds to show negative correlation with stocks, or "merely" zero).

The slice-and-dicers would have us believe that you can get extra, similarly robust and valuable benefits by looking inside the universe of a single major asset class, stocks, and pulling out subsets of a single asset class--which are then rechristened as "asset classes" in themselves--according to various filtering criteria. And the argument is made that there will almost automatically be improvement as long as the asset classes have "imperfect" correlation, therefore it is almost a sure thing that well-chosen lumpy weighting will improve the portfolio as a whole.

Now, I can't reproduce your example exactly, but pretty close. As you will see, the results I get do not completely confirm my point of view, but they support it partially. My point of view, or bias, is that the MPT magic (the whole is better than any of its parts, measuring by Sharpe ratio) is large and robust for the specific case of stocks and bonds--but tenuous, feeble, and capricious (e.g. with regard to choices of endpoints, indexes, etc.) for subclasses within the major asset classes.

(I have to say, though, that I don't understand how 30-day Treasury bills can have an 0.16 Sharpe ratio. I wonder what source they are using for the "riskless asset?" Oh, OK, I see: "1-month Treasury Bills 1972+" Nope, I still can't get it; if I use CASHX instead of the SBBI bills data I still get a virtually zero Sharpe ratio for bills. Well, never mind. I repeated my analysis using CASHX instead of Treasury bills and the numbers are the same to within roundoff error).

Here's the thing. In your example, you used a 6-way equal weight portfolio of two stock assets and four bond assets. I'm going to claim that most of the improvement can be attributed to the diversification between both stocks and bonds, and that little of it came from diversification within the stock classes or within the bond classes.

I am getting these Sharpe ratios, 1979 through 2017 inclusive Mine are in square brackets, yours in parentheses. I think they are close enough.
  • [0.00](0.16) IA SBBI US 30 Day TBill
  • [0.39](0.40) IA SBBI US LT Government
  • [0.48](0.46) IA SBBI US LT Corporate
  • [0.40](0.47) IA SBBI US IT Government TR
  • [0.54](0.52) IA SBBI US Small Stock
  • [0.54](0.54) IA SBBI US Large Stock
For your six-way equal-weighted portfolio I get 0.75, you got 0.71.

So I feel that I've reproduced your results pretty well. I'm using annual data; differences might be due to your using monthly data.

However: if I ask "well, what if we just use 33.3% large-cap stocks and 66.7% long-term government bonds," i.e. diversifying between stocks and bonds but not diversifying within either asset class?" I get 0.64.

So, not using within-class diversification I still get the result that the portfolio Sharpe ratio is higher than that of any of its components. Just using stocks and bonds adds +0.10 to the Sharpe ratio for stocks. Going to your 6-way split adds an additional +0.11.

Notice that this sort of half-confirms, half-contradicts my point of view. You can spin it either way. For these date endpoints and these data sets, yes, you got an extra increment in Sharpe ratio by using multiple asset subclasses within each asset class.

But in any case, stocks/bonds was a big deal, and just including both stocks and bonds made the whole-is-better-than-any-of-its-parts magic happen.

For a two-way portfolio of large and small stocks, I get 0.58 for the Sharpe ratio. So, in a portfolio of stocks alone, the diversification within stocks adds 0.04 to the Sharpe ratio. Yes, a little magic, but considerably less.

For a four-way portfolio of the four bond classes, I get 0.43 for the Sharpe ratio, which is higher than that two of the constituents (long-term and intermediate-term government) but lower than long-term corporate. The magic did not happen here.

In other words, the MPT-and-Sharpe-ratio case for including both stocks and bonds in portfolios is very good, but the case for departing from the total market portfolio by "diversifying" into lumpy weighting of subclasses within stocks, or with bonds, is much less clear.
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Re: Do Small Caps Outperform?

Post by vineviz » Wed Jun 13, 2018 12:01 pm

nisiprius wrote:
Wed Jun 13, 2018 10:45 am
Vineviz, how did you access the Ibbotson Associates data in PortfolioVisualizer?
I exported the returns from Morningstar, imported those into Portfolio Visualizer, and saved them as asset classes and benchmarks.
nisiprius wrote:
Wed Jun 13, 2018 10:45 am
In other words, the MPT-and-Sharpe-ratio case for including both stocks and bonds in portfolios is very good, but the case for departing from the total market portfolio by "diversifying" into lumpy weighting of subclasses within stocks, or with bonds, is much less clear.
This is something I think we agree on. I might use the word "important" instead of "clear", but we get to the same place.

Apart from making a choice about when and how much to save, I think that the most important investment choice the typical investor can make is their stock/bond allocation. This decision is at least twice as important as the next most important decision an investor must make.

I'm using "important" to refer to the expected impact on the portfolio's likelihood of meet the investor's goals.

After the equity/fixed income decision, I think the next important decision is the US/foreign equity allocation and/or the bond duration choice.

Only after that, in my opinion, do the other equity risk factors (e.g. size, value, momentum, quality, BaB) become worth thinking about.

I have concluded that those factors are worth considering, but only after the other considerations have been addressed.
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Re: Do Small Caps Outperform?

Post by BritishInvestor » Thu Jun 14, 2018 5:55 am

One thing that is not clear to me is that the choice of benchmark seems to make a difference as to how much small cap has outperformed (when looking at just last 5 years) purely in terms of returns, not risk adjusted

If I look at Vanguard Global Small Cap (as my username suggests, I'm using UK available funds, not sure if these are available globally in some form) - which has the benchmark MSCI Small Cap World Index

http://www.morningstar.co.uk/uk/funds/s ... 5OPT&tab=2

I see a 5 year annualised return of 15.32 (in GBP). Appreciate that this fund excludes emerging markets (which is approx. 8% of global IIRC, happy to be corrected) which has unperformed DM over the period, but even adjusted for this shows excess returns of around 1.5% when compared to Vanguard FTSE all world (DM and EM, large and mid cap) which has a 5 year return of 13.36

http://www.morningstar.co.uk/uk/etf/sna ... 0P0000WAHE

However, the difference is not quite so clear when comparing FTSE indices, which shows 10.2 vs 9.6 (assume USD) in small caps favour.

http://www.ftse.com/Analytics/FactSheet ... ame=GEISSC

(appreciate Global All Cap will include small, but surely this is a small percentage of all cap?)

Am I missing something obvious?

dcabler
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Re: Do Small Caps Outperform?

Post by dcabler » Thu Jun 14, 2018 9:18 am

BritishInvestor wrote:
Thu Jun 14, 2018 5:55 am
One thing that is not clear to me is that the choice of benchmark seems to make a difference as to how much small cap has outperformed (when looking at just last 5 years) purely in terms of returns, not risk adjusted

If I look at Vanguard Global Small Cap (as my username suggests, I'm using UK available funds, not sure if these are available globally in some form) - which has the benchmark MSCI Small Cap World Index

http://www.morningstar.co.uk/uk/funds/s ... 5OPT&tab=2

I see a 5 year annualised return of 15.32 (in GBP). Appreciate that this fund excludes emerging markets (which is approx. 8% of global IIRC, happy to be corrected) which has unperformed DM over the period, but even adjusted for this shows excess returns of around 1.5% when compared to Vanguard FTSE all world (DM and EM, large and mid cap) which has a 5 year return of 13.36

http://www.morningstar.co.uk/uk/etf/sna ... 0P0000WAHE

However, the difference is not quite so clear when comparing FTSE indices, which shows 10.2 vs 9.6 (assume USD) in small caps favour.

http://www.ftse.com/Analytics/FactSheet ... ame=GEISSC

(appreciate Global All Cap will include small, but surely this is a small percentage of all cap?)

Am I missing something obvious?
It's not just a benchmark, it's an actual index. Even here in the US, three are numerous indices which track small cap and each index owner has their own definition of exactly what small cap means. No reason to believe its any different for international small caps.

Examples: https://www.bogleheads.org/wiki/US_smal ... ex_returns

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