"Indexing Can Capture Small-Cap Premiums"

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gkaplan
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"Indexing Can Capture Small-Cap Premiums"

Post by gkaplan » Thu Sep 07, 2017 5:58 pm

Small caps won't always outperform but small-cap index investing is something investors should consider, says Craig Lazzara of S&P Dow Jones Indices. . . .

http://news.morningstar.com/cover/video ... ?id=824846
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Sat Sep 30, 2017 7:50 pm

I have owned an S&P 600 Small-Cap Index ETF since September 2004 and I have been quite please with it. I also own the Vanguard Small-Cap Value Index ETF, which I purchased in October 2008, and I have been very happy with that investment too. I have been a big believer in Small/Mid-Cap investing for many years. Obviously, I am a believer in the size premium that favors smaller stocks.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nisiprius » Sun Oct 01, 2017 1:13 pm

Disappointing in two respects. It talks only about the existence of a small-cap "premium," and not at all about whether small-caps have a higher risk-adjusted return or whether the premium is simply compensation for risk. If it is only compensation for risk, then the next question is whether it has a low enough correlation with the market as a whole to have value as a diversifier. (Unlikely in my opinion, but if the justification for small-caps is low-correlation and diversification, that should be stated and supported).

The second disappointment is that it supports the claims specifically by mentioning "the Ibbotson Sinquefield Database in, I think, 1926." But according to the SBBI Ibbotson SBBI Classic Yearbook, the data from 1926-1981 are "represented by the historical series developed by Professor Rolf W. Banz." The reference is to the actual paper published by Banz in 1981, and I can't find any indication that this data has been adjusted or corrected. In 1999 researchers Shumway and Warther said that the Banz data was affected by delisting bias. I think it's widely acknowledged that Banz's data exaggerated the size effect (and I think the CRSP data has actually since been adjusted to correct for that).

In other words, Lazzara fails to say whether he's merely talking about a small-cap premium that does no more than compensate for higher risk, or whether small-caps actually have higher risk-adjusted return. And he specifically mentions a data set that may be misleading, without clarifying.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Sun Oct 01, 2017 1:20 pm

My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by rkhusky » Mon Oct 02, 2017 7:21 am

nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
I don't recall risk being a part of the Fama-French formulation. I thought it simply computed correlations between time series of returns.

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Re: "Indexing Can Capture Small-Cap Premiums"

Post by triceratop » Mon Oct 02, 2017 7:41 am

nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
As mentioned above, the Size factor can exist without having a higher risk adjusted return than the broad stock market. Its existence just means it is necessary to fully explain overall returns (i.e. what is the expected return for a company with a certain beta, a certain size, and a certain fundamental/book value).

Of course, less than perfectly correlated assets can improve the efficiency at a portfolio level.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nisiprius » Mon Oct 02, 2017 8:37 am

triceratop wrote:
Mon Oct 02, 2017 7:41 am
...less than perfectly correlated assets can improve the efficiency at a portfolio level...
IF certain conditions apply, and they often don't, or not very strongly. Yes, they can... IF the the correlation between the proposed diversifier and the rest of the portfolio is low enough. How low does it need to be? It needs to be less than the lower Sharpe ratio of the two divided by the higher Sharpe ratio of the two.

For example... I am putting this forward as a specific case, showing how the relationship works over one period of time, not making any statements about expectations or the long run. I picked this specific time period to illustrate a point about how the math works. Please focus on the specific question: why didn't DFSCX improve the portfolio despite having imperfect correlation?

Over the time period Jan 2004 - Sep 2017, I compared
portfolio 1, blue, 100% Vanguard Balanced Index Fund, VBINX.
portfolio 2, red, with a small-cap tilt, 80% Vanguard Balanced Index Fund, 20% DFA Micro Cap Portfolio DFSCX.

Source and results

CAGR was increased from 7.05% to 7.55%. I don't know how much of that was the "size premium" and how much of that was simply a result of the increased stock allocation, but, at any rate, it increased. And, there was "imperfect correlation," the correlation being 0.91.

And, yet, it did not improve the portfolio as measured by the Sharpe ratio, which declined from 0.71 to 0.65. (DItto the Sortino ratio, which declined from 1.05 to 0.95).

Why not? Because, over that time period, VBINX had a Sharpe ratio of 0.71 while the diversifier, DFSCX, only had a Sharpe ratio of 0.49. Measured by the Sharpe ratio, one measure of risk-adjusted return, DFSCX was a worse investment over that time period, so naïvely you would not expect it to improve the portfolio. 0.49 / 0.71 = 0.69, so despite having a lower Sharpe ratio, theoretically DFSCX could still have improved the portfolio, but only if its correlation was had been than 0.69. The "imperfect correlation" of 0.91 was not good enough. It could not overcome the much larger effect of DFSCX just not doing as well over that time period.

The reason I harp on this is that the "correlation" thing is so often presented as if low correlations were automatically good... and as if any imperfect correlation was "low."

In order for the "low correlation improves the portfolio" thing to work, the diversifier needs to have a decent risk-return relationship of its own and the correlation needs to be robustly low. And the actual measure of "how low does it need to be" depends the relative Sharpe ratios of the diversifier and the portfolio it is diversifying.

My feeling is that in real life, small-caps are pretty much of a wash. Even in the context of a portfolio as a whole, any increase in return is offset by an increase in "risk"-by-some-measures, and whether it's an overall gain or loss is the luck of the draw of the specific time period.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by triceratop » Mon Oct 02, 2017 9:40 am

I don't disagree with any of that math. (aside: that said, risk adjusted return isn't everything. If you're young and effectively 100% stocks, it's not like an increase in risk-adjusted returns at expense of CAGR does you any good: going back to the idea that you can't eat risk-adjusted returns. This is my situation)

By the way, simply using 80/20 VBINX and VTI also decreases the Sharpe/Sortino ratios (explains about 50% of the decline in efficiency) so it isn't just the CAGR which is affected by the higher stock percentage (i.e. you're overstating your case about decrease in efficiency by about 2x). Obviously, over this time period, by those measures of risk the risk-adjusted return decreased. I'm not disputing the math.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Mon Oct 02, 2017 12:23 pm

triceratop wrote:
Mon Oct 02, 2017 7:41 am
nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
As mentioned above, the Size factor can exist without having a higher risk adjusted return than the broad stock market. Its existence just means it is necessary to fully explain overall returns (i.e. what is the expected return for a company with a certain beta, a certain size, and a certain fundamental/book value).

Of course, less than perfectly correlated assets can improve the efficiency at a portfolio level.
I don't know. It just seems that over long periods of time that small stocks outperform large stocks. Sometimes people say, well, small stocks are riskier than large stocks and thus they have better returns.

I guess the other thing that confuses me is this: Isn't the whole idea of factor investing to beat the market averages? Otherwise, why bother?

The thing is, my whole point was the CAPM "more beta, more return" thesis just did not hold up. Low beta stocks had more return than predicted and High beta stocks had less return than what the model predicted. That might be what got people thinking about factors. So you could say that low beta had more return per unit of risk. The excess return per unit of risk over beta or market would be your factor premium. Isn't that pretty much the definition of a factor? This also provides a hint there might be a behavioral element in there too. Or you could say, Ned, you have it all wrong, you are defining risk incorrectly. I thought volatility was a primary measure of risk. I am really confused now.

Now I am told, well it doesn't matter if Small Cap has more risk adjusted return than Large Cap because, you know, that Large and Small don't 100% correlate and that makes the portfolio as a whole less volatile but with the same return. You seem to be making the "volatility drag" argument.

The same thing with Value. The excess returns of Value don't seem to be fully explained by additional risk. Indeed Value stocks seem to be less volatile than the market except in times of crisis. The reason is that market expectations for Value is low and thus Value stocks have less pricing risk. The risk involved with Value is fundamental risk, more leveraged balance sheets and more volatile earnings. The fundamental risk is why Value stocks are more volatile in times of crisis, there is less certainty the Value companies will survive. But yet, there seems to be a behavioral element too.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Mon Oct 02, 2017 12:29 pm

rkhusky wrote:
Mon Oct 02, 2017 7:21 am
nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
I don't recall risk being a part of the Fama-French formulation. I thought it simply computed correlations between time series of returns.
Ugggh! Man, I just give up. I thought the whole idea of factor investing (mostly Small/Value tilting) was so that an investor could booth boost returns a bit and reduce overall portfolio volatility. Correlations are part of it, but the advocates of factor investing talk about risk all of the time.

Am I living in an alternate universe? Have I completely misunderstood all of this? I don't think so.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by rkhusky » Mon Oct 02, 2017 3:24 pm

nedsaid wrote:
Mon Oct 02, 2017 12:29 pm
rkhusky wrote:
Mon Oct 02, 2017 7:21 am
nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
I don't recall risk being a part of the Fama-French formulation. I thought it simply computed correlations between time series of returns.
Ugggh! Man, I just give up. I thought the whole idea of factor investing (mostly Small/Value tilting) was so that an investor could booth boost returns a bit and reduce overall portfolio volatility. Correlations are part of it, but the advocates of factor investing talk about risk all of the time.

Am I living in an alternate universe? Have I completely misunderstood all of this? I don't think so.
The Fama-French formulation just tells you how much exposure a given portfolio has to the factors. One must use additional analysis to show that those factors indeed have higher return or higher risk adjusted return. Proponents talk about behavioral aspects that aren't arbitraged away.

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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Mon Oct 02, 2017 3:33 pm

rkhusky wrote:
Mon Oct 02, 2017 3:24 pm
nedsaid wrote:
Mon Oct 02, 2017 12:29 pm
rkhusky wrote:
Mon Oct 02, 2017 7:21 am
nedsaid wrote:
Sun Oct 01, 2017 1:20 pm
My best guess is that Small-Cap stocks have a better risk adjusted return than the stock market as a whole. Otherwise, why would there be a Size factor identified by the academics? As I recall, they discovered a flaw in the Capital Asset Pricing Model when they found that high beta stocks had lower returns than expected and that low beta stocks had better returns than expected. There clearly was something amiss, more risk was not more return as the model predicted. In fact, I would say that all the factors have better risk adjusted returns than the broad stock market or they would not be factors.
I don't recall risk being a part of the Fama-French formulation. I thought it simply computed correlations between time series of returns.
Ugggh! Man, I just give up. I thought the whole idea of factor investing (mostly Small/Value tilting) was so that an investor could booth boost returns a bit and reduce overall portfolio volatility. Correlations are part of it, but the advocates of factor investing talk about risk all of the time.

Am I living in an alternate universe? Have I completely misunderstood all of this? I don't think so.
The Fama-French formulation just tells you how much exposure a given portfolio has to the factors. One must use additional analysis to show that those factors indeed have higher return or higher risk adjusted return. Proponents talk about behavioral aspects that aren't arbitraged away.
That sounds better, more in line with what I have been told. Some factors have more of a premium than others. My understanding is that the factors explain something like 95% or so or the market return. It seemed like CAPM explained something like 2/3 or so.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nisiprius » Mon Oct 02, 2017 3:57 pm

triceratop wrote:
Mon Oct 02, 2017 9:40 am
I don't disagree with any of that math. (aside: that said, risk adjusted return isn't everything. If you're young and effectively 100% stocks, it's not like an increase in risk-adjusted returns at expense of CAGR does you any good: going back to the idea that you can't eat risk-adjusted returns. This is my situation)

By the way, simply using 80/20 VBINX and VTI also decreases the Sharpe/Sortino ratios (explains about 50% of the decline in efficiency) so it isn't just the CAGR which is affected by the higher stock percentage (i.e. you're overstating your case about decrease in efficiency by about 2x).
Yeah. Unfortunately, I haven't yet figured out how to get PortfolioVisualizer to give me a correlation coefficient between a portfolio and an asset. I started out by comparing a 60/40 Total Stock and Total Bond portfolio to one in which I replaced the 60 with 45% Total Stock and 15% NAESX, but then couldn't figure out how to calculate the correlation over that time period.
Obviously, over this time period, by those measures of risk the risk-adjusted return decreased. I'm not disputing the math.
I stand corrected.

My point, though, is that the more I look at it, the more I am convinced that the value of "low correlation" is, frequently, way overstated. There are cases where the low correlation isn't low enough to overcome the drag of the diversifier not being good in itself, and others in which the effect is so small that it is far smaller than the sampling variation between different time periods. "Low correlation" is used as a secret miracle ingredient to sell asset classes that are probably no better and no worse than what you have already, and in some cases actually might be worse.

The important point is that "imperfect" correlation is not guaranteed to give you any improvement at all, not even a small incremental improvement. It might if the diversifying asset is a pretty good investment in itself--the whole is slightly better than the sum of its parts--but not if the diversifying asset is not good. It's a balance. The correlation has to be low enough and the diversifying asset has to be good enough..
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by rkhusky » Mon Oct 02, 2017 6:56 pm

nedsaid wrote:
Mon Oct 02, 2017 3:33 pm
My understanding is that the factors explain something like 95% or so or the market return. It seemed like CAPM explained something like 2/3 or so.
That sounds about right. And the math is pretty solid. However, just explaining investment returns is only part of the issue. The hard part is showing that the factors will outperform the market going forward. That's what most of the discussion revolves around.

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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Mon Oct 02, 2017 8:48 pm

rkhusky wrote:
Mon Oct 02, 2017 6:56 pm
nedsaid wrote:
Mon Oct 02, 2017 3:33 pm
My understanding is that the factors explain something like 95% or so or the market return. It seemed like CAPM explained something like 2/3 or so.
That sounds about right. And the math is pretty solid. However, just explaining investment returns is only part of the issue. The hard part is showing that the factors will outperform the market going forward. That's what most of the discussion revolves around.
It really is an exercise in faith. The factors worked in the past, and if they are caused by human nature and human behavior, they are likely to work in the future. The thing is, we don't know what the future holds. It could be that the robots will take all of this away. Also greater awareness of factors could also take them away too.
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Re: "Indexing Can Capture Small-Cap Premiums"

Post by printer » Tue Oct 03, 2017 2:58 am

nedsaid wrote:
Mon Oct 02, 2017 8:48 pm
rkhusky wrote:
Mon Oct 02, 2017 6:56 pm
nedsaid wrote:
Mon Oct 02, 2017 3:33 pm
My understanding is that the factors explain something like 95% or so or the market return. It seemed like CAPM explained something like 2/3 or so.
That sounds about right. And the math is pretty solid. However, just explaining investment returns is only part of the issue. The hard part is showing that the factors will outperform the market going forward. That's what most of the discussion revolves around.
It really is an exercise in faith. The factors worked in the past, and if they are caused by human nature and human behavior, they are likely to work in the future. The thing is, we don't know what the future holds. It could be that the robots will take all of this away. Also greater awareness of factors could also take them away too.
I agree with what you say here, nedsaid, except that I think the first sentence is misleading and probably not exactly what you meant to say. Factors as defined by at least some people are not an exercise in faith. They are falsifiable, improvable in the presence of compelling contrary evidence, and are an attempt to use a scientific, evidence-based approach to continually improve understanding of returns and risk. Larry Swedroe, for example, has written about specific criteria that he believes something must meet to be considered a factor. (I have not seen an explanation of *why* a given criterion makes sense, nor a way to objectively evaluate the criteria themselves. Nevertheless I agree with the criteria of his that I've read about.) Examples are persistence in time, and consistency across diffferent marketplaces. You can look for writing by Larry Swedroe about criteria he uses to assess whether an effect should be considered a factor.

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Re: "Indexing Can Capture Small-Cap Premiums"

Post by nedsaid » Tue Oct 03, 2017 11:06 am

printer wrote:
Tue Oct 03, 2017 2:58 am
nedsaid wrote:
Mon Oct 02, 2017 8:48 pm
rkhusky wrote:
Mon Oct 02, 2017 6:56 pm
nedsaid wrote:
Mon Oct 02, 2017 3:33 pm
My understanding is that the factors explain something like 95% or so or the market return. It seemed like CAPM explained something like 2/3 or so.
That sounds about right. And the math is pretty solid. However, just explaining investment returns is only part of the issue. The hard part is showing that the factors will outperform the market going forward. That's what most of the discussion revolves around.
It really is an exercise in faith. The factors worked in the past, and if they are caused by human nature and human behavior, they are likely to work in the future. The thing is, we don't know what the future holds. It could be that the robots will take all of this away. Also greater awareness of factors could also take them away too.
I agree with what you say here, nedsaid, except that I think the first sentence is misleading and probably not exactly what you meant to say. Factors as defined by at least some people are not an exercise in faith. They are falsifiable, improvable in the presence of compelling contrary evidence, and are an attempt to use a scientific, evidence-based approach to continually improve understanding of returns and risk. Larry Swedroe, for example, has written about specific criteria that he believes something must meet to be considered a factor. (I have not seen an explanation of *why* a given criterion makes sense, nor a way to objectively evaluate the criteria themselves. Nevertheless I agree with the criteria of his that I've read about.) Examples are persistence in time, and consistency across diffferent marketplaces. You can look for writing by Larry Swedroe about criteria he uses to assess whether an effect should be considered a factor.
There are a couple reasons I say that factors are an exercise in faith. First, we know what happened in the past but don't know what will happen in the future. Second, not everyone believes in the academic research. I have read that Warren Buffett and in particular Charley Munger have disdain for academic research. Posters that I respect regard all of this as fancy back testing and data mining. People either believe or they don't.

As the cowardly Lion might have said, "I do believe in factors. I do believe in factors. I do, I do, I do."

I am in the Larry Swedroe camp. I believe in the academic research and factors and I agree with Swedroe's criteria. My belief is that factors are rooted in human nature and human behavior and thus are unlikely to go away. I remember when Larry posted that his firm hired someone with a PhD in psychics, I got a chuckle out of that as he meant physics. It was sort of a Freudian slip. Another reason that I chuckled is that the research isn't as scientific as they claim. I believe the academics are doing the very best they can but this isn't "plug and chug" physics. For one thing, there are no constants that I am aware of with investing. A lot of this is also time period dependent. There is also a difference between being able to see something in the data and being able to capitalize upon it in real life. Rick Ferri once posted that he believed in Small Value tilting but that his expectation was that the excess return would cover his fees.

Pretty much, I am saying the academic research explaining stock and bond market returns is not a 100% hard science. It is better than a soft science, maybe I would give it 75% on the hardness scale. The use of statistics is very helpful. The thing is, investors in a state of euphoria or in a state of panic will do utterly crazy things, and this crazy behavior pretty much throws the academic theories out the window until sanity returns. The statisticians do an excellent job but people can be even crazier than what past behavior would indicate was possible. In other words, markets will do the very thing the experts didn't expect.
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