Nit-picking DFA's presentation of "diversification"

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nisiprius
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Nit-picking DFA's presentation of "diversification"

Post by nisiprius » Sat May 11, 2013 6:08 am

I'm going to begin by biasing you by pre-poisoning your mind with my own chart. Look at this chart, first. Stare at it, let it sink into your mind, you are getting sleeeeepy, sleeeep... Suppose you needed to describe it briefly to a blind person in words. What would you say, beginning with "The chart has three blue bars, labelled A, B, and C. Bar A is ..."

Image

Now, here's the context. (To make the chart above, I screen-captured their chart, erased text, re-colored and re-labeled the bars).

http://www.dfaus.com/philosophy/diversification.html
Image

To their credit, as nearly as I can tell, the heights of the three bars are in fact rendered as accurately as the screen resolution allows. The dark blue bar is two or three pixels higher than the light blue one (blurry at the top due to antialiasing), and that's the quantitatively correct amount.

Let me ask the following leading questions.
  • Would you have even noticed the difference in height between the first bar and the third if they hadn't emphasized it by choice of color and numeric label?
  • What, exactly, is the second bar? The text refers to "Take, for example, a portfolio that holds just US stocks (S&P 500 Index), a portfolio that holds just Japanese stocks (MSCI Japan Index), and a portfolio that holds both. As illustrated above..." Why is the illustration labelled "MSCI EAFE index" rather than "MSCI Japan index?"
  • Does DFA recommend, or has DFA ever recommended a portfolio consisting of a mix of just U. S. and Japanese stocks? Is U.S. + Japan a good practice and reasonable model for illustrating diversification? Since DFA's only Japanese stock fund is the "Japanese Small Company Portfolio," wouldn't it have been more appropriate to use the MSCI Japan Small-cap index, in order to tie the illustration to something actually realizable in practice using their funds?
  • If one assumes that U.S. + Japan is an intentionally exaggerated example--to show a principle and not to represent a good practice--could 10.1%, compared to 9.9%, be taken as the best that diversification can do, i.e. an extra 0.2% of return?
  • Is "number of down quarters" a standard metric for risk? Why is it the only one presented? Is it a good metric? Should a small down be counted the same as large down?
Last edited by nisiprius on Sat May 11, 2013 7:24 am, edited 1 time in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Random Musings
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Re: Nit-picking DFA's presentation of "diversification"

Post by Random Musings » Sat May 11, 2013 7:21 am

Maybe DFA just got a case of the Vapors.

They're turning Japanese
I think they're turning Japanese
I really think so

RM
I figure the odds be fifty-fifty I just might have something to say. FZ

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Re: Nit-picking DFA's presentation of "diversification"

Post by larryswedroe » Sat May 11, 2013 7:25 am

Few comments for you
First, RE the label MSCI EAFE, clearly that is just a typo, an error that someone missed.

Second, DFA doesn't recommend any portfolios, period. They provide the tools to use to construct portfolios.

Third, the example is meant as illustration of a few key things
a) the only right way to think about an asset class is how it's addition impacts the risk and return of the entire portfolio

The S&P returned 9.9 with SD of just 15.6 and the MSCI Japan returned just 8.9 with SD of 21.2. Shown this I am certain that virtually no investor knowing the results after the fact would have wanted to own the Japan index in the portfolio. After all why add an asset with both lower returns and much higher volatility. Yet the low correlation of the assets resulted in the higher portfolio return. The diversification benefit of adding Japan was 20b for the portfolio. However, the way to think about it is that the IMPACT of adding Japan was as if it returned 10.3% (weighted average of the two components) or 1.4% more than the actual return of the asset. Great example of why thinking in isolation is bad idea. (Note with CCF I have often see impact be as much as 4-5% more than the actual return of the asset due to its high SD and low/negative correlation with other portfolio assets)

Fourth, the number of negative quarters/years IMO is an important metric, certainly in withdrawal phase it matters and certainly it helps keep investors disciplined. We are all risk averse (just question of degree) and thus we prefer fewer down periods.

Hope that is helpful
Larry

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Re: Nit-picking DFA's presentation of "diversification"

Post by lwfitzge » Sat May 11, 2013 7:31 am

Random Musings wrote:Maybe DFA just got a case of the Vapors.

They're turning Japanese
I think they're turning Japanese
I really think so

RM

lol, I got it...wondering the breakdown of BH's that got it...

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Re: Nit-picking DFA's presentation of "diversification"

Post by nisiprius » Sat May 11, 2013 8:15 am

larryswedroe wrote:Fourth, the number of negative quarters/years IMO is an important metric, certainly in withdrawal phase it matters and certainly it helps keep investors disciplined. We are all risk averse (just question of degree) and thus we prefer fewer down periods.

Hope that is helpful
Larry
But I don't see why such illustrations usually compare portfolios that differ both in risk and in return. Wouldn't it have been better to have mixed the portfolio in such a way as to match risk, to show how much more return you can get for the same risk? And, again, why is NUMBER of negative quarters so important? Counting them just seems wrong-headed to me. A small number of quarters with huge losses could be worse than a larger number of small losses. I'm not saying that happened here, I'm saying that just displaying a count is as relevant as saying "from 1991 to 2008 Bill Miller's Legg Mason Value Trust beat the S&P 15 years and lost to it in only 3 years."
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Re: Nit-picking DFA's presentation of "diversification"

Post by larryswedroe » Sat May 11, 2013 8:42 am

nisiprius
No idea why they chose that particular example accept to point out as I did it shows clearly that adding even a lower returning and higher volatility asset (which no person likely would do) actually improved returns
Basically I think you are "nit picking"

Clearly they could have shown many other examples, as I have done say with commodities which has the highest "diversification return" due to its high vol and low/negative correlation with stocks/bonds

And while I understand the point you make about NUMBER of negative quarters, while you may think that number of negative quarters doesn't matter, IMO anyone who has worked as an advisor will tell you that it matters and it matters a great deal. Now showing the largest losses and the size of the tails (how many quarters with losses of say worse than 15/20/25/30 percent) would add more value. But it's only a simple example.

Not what you are suggesting is EXACTLY the way I show the benefits of the "Larry Portfoli"--showing the fat tails as defined in various amounts, and the number of negative YEARS (though negative quarters would also be worthwhile--just so much you can put on one slide though (:-))

I hope that helps
Larry

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Re: Nit-picking DFA's presentation of "diversification"

Post by TomatoTomahto » Sat May 11, 2013 9:18 am

lwfitzge wrote:
Random Musings wrote:Maybe DFA just got a case of the Vapors.

They're turning Japanese
I think they're turning Japanese
I really think so

RM

lol, I got it...wondering the breakdown of BH's that got it...
I'm old enough to have gotten it.

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Re: Nit-picking DFA's presentation of "diversification"

Post by richard » Sat May 11, 2013 9:34 am

nisiprius wrote:Larry
But I don't see why such illustrations usually compare portfolios that differ both in risk and in return. Wouldn't it have been better to have mixed the portfolio in such a way as to match risk, to show how much more return you can get for the same risk?[/quote]
You can match standard deviations, but in order to match risk you need a quantitative definition of risk. Possibilities include SD, exposure to Fama French factors, correlation to income (something is riskier if it does worse in bad times, etc.). SD is popular because it's easy, but if you believe FF or care more about bad performance in bad times or any number of other possibilities, it's a lousy measure of risk.
nisiprius wrote:And, again, why is NUMBER of negative quarters so important? Counting them just seems wrong-headed to me. A small number of quarters with huge losses could be worse than a larger number of small losses. I'm not saying that happened here, I'm saying that just displaying a count is as relevant as saying "from 1991 to 2008 Bill Miller's Legg Mason Value Trust beat the S&P 15 years and lost to it in only 3 years."
Agreed. As I'm fond of saying, risk is primarily economic, although there is a psychological component. Portfolio size or performance at relevant times would seem clearly more important for economics than number of up or down quarters and might be more important for psychological reasons. The major psychological difference between +0.01% and -0.01% is not obvious to me.

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Re: Nit-picking DFA's presentation of "diversification"

Post by Scooter57 » Sat May 11, 2013 9:44 am

Nisi,

You've nailed a good example of using cherry picked data to generate compelling graphs. Graphs are far more persuasive than reasoned arguments for most people--especially males who tend to be more visual than verbal.

This technique isn't exclusive to DFA Vanguard does it, too.

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Re: Nit-picking DFA's presentation of "diversification"

Post by #Cruncher » Sat May 11, 2013 10:03 am

The DFA web page certainly does a poor job of presenting. Besides the apparent typo in the middle bar label referring to the EAFE index instead of the Japan index, I see some more "nits" to pick:
  1. It doesn't say how much of each index is in the combined portfolio. Maybe 50-50 since the word "Balanced" is used? If so, how many US investors would split their equity portfolios evenly between the US and any other single country? If the Japan fund is less than 50% of the total, that should certainly be mentioned since it further strengthens the point Larry makes (see nit # 3 below).
  2. It doesn't consider expenses. For example EWJ, the iShares MSCI Japan ETF, has expenses of 0.51%, while IVV, the iShares Core S&P 500 ETF, has only 0.07%. Assuming a 50-50 mix, the difference between 0.07% and the 0.29% average of the two would cancel out the 0.2% benefit from the combined index return.
  3. But most importantly, the page leaves out the excellent point that Larry states: "adding even a lower returning and higher volatility asset (which no person likely would do) actually improved returns". Why choose this example, and not make that striking point?

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Re: Nit-picking DFA's presentation of "diversification"

Post by bertilak » Sat May 11, 2013 10:04 am

Scooter57 wrote:You've nailed a good example of using cherry picked data to generate compelling graphs.
One of my first thoughts as I read the initial post was "is that the best they can show?" If it was meant to be compelling, I think they failed. Perhaps they need a better cherry picker.

In the context of Larry's explanation I can see how it does illustrate an important point, although I have seen that point illustrated more effectively elsewhere, perhaps even by Larry.
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Re: Nit-picking DFA's presentation of "diversification"

Post by tacster » Sat May 11, 2013 10:08 am

Random Musings wrote:Maybe DFA just got a case of the Vapors.

They're turning Japanese
I think they're turning Japanese
I really think so

RM
lol haven't heard that song in ages. Thanks for the memory rush.
INSERT PITHY QUOTE HERE

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Re: Nit-picking DFA's presentation of "diversification"

Post by Blues » Sat May 11, 2013 10:10 am

One thing I haven't cared for when reading some DFA material in the past is how their funds were compared to Vanguard's "investor" shares rather than "admiral" in order to downplay the expense differential. I am not familiar enough with their offerings to know if this is the norm or not.
(I'm guessing that most folks who could afford to invest with DFA funds would be eligible for "admiral" shares.)

(Oh, and now I've got that dang song playing in loop in my head. :oops: )
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Re: Nit-picking DFA's presentation of "diversification"

Post by rmelvey » Sat May 11, 2013 10:53 am

This is basically another case of volatility harvesting (rebalance return, diversification return ,whatever you want to call it!) I posted about it in another thread where lots of people laughed it off as arithmetic voodoo :D

As Larry mentioned, it is strongest with assets that exhibit high volatility and low correlation. The 20bps difference in their example is quite small because Japan and US stocks are not that different, but between asset classes the affect can be meaningful. For example a portfolio of stocks, LTT, bills, and gold has a CAGR that is over 1% higher than the weighted CAGR's of the portfolios components. That is why portfolio returns can not be predicted by just calculating expected returns looking at the individual assets. Some estimate of the rebalance return is necessary as well.

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Re: Nit-picking DFA's presentation of "diversification"

Post by baw703916 » Sat May 11, 2013 10:56 am

The situation for a combination of S&P 500 and EAFE is actually quite similar. Here's a post from a thread a few years ago that nisi may remember, since he posted on it.
Alex Frakt wrote:Thanks Trev. Hope you don't mind if I cut your numbers down to the essentials:
Trev H wrote:0.6582 = TSM and EAFE/Intl Developed

1970-2008 (yearly rebalancing)

100% TSM
========
9.19 CAGR
18.44 StDev
0.2730 Sharpe

100% EAFE (Developed Only)
========
9.08
23.00
0.2474

80% TSM 20% EAFE
========
9.36
18.12 <---- Volatility Bottom
0.2851

70% TSM 30% EAFE
========
9.41
18.21
0.2873 <---- Max Sharpe (best volatility adjusted return)

60% TSM 40% EAFE
========
9.43
18.47
0.2868

50% TSM 50% EAFE
========
9.43 <---- Max Return
18.89
0.2838

40% TSM 60% EAFE
========
9.41
19.47
0.2788
Not only does this illustrate my point about greater returns, you'll note that adding EAFE lessens overall volatility up to 40%. And you still get a better Sharpe Ratio all the way to 60%.

You can also see why anything from 20%-50% is reasonable. After factoring in the few extra basis point EAFE costs, there should be basically no difference in the returns of real-life portfolios in this range.
The point is that there really is a diversification/rebalancing benefit. Even though EAFE (and for that matter, Japanese small-caps) has historically had lower returns and higher volatility (the latter presumably due to currency fluctuations), mixing it together with U.S. stocks improves the return and the volatility. Maybe "number of down quarters" is a weird measure of volatility, but you do get the same conclusion if you use the standard measures. Also, having your portfolio value drop (or not) during a three month period is something everyone can visualize. A sales pitch "Invest with us, and improve your Sharpe ratio by 0.0143!!!" isn't going to bring in much business.
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Re: Nit-picking DFA's presentation of "diversification"

Post by Calm Man » Sat May 11, 2013 3:03 pm

I doubt the columns that nisi showed if they included the 95% confidence intervals would be statistically significantly different. And it is based on the past. I am a strong believer in the non-tilt Vanguard total market approach so I am biased. But what it has done is kept my expenses at rock bottom and permitted me to do my own investing without requiring a DFA advisor. I don't like having an advisor because I have to pay him or her plus I don't like people knowing my business.

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Re: Nit-picking DFA's presentation of "diversification"

Post by baw703916 » Sat May 11, 2013 3:35 pm

One doesn't need an advisor to tilt, of course, only to access DFA funds. It's quite easy to put together a tilted portfolio with publicly-available ETFs
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