Equal weighting or market cap weighting?

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Re: Equal weighting or market cap weighting?

Postby Rodc » Thu Jan 10, 2013 5:19 pm

Barry Barnitz wrote:Here are current EW index returns as of 1/9/2013. The Russell and S&P EW indexes are investable (Guggenheim ETFS). The Wilshire EW index is not currently investable. Also Wilshire only has data for this series as of 12/31/2012.


Code: Select all
                     3 yr   5 yr   10yr
Russell 1000      11.00%   3.40%   7.20%
Russell 1000 EW   12.90%   8.20%  12.60%
Russell 2000      12.40%   5.80%   9.70%
Russell 2000 EW   10.80%   5.70%  11.00%
         
S&P  500          10.79%    3.00%    n/a
S&P  500 EW       12.47%    5.00%    n/a
S&P  400          13.64%    7.36%    n/a
S&P  400 EW       13.62%   10.11%    n/a
S&P  600          14.24%    7.24%    n/a
S&P  600 EW      14.11%    9.60%     n/a
         
Wilshire 5000     11.15%   2.03%   7.85%
Wilshire 5000 EW   8.55%   5.52%  14.08%


LInks (which provided the returns data) are in the wiki :Equal Weighted Indices - Bogleheads. The page now has a more complete table (1971-2012) series of returns for the Wilshire 5000 EW index.

regards,


Very interesting. Splitting things up so you don't equal weight the largest and the smallest certainly helps on the practical side.
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Re: Equal weighting or market cap weighting?

Postby JeffK » Fri Jan 18, 2013 10:19 pm

Rick Ferri wrote:There is no free lunch. As others have pointed out, the reason S&P 500 equal weight (EW) has outperformed cap weight (CW) is because mid-cap stocks outperformed large cap stocks over the period being measured. That being said, if EW is your method for buying mid-cap stocks, then it's fine.

Rick Ferri


Rick, I suspect that some of the superior returns of the Russell 1000 Sector Equal Weight index are attributable to reweighting of underperforming sectors at 3 month intervals. Here are the 10 year total returns for this index, the new CRSP 10 year indices, and select Vanguard Funds through Dec 31, 2012

Russell 1000 Sector Equal Weight 12.77
CRSP US Mid Cap Index 10.17
CRSP US Mid Cap Value Index 9.64
CRSP US Small Cap Index 11.51
CRSP US Small Cap Value Index 11.41
Vanguard Mid Cap Index 9.90
Vanguard Small Cap Index 10.83
Vanguard Small Cap Value 9.61

EWRI tracks the Russell 1000 Sector Equal Weight Index. This ETF is still very small (only $ 44 million in assets), but I wonder whether this sector equal weight strategy will yield returns superior to these other mid cap and small cap indices in the years to come.

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Re: Equal weighting or market cap weighting?

Postby YDNAL » Sat Jan 19, 2013 8:17 am

.

Morningstar doesn't have 4Q12 holdings, so we are looking at a couple of 3Q12 holdings in S&P 500 Equal Weight VADBX:
Code: Select all
Component         Shares  Change from prior
MetroPCS         228,303  -117,202 -33.9%
Sprint Nextel    461,383  -251,244 -35.3%

MetroPCS ($3.42B mkt wt now), for instance, spiked from $5.59 at end-June 2012 to $13.57 end-September 2012 (early October). To maintain equal weights, VADBX must rebalance to account for market pricing that otherwise may be insignificant at market-weighted allocations - considering behemoths in Top 15.
Code: Select all
Top 15 Holdings
ExxonMobil Corporation               3.09
Apple, Inc.                          2.40 <-- wow!
Microsoft Corporation                1.94
Procter & Gamble Compa               1.83
Johnson & Johnson                    1.70
International Business Machines Corp 1.69
General Electric Company             1.63
J.P. Morgan Chase & Co.              1.60
Bank of America Corporation          1.56
AT&T, Inc.                           1.50
Chevron Corporation                  1.48
Wells Fargo Company                  1.44
Berkshire Hathaway Inc. B            1.35
Cisco Systems, Inc.                  1.34
Coca-Cola Company                    1.24

Rick Ferri wrote:There is no free lunch. As others have pointed out, the reason S&P 500 equal weight (EW) has outperformed cap weight (CW) is because mid-cap stocks outperformed large cap stocks over the period being measured. That being said, if EW is your method for buying mid-cap stocks, then it's fine.

Rick Ferri

If you own the S&P 500 "companies" as core holding, as many Bogleheads are forced through options in 401Ks, etc, why should equal-weights be classified as a "method for buying mid-caps stocks?" Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
Last edited by YDNAL on Sat Jan 19, 2013 5:38 pm, edited 2 times in total.
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Re: Equal weighting or market cap weighting?

Postby nisiprius » Sat Jan 19, 2013 5:36 pm

YDNAL wrote:Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
No, it isn't, and this "market cap = concentration" meme is something new and pernicious. Market cap means you are sampling evenly over the dollars in the market. "Equal" weight means you are sampling evenly over ticker symbols.

Would you say "I approve of this list of ingredients for bread, but I do not want to have a 'concentration' in flour, so I will use 2 cups of flour, 2 cups of salt, 2 cups of yeast, and 2 cups of water?"

Why doesn't 3-1/2 cups of flour, 2 teaspoons of salt, 1 teaspoon of yeast, and 1-1/2 cups of water represent a "concentration" into flour? Why wouldn't we even think of trying the "equally weighted" recipe? Because we are not playing an abstract mathematical game, we are trying to replicate the composition of bread dough.
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Equal weighting or market cap weighting?

Postby YDNAL » Sat Jan 19, 2013 5:46 pm

nisiprius wrote:
YDNAL wrote:Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
No, it isn't,...

Yes it is!

By the end of 3Q12 you would have invested 4+ cents of $1 in APPL at market weights (concentrated) - worth 1.6 cents today - and I would invest 0.2 cents of $1 (not concentrated).

ps. I don't eat bread.
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Re: Equal weighting or market cap weighting?

Postby umfundi » Sat Jan 19, 2013 6:06 pm

nisiprius wrote:
YDNAL wrote:Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
No, it isn't, and this "market cap = concentration" meme is something new and pernicious. Market cap means you are sampling evenly over the dollars in the market. "Equal" weight means you are sampling evenly over ticker symbols.

Would you say "I approve of this list of ingredients for bread, but I do not want to have a 'concentration' in flour, so I will use 2 cups of flour, 2 cups of salt, 2 cups of yeast, and 2 cups of water?"

Why doesn't 3-1/2 cups of flour, 2 teaspoons of salt, 1 teaspoon of yeast, and 1-1/2 cups of water represent a "concentration" into flour? Why wouldn't we even think of trying the "equally weighted" recipe? Because we are not playing an abstract mathematical game, we are trying to replicate the composition of bread dough.

Actually, my bread recipe has a 25% tilt towards rye.

Nisiprius is correct. Why should any set of commodities or selection of resources be equally weighted? Time in your day. Things you buy at the supermarket.

Dang! Just bought that new phone. Now I need to spend $99 on potatoes. :oops:

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Re: Equal weighting or market cap weighting?

Postby YDNAL » Sun Jan 20, 2013 7:02 am

umfundi wrote:Nisiprius is correct. Why should any set of commodities or selection of resources be equally weighted? Time in your day. Things you buy at the supermarket.

Dang! Just bought that new phone. Now I need to spend $99 on potatoes. :oops:

Keith

That is a ridiculous assertion bordering on childish..... emoticon included!

As a consumer in free markets, you have the option to spend the amount you want on the item you want. You may need to spend $0.99 in potatoes (presumably to eat and not something else) and ALSO spend $0.99 on a new phone - since some plans (like AT&T) will give long-term customers a 4G I-Phone for that amount.

As an investor, you can choose to invest $1 where 4 cents is allocated to AAPL or can choose to invest $1 where 0.2 cents goes to AAPL.

The choices are ours. Nothing further.
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Re: Equal weighting or market cap weighting?

Postby hafius500 » Sun Jan 20, 2013 8:46 am

YDNAL wrote:
nisiprius wrote:
YDNAL wrote:Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
No, it isn't,...

Yes it is!...


No, it is not "concentrating one's wealth".

I suspect those assumptions about 'better diversification' can be distorted by cognitive biases like, e.g., Framing:
drawing different conclusions from the same information, depending on how or by whom that information is presented.

Under uncertainty people (investors) often choose 'naive diversification' and equal-weight all alternatives

If your data sample sorted companies
- by company names, you would equal-weight all companies (and, e.g., risk of fraud)
- by sector, you would equal-weight sectors (and, e.g. economic risks),
- by location of the headquarter, you would equal-weight geographical regions (and, e.g. political risks),
- by the numbers of chairs in the companies, you would weight the companies in such a way that you pay the same price for every chair (Arnott said this would work like 'fundamental indexation').

You see that equal-weighting decreases exposure to one risk factor but increases the exposure to other risk factors. This would make sense if, e.g., you believed that the market mispriced economic or political risks.

Sharpe wrote investors must ask themselves if they are macro-consistent:

"If I advised everyone in the world, would markets clear?".
Source

"-Everybody should diversify because diversification improves risk-adjusted returns.
- Equal-weighting (or factor-tilting) improves diversification.
- Therefore, everybody should and would want to equal-weight (tilt)." - which is impossible.
Obviously you need other arguments to recommend equal-weighting or tilting.
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Re: Equal weighting or market cap weighting?

Postby Rodc » Sun Jan 20, 2013 10:04 am

Sharpe wrote investors must ask themselves if they are macro-consistent:

"If I advised everyone in the world, would markets clear?".

Source

"-Everybody should diversify because diversification improves risk-adjusted returns.
- Equal-weighting (or factor-tilting) improves diversification.
- Therefore, everybody should and would want to equal-weight (tilt)." - which is impossible.
Obviously you need other arguments to recommend equal-weighting or tilting.


I think that is a useful question, but we should also remember that we as individuals are not the world.

For example, this would mean we should all have the same bond and cash allocation. But since we as individuals have different levels of ability to weather risk this would be poor advice.
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Re: Equal weighting or market cap weighting?

Postby YDNAL » Sun Jan 20, 2013 10:57 am

hafius500 wrote:
YDNAL wrote:
nisiprius wrote:
YDNAL wrote:Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index. Holding market weights is rather the opposite by concentrating one's wealth.
No, it isn't,...

Yes it is!...

No, it is not "concentrating one's wealth".

First, I suggest that you carefully read the origin of the "partial" quote selected by Nisiprius which has been surgically altered.
YDNAL wrote:
Rick Ferri wrote:There is no free lunch. As others have pointed out, the reason S&P 500 equal weight (EW) has outperformed cap weight (CW) is because mid-cap stocks outperformed large cap stocks over the period being measured. That being said, if EW is your method for buying mid-cap stocks, then it's fine.

If you own the S&P 500 "companies" as core holding, as many Bogleheads are forced through options in 401Ks, etc, why should equal-weights be classified as a "method for buying mid-caps stocks?" Holding equal weights is a method to spread one's wealth amongst companies that the S&P 500 committee feel are the largest and most representative for the Index....

Second, you may choose to "concentrate" a $1 investment in companies 1 - 500 based on size, while I may choose to "spread" my $1 equally. You concentrate your $1 similarly as you did pre-millenium (1999) - the results of which are part of history.
Code: Select all
1 Microsoft (#3 now)
2 General Electric (#7 now)
3 Exxon Mobil (#1 now)
4 Royal Dutch Shell (not top 10)
5 Merck (not top 10)
6 Pfizer (not top 10)
7 Intel Corporation (not top 10)
8 The Coca-Cola Company (not top 10)
9 Wal-Mart (not top 10)
10 IBM (#6 now)
Roll forward 13 years.
Code: Select all
1 ExxonMobil Corporation               3.09
2 Apple, Inc.                          2.40
3 Microsoft Corporation                1.94
4 Procter & Gamble Compa               1.83
5 Johnson & Johnson                    1.70
6 International Business Machines Corp 1.69
7 General Electric Company             1.63
8 J.P. Morgan Chase & Co.              1.60
9 Bank of America Corporation          1.56
10 AT&T, Inc.                          1.50

Second, sure it is concentrating wealth!
  1. Vanguard VFINX held 8,606,953 shares of AAPL valued at $5.743 billion as of September 30, 2012.
  2. 8,606,953 shares are valued at $4.3 billion as of Friday.
  3. 1/4 of your "concentrated" investment gone in a few short months.

This thread has run its course (borrowing from LadyGeek) as far as I'm concerned.
Last edited by YDNAL on Sun Jan 20, 2013 11:52 am, edited 2 times in total.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 20, 2013 11:50 am

I've got a few comments are are mostly for informational purposes only. I think that as a practical matter market-cap weighting generally makes sense. But there are counter-points to the pros you raised that are worth mentioning.

nisiprius wrote:First off, that article is garbage. His authority, Arnott, makes the plausible argument that it might make "more sense for indexes to weight companies by their economic footprint -- things like revenue, earnings, and dividends." That shouldn't be presented as support for an equal-weighted index, in which companies with small revenues, earnings and dividends are given equal weight with companies that have huge revenues, earnings, and dividends! It is an argument for a tweaked, adjusted, tuned, or modified version of a cap-weighted index--such as those which Mr. Arnott's firm provides


There's a PIMCO fund that goes long an economic impact index and short the S&P500 (so that you earn the excess return of the economic impact index on top of the bond returns). Transactions costs aside, economic impact should have higher returns because the forced rebalancing will make geometric returns closer to arithmetic returns. I don't know how much of a drag the lack of rebalancing represents on a market-cap weighted index, but I'd guess that it should be at least a couple of % given how volatile stocks are (but it can't be too high because of the correlations). As for the rest of the excess returns to this sort of index, I don't know how much of them are explainable in terms of value and size tilts and how much are because such an index is "better".

1) Market-cap weighting is the weighting that cancels out the effect of speculative trading and leaves you with the returns generated by the stock-issuing businesses. If someone makes a huge speculative sale of Millepore stock and buys the same dollar value of, let's say, Zimmer stock, the price of Millespore stock moves down and the price of Zimmer stock moves up. Under appropriate assumptions, if you are holding a cap-weighted total stock market portfolio, this does not affect the dollar value of your holdings at all. However, anyone who is holding any other portfolio will either have more weight in Millespore or more weight in Zimmer, and the value of their holding will change.


This also represents a disadvantage because to the extent that people overvalue some stocks and undervalue others, you'll be over-weight in those that are too high and underweight in those that are valued too low. For example, in the late 90s, a large part of the last leg of the S&P run-up was caused by a small number of mega-cap firms having P/E ratios disproportionately high to the rest of the index. Because of their market-caps, the rising valuations pulled the index up with it and then pulled it back down in 2001 when their valuations fell back to more reasonable levels. Some other indexing method wouldn't have been up as much before hand and wouldn't have fallen by as much afterward. (And similar expected returns for less volatility is generally considered a good thing.)

2) Market-cap weighting incurs lower trading expenses for a mutual fund, because it automatically stays in balance. There is no need to buy or sell shares merely to match the index weighting.


The trade-off is that you give up the one free lunch in investing which is the positive return effect of rebalancing.

3) In the words of Jeremy Siegel--let me note upfront that he says the stated assumptions are not true and that "fundamentally-weighted" indexes are better--but, nevertheless:
Capitalization-weighted indexes... under certain assumptions give investors the "best" tradeoff between risk and return. That means that for any given risk level, these capitalization-weighted portfolios give the highest returns, and for any given return, these portfolios give the lowest risk. This property is called mean-variance efficiency.
Equal weighting is one of an infinite number of non-market-cap weightings. It's not clear what special properties it's supposed to have. I cannot for the life of me see some obvious reason why I'd want to own the same dollar value of Zimmer stock and Exxon Mobil stock. It just seems goofy to me. Can anyone give any reason other than "it outperformed the cap-weighted S&P?"


The problem, as you point out is that the assumptions are not actually true and that no one seriously believes they could be. In fact, their not being true is the reason that volatility minimizing indexes (E.g. the MSCI All World Minimum volatility index) have historically returned about the same as the market (a little more actually), with 30-40% less volatility. I can't offer a justification for equal weighting, but I can say that there are some good arguments for this volatility minimizing approach, especially once you consider that it works even if it turns out to have slightly lower returns. As long as the returns are not reduced by as much as volatility, you can increase your relative weight to stocks to return your portfolio's volatility to what it was with the market cap weighting and have higher overall returns as a result.

Until recently there were only a couple of active funds in this space, but iShares came out with a low-cost index tracking ETF back in mid-2011 (ACWV and friends).

Like many weightings, it overweights small-caps--obviously--so it does the things that overweighting small-caps does. Some people, perhaps many in this forum, think that's beneficial. But why equal weight, rather than, say, cap-weighted within the small-cap category? To the unaided eyeball, what, exactly, has RSP done that Vanguard Small-Cap Index fund didn't do more of? And that's the plain-Jane Vanguard fund the connoisseurs sneer at. The gourmet funds like DFA Small-Cap did even more.


The *big* effect that impacts market-cap weighted funds is the value effect. The Fama-French value factor reduces volatility and improves your portfolio even if value stocks have no excess return. (And historically they have had excess returns on average.) The small-cap effect is secondary and requires that small cap's historically higher returns are persistent and not an artifact of higher trading costs, etc. (A naive statistical analysis seems to indicate that the out-performance of small caps has fallen off with increased availability of cost-effective exposure. Whether they still out-perform by enough to justify the extra volatility is a more difficult question.)
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 20, 2013 12:01 pm

nisiprius wrote:Barry, as alway I appreciate your data and the Wiki article. From which I learn that the index was only launched in 2003. I don't know how many years of data it would take to make me feel that there's enough data to conclude anything, but five years or even eight ain't it. Anything can outperform anything for eight years.


Well the first thing you should do is look up the formula for how much of a lift the rebalancing gives you and plug in estimated correlations and variances and see what that number is. That would be a good estimate of how much you'd expect these equal weight funds to over-perform once all other effects are excluded.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 20, 2013 12:05 pm

Rodc wrote:Also, basic least squares math says that if you want to mean optimize a portfolio you weight based on mean, standard deviation and correlation. In real life you can't estimate those things worth a darn, but if you could that is what you would do.


Well, expected returns ("mean" as you call it) isn't predictable, but the covariance matrix is (standard deviation and correlation). So you can't mean/variance optimize, but you can do variance minimization. And there are indexes that track this, as I said above.
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Re: Equal weighting or market cap weighting?

Postby umfundi » Sun Jan 20, 2013 12:21 pm

YDNAL wrote:That is a ridiculous assertion bordering on childish..... emoticon included!

I apologize for the tone of my message.

And, yes, you can choose anything you want.

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Re: Equal weighting or market cap weighting?

Postby Rodc » Sun Jan 20, 2013 12:49 pm

Akiva wrote:
Rodc wrote:Also, basic least squares math says that if you want to mean optimize a portfolio you weight based on mean, standard deviation and correlation. In real life you can't estimate those things worth a darn, but if you could that is what you would do.


Well, expected returns ("mean" as you call it) isn't predictable, but the covariance matrix is (standard deviation and correlation). So you can't mean/variance optimize, but you can do variance minimization. And there are indexes that track this, as I said above.


I believe you are mistaken in your belief that we can estimate the covariance matrix with enough accuracy to be useful in this process. It is unlikely it is even stationary. Estimating correlations is harder than estimating expected returns (mean or central tendency of the underlying unknown distribution). If you can't estimate the mean, how can you estimate the variance about the mean?

Of course one can do the math and put out an index. And one can backtest to develop the index (so of course it works well on past data, you don't publish the index if you couldn't get it to backtest). The question is "Is it accurate enough to be useful going forward?"

Do you have live results of using such an index to build a real world fund? And if you do, how long a track record does it have?

The world is filled with quant strategies, not many have worked going forward after development on old data.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 20, 2013 1:33 pm

Rodc wrote:
Akiva wrote:
Rodc wrote:Also, basic least squares math says that if you want to mean optimize a portfolio you weight based on mean, standard deviation and correlation. In real life you can't estimate those things worth a darn, but if you could that is what you would do.


Well, expected returns ("mean" as you call it) isn't predictable, but the covariance matrix is (standard deviation and correlation). So you can't mean/variance optimize, but you can do variance minimization. And there are indexes that track this, as I said above.


I believe you are mistaken in your belief that we can estimate the covariance matrix with enough accuracy to be useful in this process. It is unlikely it is even stationary. Estimating correlations is harder than estimating expected returns (mean or central tendency of the underlying unknown distribution). If you can't estimate the mean, how can you estimate the variance about the mean?


The EMH says that you can't predict expected returns better than the market. It doesn't say that you can't predict expected covariances, and in fact the standard wisdom on the statistical properties of market returns is that these are predictable in principle.

As for how you go about doing that, it's substantially more complicated than just calculating historic covariances, and even most institutional investors pay specialists to do the math for them. (E.g. They license the BARRA GEM model.) But conceptually this is not too different from the Fama-French factor model except that instead of trying to estimate expected returns, you are using a factor model to account for return dispersion.

Of course one can do the math and put out an index. And one can backtest to develop the index (so of course it works well on past data, you don't publish the index if you couldn't get it to backtest). The question is "Is it accurate enough to be useful going forward?"


The econometrics behind estimating covariances is well established completely non-controversial stuff. The novel part is using them to do a volatility minimization while keeping your exposure to *priced* risk factors roughly in line with the market. (As opposed to forecasting returns and then using the covariances to do a mean variance optimization of an active portfolio.)

Do you have live results of using such an index to build a real world fund? And if you do, how long a track record does it have?


There are some active funds with very good track records. (That's not a justification for investing in them.) And there are a couple of index tracking funds. If you want to count hedge funds as well, almost all of the stock oriented ones use a factor model as part of their portfolio optimization process.

The world is filled with quant strategies, not many have worked going forward after development on old data.


This isn't a "quant" strategy because it's entirely passive. It's conceptually the same sort of thing as these fundamentally derived indexes -- a different way of estimating what weights you should assign in an attempt to overcome various problems with capitalization weights. The only difference is that it uses somewhat more sophisticated mathematics that happen to have better theoretical support. (The method also has some theoretical justification from behavioral finance.)
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Re: Equal weighting or market cap weighting?

Postby Rodc » Sun Jan 20, 2013 1:52 pm

Well, there may be more for me to learn here, though without a great deal more information than just generalities I remain deeply skeptical.

I note that hedge funds do not have a great track record from all I can discern.

This has nothing to with EMH near I can tell rather than just basic error analysis of estimation of parameters.

I'd call it a quant strategy even if it does not result in a lot of trading. A lot of math is used to develop and maintain the allocation.

If it requires a bunch of high priced experts, I am not really interested from a practical standpoint though the theory might be fun. Practice shows that in these cases if any excess returns are generated they are kept, and generally much more, by the advisers and they do not flow to the investor. And if excess returns are not generated, well you pay anyway.

I also not as a point of caution Long Term Capital Management.

But if you have citations I'd be interested.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 20, 2013 2:20 pm

Rodc wrote:Well, there may be more for me to learn here, though without a great deal more information than just generalities I remain deeply skeptical.

I note that hedge funds do not have a great track record from all I can discern.


Well, the idea with hedge funds is that they get you somewhat less returns than the stock market with much less volatility. The HFR fund of funds index returned 7.4% CAGR with 6% standard deviation over the last ~22 years. The market returned 8.2% with a standard deviation of ~15% over the same time period. The market had 2 ~50% declines over that time period. The worst decline in the HRF index was 22%. (This is after fees. Usually you see before fee numbers quoted and they are much more impressive, but totally irrelevant. There's also the issue of how well a normal investor would have been able to track this index with a reasonable allocation to 20-30 fund of funds. And the index data has some bias issues. But that's all stuff that's not really relevant to this discussion. My point was just that lots of people use the mathematics here.)

This has nothing to with EMH near I can tell rather than just basic error analysis of estimation of parameters.


The EMH says that market prices have no first order correlations. Covariances are second-order and therefore predicting them isn't ruled out. (And in practice, they can be estimated.)

I'd call it a quant strategy even if it does not result in a lot of trading.


Then you don't understand how quant strategies work.

A lot of math is used to develop and maintain the allocation.


It isn't "a lot of math". This is the same basic math that you use for testing the Fama-French three factor model that everyone on this board will basically agree with. Just because actually doing the statistics is graduate level work, no one says that small-cap and value tilts are "quant" strategies.

If it requires a bunch of high priced experts,


These risk models are standardized products with affordable pricing. Companies only pay for them because there's no point in doing the math in house when you can pay some company that has a team of statisticians to run the math for you.

I am not really interested from a practical standpoint though the theory might be fun. Practice shows that in these cases if any excess returns are generated they are kept, and generally much more, by the advisers and they do not flow to the investor. And if excess returns are not generated, well you pay anyway.


I don't know why you keep talking about this like it is an active strategy. This thread is discussing alternative ways to weight an index. I'm bringing up an alternative that wasn't considered and seems to have more actual scientific merit than the equal weighting and value weighting that were being discussed.

As for fees, the global index tracking fund ACWV has a .34% expense ratio. The US only one, USMV has a .15% expense ratio. These are in between the fees on the Vangaurd market-cap weighted indexes and the value and small-cap tilted funds. (As should be expected from having a set of weights that's intermediate between them.)

I also not as a point of caution Long Term Capital Management.


What does that have to do with anything under discussion in this thread?

But if you have citations I'd be interested.


You don't seem to have read what I've written so far, so I'm afraid that my time would be wasted if I produced them, but you could do a google search for Eric Falkenstein, he's done some writing on this topic.
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Re: Equal weighting or market cap weighting?

Postby Rodc » Mon Jan 21, 2013 9:52 am

You seem to believe you have the only definitions of quant fund and active, and perhaps EMH; I guess I have a different dictionary.

There are several definitions of EMH. The ones I know don't say you can't estimate mean, they say you can't predict price movements.

If I have time I'll see if I can find a paper on what you are talking about

I have read what you have posted, but it is largely content free. You simply state things without support. There may be support, but you did not provide it.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Mon Jan 21, 2013 11:46 am

Rodc wrote:You seem to believe you have the only definitions of quant fund and active, and perhaps EMH; I guess I have a different dictionary.


These are standard financial terms, you don't get to make up definitions to suit your argument.

There are several definitions of EMH. The ones I know don't say you can't estimate mean, they say you can't predict price movements.


All of the verbal definitions you are familiar with are just different ways of stating the same mathematical property.

If I have time I'll see if I can find a paper on what you are talking about

I have read what you have posted, but it is largely content free. You simply state things without support. There may be support, but you did not provide it.


Google is very good about finding things on topics people are interested in. I'm only trying to post enough information to enable people who find the idea interesting to do further research.
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Re: Equal weighting or market cap weighting?

Postby steve r » Mon Jan 21, 2013 3:11 pm

Akiva wrote:... (market cap weight) represents a disadvantage because to the extent that people overvalue some stocks and undervalue others, you'll be over-weight in those that are too high and underweight in those that are valued too low.


I would like to discuss this comment theoretically / abstactly.

To my way of thinking, it makes a lot of intuitive sense. EMH suggests "markets" are effecient, but not necessarily the price of each stock. Some stocks are overvalued, some are undervalued - but EMH states one can not determine which ones.

It is unknown if a stock is overvalued or undervalued. If (emphasis added) some stocks are overvalued, then market cap weights will overweight such stocks. In the short run, this can turn out to be a good thing if overvalued stocks become more overvalued, particularly if they are mega-cap sized (late 1990s), but not over the long run.

It seems likely that the expected returns on the mega large caps are no different than the smallish large caps (hardly small cap) and vice versa. Thus, any benefit from equal weighting must, in the long run, come from not overweighting overvalued stocks and underweighting undervalued stocks. The recent gains reflect this and a nice run in mid caps. The nice run in mid caps will likely fade in time.

For what it is worth, the article this idea is posted in is from a reputable journal in academics - Financial Analyst Journal.

The counter argument journal is more of a trade journal - Advisor Perpective. Not sure this matters. That article seems to suggest mathmatically that since the the expected pricing error on each stock is zero, cap weighted indexes are efficient. While it is true that expected price errors is zero on each individual stock (basically an equal chance of a particual stock being overvalued or undervalued) ... it sort of misses the point that some stock are wrongly valued (and that which ones are wrongly valued is NOT known).

Whether this is worth 35 basis points or so is another issue.

It also strikes me as a plausible explaination for the long term performance of Wellington / Wellsley which tilts value (avoiding overvalued stocks) and does not weight its holdings by market caps. Each holds several dozen stocks in "comparatively" equal amounts (when compared to a cap weighted index). Fidelity's Puritain Fund, in contrast, is growth and comparatively more cap weighted. AAPL is 4.3 percent of its overall holdings (and a higher percentage of its stock holdings), its 25th largest holding is about one sixth this amount, and it has over 200 stock holdings. Puritain significanly underperforms Wellington even after accounting for differences in expense ratios. Wellington and Wellsleys largest holdings are nearer 2 percent overall, with its 25th largest holding a little less than half this, and each with less than 100 stock holdings. That is to say relatively more equal. More in line with the dart throwing model suggest above.

It maybe the case that the Vanguard funds performed better because of superior management, but I suspect most Bogleheads would be suspicous of such a claim.

Lastly - and perhaps a counter agrument to what I stated above - if any non-cap weighted index outperforms - the level of outperformance will likely disappear over time as investors try to replicate such performance.

In anyevent, the quote I started with makes sense to me, I wonder if it makes sense or no sense to others reading this thread.
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Re: Equal weighting or market cap weighting?

Postby Rodc » Mon Jan 21, 2013 4:16 pm

Akiva,

I'm not inventing my own definitions. What exactly the EMH is and what is means is hardly a settled matter. Same for other terms like "quant fund" and "active".

http://comp.uark.edu/~tjandik/papers/emh.pdf (for only one example)

What one can and cannot estimate with sufficient accuracy to be useful and trustworthy, mean, variance or whatever, is likewise not a settled matter. So called experts often do the math incorrectly or poorly, or rely on shaky hypotheses and premises. Even things like the validity of the FF 3 factor model are far from settled matters.

They may be settled in your mind, and that is ok.

I do appreciate your bring up some ideas new to me. I do hope though that you realize I'd have to be pretty gullible to simply take the word of some new anonymous poster for these ideas being settled matters, when so few things in this business are settled at all.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Mon Jan 21, 2013 4:24 pm

Rodc wrote:Akiva,

I'm not inventing my own definitions. What exactly the EMH is and what is means is hardly a settled matter. Same for other terms like "quant fund" and "active".


No one will contend that the EMH says that you can't predict covariances, nor will they confuse a quant fund with portfolio mathematics, nor will they mistake an indexing method as being a form of active management.

What one can and cannot estimate with sufficient accuracy to be useful and trustworthy, mean, variance or whatever, is likewise not a settled matter.


The "stylized facts" about market data are well settled. And those facts say that you can predict covariances because volatility follows a long memory process.

So called experts often do the math incorrectly or poorly, or rely on shaky hypotheses and premises.


There are a lot of people who claim expertise that don't have it. That doesn't mean that the people who actually study markets are wrong. (If they were you shouldn't be listening to the advice on this board.)

Even things like the validity of the FF 3 factor model are far from settled matters.


That the model accounts for more variance than CAPM is settled. How to interpret this is not.
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Re: Equal weighting or market cap weighting?

Postby hafius500 » Tue Jan 22, 2013 7:24 am

Akiva wrote:...no one says that small-cap and value tilts are "quant" strategies...........This isn't a "quant" strategy because it's entirely passive. It's conceptually the same sort of thing as these fundamentally derived indexes -- a different way of estimating what weights you should assign in an attempt to overcome various problems with capitalization weights. The only difference is that it uses somewhat more sophisticated mathematics that happen to have better theoretical support. (The method also has some theoretical justification from behavioral finance.)


So you call an investor, who attempts,...who estimates...who tries to avoid less sophisticated maths...who searches theorectical support that is better than average... a passive investor?? And the active investor would be the investor who uses less sophisticated maths or the monkey that randomly selects stocks??

DFA funds are quant funds. Quant funds are always active funds by definition. Google ("DFA + quant") found, e.g.,:
What Will Be Obvious 20 Years From Now? (With a Sharpe of 0.76)?. August 22nd, 2012 by Mebane Faber
What is really interesting to me is that often the great investment approaches seem so obvious in retrospect. Buffett has one of the best track records ever by buying cheap, safe, high quality stocks in a structure that allows for sub Tbill leverage. But the key is that he came to this realization before most. Ditto for the top endowments like Harvard and Yale...– it is quite obvious now, but they were pioneering these concepts decades ago. The pioneering trendfollowers and managed futures shops caught onto an idea long before computers made it simple, as did Bogle (indexing), and DFA (quant multifactor)

Several posts on the Fama/French forum mention "passive" growth- or value-tilted portfolios. This quote (Gene Fama) demonstrates the errors of such propositions:
Mission Impossible: beating the market over long periods of time, Jun 30 2011 by Wesley R. Gray, Ph.D. in Turnkey Brainwave
I am continually haunted by a note I received from one of my dissertation advisors at the University of Chicago–Gene Fama. He wrote the a response to an early draft of my paper...In the document I sent, I stated proudly: “…this paper shows value investors outperform the market” (where outperforming the market is defined as earning average excess returns after controlling for a variety of market risks). Here was the response:

“Your conclusion must be false. Passive value managers hold value-weight portfolios of value stocks. Thus, if some active value managers win, it has to be at the expense of other active value managers. Active value management has to be a zero sum game (before costs).”

To my chagrin, Fama’s comments were spot on…I did not show that “value investors outperform the market”

Several posters refuted Fama's comment and I agree:
Ezekiel Kruglick replied:
I think the Fama comment, at least as summarized, is tautological and appears false...The inherent assumption in this statement is that value investors buy and sell from and to other value investors....Successful value investments are thus sold to momentum investors, growth investors, sector rotation investors, etc…
This doesn’t establish that value investors ARE average outperformers, mind you, but it eliminates the argument presented.


Active (or "passive") value investors trade against other active investors but they cannot trade against passive investors who hold the market-weighted portfolio because these investors do not trade. It would make no sense to call the seller of X a passive (value) investor and the buyer an active investor. Why not the other way around? The stock-picker or the technical investor would be passive investors as well, especially, if they "passively" stayed the course.
IMO Fama's definition is tautological because the value benchmark is arbitrary and can be replaced arbitrarily:

"Passive stock-pickers who buy undervalued stocks hold value-weighted portfolios of undervalued stocks."

As I wrote in another post, the only sensible defintion of active vs. passive investing that I have seen refers to the costs of information: Active investors make informed trades (value investors need to define and search value stocks), passive investors make informationless trades. Samuelson wrote about the impossibility of informationally efficient markets and justified the profits of active investors who collect and process information.
Last edited by hafius500 on Tue Jan 22, 2013 10:37 am, edited 2 times in total.
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Re: Equal weighting or market cap weighting?

Postby hafius500 » Tue Jan 22, 2013 7:41 am

steve r wrote:For what it is worth, the article this idea is posted in is from a reputable journal in academics - Financial Analyst Journal.

The counter argument journal is more of a trade journal - Advisor Perpective. Not sure this matters. That article seems to suggest mathmatically that since the the expected pricing error on each stock is zero, cap weighted indexes are efficient. While it is true that expected price errors is zero on each individual stock (basically an equal chance of a particual stock being overvalued or undervalued) ... it sort of misses the point that some stock are wrongly valued (and that which ones are wrongly valued is NOT known).


Maybe I misunderstand. But if you refer to the articles I had posted you are wrong:
All of them have been published in the FAJ. Advisorperspectives and the other quoted sources simply summarized these papers. All of them agree with the maths of the two authors. The latter do not miss the point that some stocks are wrongly valued. Their proof assumes that securities are randomly mispriced ( overvalued and undervalued).

Edited to add:
A summary of academic papers on fundamental and other non-price related weighting schemes (list of papers at the bottom):

Does Theory justify fundamental weighted indices?, Financial Times, FTfm EDHEC-risk Forum

In particular, Arnott and Hsu (2008), coming to similar conclusions as Hsu (2006), claim that pricing errors and market capitalisation are positively related. This means that the securities with higher market cap will tend to have below average returns and hence a cap-weighted index will result in a drag on returns. This has been coined the “noisy markets hypothesis”. However, a first issue with such a claim is that such a theory does not justify any particular fundamentals-based weighting scheme. Rather, such a theory suggests that any non-price related weighting scheme, including for example equal or random weights, would lead to higher performance than using cap-weighting.

A second issue is that the “noisy markets hypothesis” theory is flawed as it relies on invalid assumptions. Perold (2007) points out that the result of the “noisy market hypothesis” depends on the completely unrealistic assumption that the fair value of each stock is observable....
(emphasis added)
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Re: Equal weighting or market cap weighting?

Postby Akiva » Tue Jan 22, 2013 2:16 pm

hafius500 wrote:
Akiva wrote:...no one says that small-cap and value tilts are "quant" strategies...........This isn't a "quant" strategy because it's entirely passive. It's conceptually the same sort of thing as these fundamentally derived indexes -- a different way of estimating what weights you should assign in an attempt to overcome various problems with capitalization weights. The only difference is that it uses somewhat more sophisticated mathematics that happen to have better theoretical support. (The method also has some theoretical justification from behavioral finance.)


So you call an investor, who attempts,...who estimates...who tries to avoid less sophisticated maths...who searches theorectical support that is better than average... a passive investor?? And the active investor would be the investor who uses less sophisticated maths or the monkey that randomly selects stocks??


There's a lot of really sophisticated math that goes into the theory of market cap weighting as well (e.g. stochastic discount factors and intertemporal general equilibrium models), not to mention a whole raft of (absurdly) unrealistic assumptions about utility functions, risk preferences, etc. that you need to derive the conditions under which a market cap index makes sense.

In some sense, the alternative that I'm referencing is actually simpler, since it relies only on (advanced) econometrics and basic portfolio mathematics. In fact, but for the above complicated theory telling you that market cap weighting was right, the logical thing to do would be to use a risk factor model to estimate covariances and then solve for the minimum variance portfolio. (i.e. you admit that you can't predict returns, and unlike above, you say that you don't even know which risks will be compensated and which won't, so all you can do is minimize your overall risk.) IOW, the only reason you think that market cap weighting is passive and volatility minimizing weights are not is because there's a popular theory telling you this is the case for various esoteric reasons that most on this board don't understand and don't care to. Under different sets of assumptions, each of the various alternatives being discussed in this thread will be the resulting "market" portfolio and would thus represent the "passive" investment.

DFA funds are quant funds.


Everyone I know who works at an actual quant fund would take exception to this. DFA offers funds based around implementing the best academic evidence on investing. Nothing they do is proprietary or secret, and their turn-over is way too low to be considered "active".

Neither of the links you bring are technically apropos to this discussion because they are talking about the phenomena that a fund with returns of much above 20% ends up holding ludicrous amounts of the market over a period of time (and thus brings the market average in line with its returns). I presume the point of all this is to challenge my claim that small cap and value tilts are passive, but I would suggest that you just look around the board. No one here is going to claim that the tilts that Bogleheads use make these investments "active".

Quant funds are always active funds by definition. Google ("DFA + quant") found, e.g.,:
What Will Be Obvious 20 Years From Now? (With a Sharpe of 0.76)?. August 22nd, 2012 by Mebane Faber
What is really interesting to me is that often the great investment approaches seem so obvious in retrospect. Buffett has one of the best track records ever by buying cheap, safe, high quality stocks in a structure that allows for sub Tbill leverage. But the key is that he came to this realization before most. Ditto for the top endowments like Harvard and Yale...– it is quite obvious now, but they were pioneering these concepts decades ago. The pioneering trendfollowers and managed futures shops caught onto an idea long before computers made it simple, as did Bogle (indexing), and DFA (quant multifactor)


This post has nothing to do with DFA. Second you are confusing the use of a multifactor investment strategy with quantitative investing. Tilting towards value and small cap is not a quant strategy and the Fama French 3 factor model has nothing to do with quantitative investing.

Wikipedia gives a short explaination of what a quant fund does:

Quantitative investing represents an investing technique typically employed by the most sophisticated, technically advanced hedge funds. These quant shops employ fast computers to find predictable patterns within financial data. Some of the larger quant shops include but are not limited to Renaissance Technologies' Medallion Fund, Winton Capital Management, D. E. Shaw & Co., Barclay's Global Investments (now known as Blackrock), Numerics, GMO, First Quadrant, Robeco, etc.

Typically, quant investing is implemented by people who have spent time in the physics, math, computer science, or statistics disciplines. The condensed results of quantitative analyses, however, can be readily accessible to all far-from-quantitative investors, when presented in an intuitive framework.

The process consists of thorough examination of vast databases searching for repeating patterns—persistent occurrences of a phenomenon, correlations among liquid assets ("statistical arbitrage" or "pairs trading"), or price-movement patterns (trend following or mean reversion).


DFA is academic finance people (no hedge fund hires these guys), and they aren't looking for patterns in price data to arbitrage away, they are looking to implement the best academic understanding of passive investing.

Several posts on the Fama/French forum mention "passive" growth- or value-tilted portfolios. This quote (Gene Fama) demonstrates the errors of such propositions:


1) Fama's quote is provided without relevant context, but the argument seems to be that passive exposure to his "value" risk factor shouldn't entail trading and so the active managers have to cancel each other out, thus leaving their net returns due to value exposure to be equal to his passive benchmark less fees. Unfortunately he inserted the word "value" which makes his statement confusing -- it seems like you could say that if the active value managers win, it could be at the expense of other types of active managers, but Fama's point is that we have fully accounted for the returns to value investing with the "value" factor. So any active value manager that overweights some value stocks and underweights others is winning at the expense of other value managers, on net "value" investors can't beat the value index. The flaw in this argument is that his value index doesn't capture what active value managers typically do. Instead of using ratios, they use a discounted cash-flow model. So they aren't giving just a mix of exposure to the market factor and the value factor. There are other things going on, and consequently they could be winning at the expense of other (non-value) active managers.

2) More on topic, you are confusing someone who manages an active value fund with someone who tilts his portfolio towards value stocks as defined by exposure to Fama's own "value" risk factor. That post was about the ability of active value investors to beat the market by a substantial amount over a long period of time.

3) It is worth noting that from Fama's perspective you don't "beat the market" by tilting towards value, you simply earn an incremental return for taking incrementally more risk. But he would certainly admit that tilting in this way is entirely passive; in fact that's who he's talking about when he says "passive value managers holed value-weight portfolios of value stocks."

Active (or "passive") value investors trade against other active investors but they cannot trade against passive investors who hold the market-weighted portfolio because these investors do not trade. It would make no sense to call the seller of X a passive (value) investor and the buyer an active investor. Why not the other way around? The stock-picker or the technical investor would be passive investors as well, especially, if they "passively" stayed the course.


It does make sense to call a value tilt passive because just like holding "the market" in a market cap weighted portfolio, you are accepting known risk exposure based on market valuations.

IMO Fama's definition is tautological because the value benchmark is arbitrary and can be replaced arbitrarily:


While I take issue with the way many understand Fama's value factor, his benchmark is far from arbitrary.

"Passive stock-pickers who buy undervalued stocks hold value-weighted portfolios of undervalued stocks."


You obviously don't understand how the Fama-French three factor model works because there's no "stock-picking" involved.

As I wrote in another post, the only sensible defintion of active vs. passive investing that I have seen refers to the costs of information:


There are different methods of active management. Broadly speaking they can be grouped into two categories 1) those who try to predict returns (and thus earn higher returns for the same risk) and 2) those who try to predict how risks will change (and thus beat the market by getting equivalent returns for less risk).

Neither of these categories of techniques apply to what we are discussing here. Value-weighted indexes don't predict returns or risk, they simply weight by economic impact instead of market size. Equal-weighted indexes don't weight at all. Volatility minimizing indexes assume that risks from risk factors are constant and that exposure to those factors does not change (in contrast to method #2 above) and minimize volatility given the risk factor exposure of the stocks in the index.

Active investors make informed trades (value investors need to define and search value stocks), passive investors make informationless trades.


And none of the alternative indexing methods discussed in this thread require information. They are all the result of seeking "market" exposure under different assumptions about investor behavior.

From your second reply:
All of them agree with the maths of the two authors. The latter do not miss the point that some stocks are wrongly valued. Their proof assumes that securities are randomly mispriced ( overvalued and undervalued).


But this is question begging. The argument from the advocates of value weighting is that security mispricing is non-random. To reply by saying that "You are wrong if we assume that mispricing is random" does in fact miss the point entirely.

And there is substantial econometric evidence to support the claim of the fundamental indexing people that mispricing is non-random. Stocks with high residual volatility for example have dramatically lower returns.
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Re: Equal weighting or market cap weighting?

Postby steve r » Wed Jan 23, 2013 10:39 am

Akiva wrote:From your second reply:
All of them agree with the maths of the two authors. The latter do not miss the point that some stocks are wrongly valued. Their proof assumes that securities are randomly mispriced ( overvalued and undervalued).


But this is question begging. The argument from the advocates of value weighting is that security mispricing is non-random. To reply by saying that "You are wrong if we assume that mispricing is random" does in fact miss the point entirely.

And there is substantial econometric evidence to support the claim of the fundamental indexing people that mispricing is non-random. Stocks with high residual volatility for example have dramatically lower returns.


My thinking on this is evolving.

Assume you have $12 to invest with two stocks to buy

O priced at $3
U priced at $1

The unknown true value for each is $2. Each has an equal number of shares outstanding so price=cap weight.

You could buy 3 shares of each (cap weight) OR buy $6 of each (equal weight).

Obviously if O and U each go to $2, you would rather equal weight. This thinking is consistant with my initial (flawed) thinking.

Now change the example:
U priced at $4 (true valued $6)
O priced at $2 (true value $1)

Now you could buy 2 shares of each (cap weight) OR buy $6 of each (equal weight).
If each returns to true value in time, you would prefer to a cap weighted approach.

If I understand, this is where the random/non-random debate kicks in. For cap weight to come out ahead, the mega caps would also need to be the stocks undervalued. This can, of course, happen, but is it random? Is it equally likely to happen as the first scenario? Maybe, maybe not.

Now change the example to be random
What if you have 4 stocks. Two high priced (one overvalued & one under) and two low priced. Each 50% off from true value.

HU priced at $4 (true value $6)
HO priced at $4 (true value $2)
LU priced at $2 (true value $3)
LO priced at $2 (true value $1).

Assume you have $24 to invest. Equal weight says you can buy $6 of each share (1.5 shares of high priced & 3 shares of low priced). Cap weight says you buy 2 shares of each.
Now, if each returns to its true value. The ending value is:
Equal weight: $24
Cap weight: $24

I suspect Akiva will say the way to get undervalued stocks is to value tilt. Equal weight tilt (this discussion) does not seem to help. (Unless small/mid outperforms mega caps as pointed out by Rick and others).

Thoughts?
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 11:06 am

steve r wrote:If I understand, this is where the random/non-random debate kicks in. For cap weight to come out ahead, the mega caps would also need to be the stocks undervalued. This can, of course, happen, but is it random? Is it equally likely to happen as the first scenario? Maybe, maybe not.


I can't honestly say that I fully grasp the rationale for equal weighting because it seems to me that these sorts of arguments are dispositive. None the less, there was a megacap bubble in the late 90s that sent market cap indexes way up (and then way back down) and there are some other similar incidents in market history, so maybe you could make the argument that those stocks are more prone to bad mispricing.

OTOH, the fundamental weighting people will argue that the stocks that they overweight relative to cap weighting are likely to be under-priced and those under-weighted are likely to be over-priced. I'm not fully convinced that their methods do this, and even if you were, it isn't clear how a Bogleheads investor could go about getting exposure to such an index. Nonetheless, this is the argument that is made.

The third possibility which I raised and suggested was a better alternative than the above two doesn't rely on this over/under pricing line of thought. Instead it simply uses normal portfolio math to weight the index in a way that minimizes the overall volatility. If you had 3 assets all uncorrelated, and had no expectations about relative returns between them, the rational thing to do would be to weight by volatility so that the price changes to each asset had an equal dollar impact on the portfolio. This would give you the highest expected sharpe ratio given your knowledge (or lack thereof). The only complication with doing this with stocks is that you can't simply weight by total volatility because they are all correlated, so you have to break the volatility out by risk factors and residuals and then do the weighting using portfolio math, but in essence this is the same thing -- you want equal dollar exposure to each possible source of risk so that the benefits of diversification are maximized, leaving you only holding non-diversifiable risk (which finance theory says is the only thing that will be compensated).

In order for the market cap weighted portfolio to do better, the market has to incorporate accurate expectations about relative returns into prices *and* people have to behave according to a long list of ludicrous assumptions. OTOH, if you assume that people's investment behavior follows cumulative prospect theory, then the market portfolio should be worse than the minimum volatility one. Unlike the mispricing arguments above, cumulative prospect theory has enormous support in the economics literature, which is why I said that I thought this alternative weighting was better supported by the academic evidence.
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Re: Equal weighting or market cap weighting?

Postby MCSquared » Wed Jan 23, 2013 11:36 am

Akiva wrote:
hafius500 wrote:
Akiva wrote:...no one says that small-cap and value tilts are "quant" strategies...........This isn't a "quant" strategy because it's entirely passive. It's conceptually the same sort of thing as these fundamentally derived indexes -- a different way of estimating what weights you should assign in an attempt to overcome various problems with capitalization weights. The only difference is that it uses somewhat more sophisticated mathematics that happen to have better theoretical support. (The method also has some theoretical justification from behavioral finance.)


So you call an investor, who attempts,...who estimates...who tries to avoid less sophisticated maths...who searches theorectical support that is better than average... a passive investor?? And the active investor would be the investor who uses less sophisticated maths or the monkey that randomly selects stocks??


There's a lot of really sophisticated math that goes into the theory of market cap weighting as well (e.g. stochastic discount factors and intertemporal general equilibrium models), not to mention a whole raft of (absurdly) unrealistic assumptions about utility functions, risk preferences, etc. that you need to derive the conditions under which a market cap index makes sense.

In some sense, the alternative that I'm referencing is actually simpler, since it relies only on (advanced) econometrics and basic portfolio mathematics. In fact, but for the above complicated theory telling you that market cap weighting was right, the logical thing to do would be to use a risk factor model to estimate covariances and then solve for the minimum variance portfolio. (i.e. you admit that you can't predict returns, and unlike above, you say that you don't even know which risks will be compensated and which won't, so all you can do is minimize your overall risk.) IOW, the only reason you think that market cap weighting is passive and volatility minimizing weights are not is because there's a popular theory telling you this is the case for various esoteric reasons that most on this board don't understand and don't care to. Under different sets of assumptions, each of the various alternatives being discussed in this thread will be the resulting "market" portfolio and would thus represent the "passive" investment.

DFA funds are quant funds.


Everyone I know who works at an actual quant fund would take exception to this. DFA offers funds based around implementing the best academic evidence on investing. Nothing they do is proprietary or secret, and their turn-over is way too low to be considered "active".

Neither of the links you bring are technically apropos to this discussion because they are talking about the phenomena that a fund with returns of much above 20% ends up holding ludicrous amounts of the market over a period of time (and thus brings the market average in line with its returns). I presume the point of all this is to challenge my claim that small cap and value tilts are passive, but I would suggest that you just look around the board. No one here is going to claim that the tilts that Bogleheads use make these investments "active".

Quant funds are always active funds by definition. Google ("DFA + quant") found, e.g.,:
What Will Be Obvious 20 Years From Now? (With a Sharpe of 0.76)?. August 22nd, 2012 by Mebane Faber
What is really interesting to me is that often the great investment approaches seem so obvious in retrospect. Buffett has one of the best track records ever by buying cheap, safe, high quality stocks in a structure that allows for sub Tbill leverage. But the key is that he came to this realization before most. Ditto for the top endowments like Harvard and Yale...– it is quite obvious now, but they were pioneering these concepts decades ago. The pioneering trendfollowers and managed futures shops caught onto an idea long before computers made it simple, as did Bogle (indexing), and DFA (quant multifactor)


This post has nothing to do with DFA. Second you are confusing the use of a multifactor investment strategy with quantitative investing. Tilting towards value and small cap is not a quant strategy and the Fama French 3 factor model has nothing to do with quantitative investing.

Wikipedia gives a short explaination of what a quant fund does:

Quantitative investing represents an investing technique typically employed by the most sophisticated, technically advanced hedge funds. These quant shops employ fast computers to find predictable patterns within financial data. Some of the larger quant shops include but are not limited to Renaissance Technologies' Medallion Fund, Winton Capital Management, D. E. Shaw & Co., Barclay's Global Investments (now known as Blackrock), Numerics, GMO, First Quadrant, Robeco, etc.

Typically, quant investing is implemented by people who have spent time in the physics, math, computer science, or statistics disciplines. The condensed results of quantitative analyses, however, can be readily accessible to all far-from-quantitative investors, when presented in an intuitive framework.

The process consists of thorough examination of vast databases searching for repeating patterns—persistent occurrences of a phenomenon, correlations among liquid assets ("statistical arbitrage" or "pairs trading"), or price-movement patterns (trend following or mean reversion).


DFA is academic finance people (no hedge fund hires these guys), and they aren't looking for patterns in price data to arbitrage away, they are looking to implement the best academic understanding of passive investing.

[quote]

You might be interested in this thread:

viewtopic.php?t=61753&mrr=1289065546&start=51


Multifactor Advisor wrote:
For Rick: DFA isn't a "quant shop", not sure where you got that. They run a form of passive fund that is considered "structured". As Bridgeway does with their Ultra Small Market Fund...You are ignoring that are two types of passive investments: indexed and structured. The only concern of an index fund is to track the predefined index with 0 tracking error every single day of the year. The index in many cases is arbitrarily defined by a 3rd party committee (see S&P or Russell), and only has a loose association with expected risk and return. Structured funds, on the other hand, do in fact have indexes they follow, but not at the expense of reducing expected returns.


Rick Ferri replied:

A rose by any other name is still a rose.

Structured indexing = quant investing.

It's all marketing. It's all sales spin.

I'm not being critical of what DFA is doing. Just call it what it is. They are not following market-cap benchmarks, nor are they trying to mimic any part of the market. What DFA does is select securities with rather sophisticated multi-factor screens, trade securities using momentum strategies, and employs an eclectic securities weighing strategy. None of this is bad, but it's not indexing either. It's quantitative investing! Even more so than what Robb Arnott has done with RAFI indexes, BTW.

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Re: Equal weighting or market cap weighting?

Postby Rodc » Wed Jan 23, 2013 11:37 am

Akiva,

The math you mention is certainly correct. I learned it as the Gauss-Markov theorem but it also goes by other names. Assuming we use TSM,ITSM,TBM or break TSM into some standard components like small or value, and assuming we can estimate the required parameters to some reasonable level of accuracy, what is a typical suggested portfolio from this process?

Thanks
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Re: Equal weighting or market cap weighting?

Postby steve r » Wed Jan 23, 2013 1:03 pm

Akiva wrote:
steve r wrote:If I understand, this is where the random/non-random debate kicks in. For cap weight to come out ahead, the mega caps would also need to be the stocks undervalued. This can, of course, happen, but is it random? Is it equally likely to happen as the first scenario? Maybe, maybe not.


I can't honestly say that I fully grasp the rationale for equal weighting because it seems to me that these sorts of arguments are dispositive. None the less, there was a megacap bubble in the late 90s that sent market cap indexes way up (and then way back down) and there are some other similar incidents in market history, so maybe you could make the argument that those stocks are more prone to bad mispricing.

OTOH, the fundamental weighting people ....The third possibility ... weight the index in a way that minimizes the overall volatility. .


I think people like equal weight because it is easy to do ...
Some points, according to the Wiki, Wilshire EW outperofrmed the Wilshire 5000 in the 1990s (and every decade). That said, I think it can safely be said this is due to micro caps.
http://www.bogleheads.org/wiki/Equal_Weighted_Indices

That said, an equal weight S&P500 underperformed the S&P500 in the 1990s. This chart compares low volatility strategy and fundamentally weighted indexes 1991-2011.

Image

Uploaded with ImageShack.us

Source: http://www.spindices.com/assets/files/sp500/pdf/EvaluatingAlternativeBetaStrategies.pdf

A bit hard to read, but the highest return over 20 years is for Equal Weight.

Also, according to the article, the source for the chart
Source: S&P Indices, FTSE, AQR Capital Management LLC. Data from December 31, 1990 to October 31, 2011. The Fundamentally Weighted Strategy is represented by MSCI USA Value Weighted Index; the Equal Weighted Strategy is represented by S&P 500 Equal Weight Index; the Low Volatility Strategy is represented by S&P 500 Low Volatility Index; and the Momentum Strategy is represented by AQR US Large Cap Momentum Index. Some of the S&P 500 Equal Weight Index and S&P 500 Low Volatility Index data reflected in this chart may reflect hypothetical historical performance. Charts are provided for illustrative purposes. Past performance is not a guarantee of future results.

I added this in an edit because I think volatility weighting and fundamentally weighted indexes means different things to different people. This is perhaps another appeal of equal weight, the methodology is easily understood (though not optimized).
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 1:39 pm

Rodc wrote:Akiva,

The math you mention is certainly correct. I learned it as the Gauss-Markov theorem but it also goes by other names.


Solving for minimum-variance portfolios with a no-short sale constraint is standard fair in advanced textbooks on portfolio theory and has nothing to do with statistics. As for the econometrics part, I'm not talking about the Gauss-Markov theorem of linear regression. Much of advanced econometrics (and some of advanced statistics) is primarily concerned with what to do when the Gauss-Markov assumptions are violated as they are in the case of stock market return data.

As a simple example of what I'm talking about, you could look at Chris Jone's heteroskedasticity-consistent version of Connor and Korajcyzk's principle components procedure. C.S. Jones "Extracting Factors from Heteroskedastic Asset Returns," Journal of Financial Economics 62 no. 2 (2001): 293-325; G. Connor and R. Korajczyk. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance 52 (1997): 327-340. Beyond this, see section 6.14 of Rand Wilcox's Introduction to Robust Estimation & Hypothesis Testing for alternative ways of doing this sort of thing.

Methods like the above are popular with researchers (though econometricians tend to disfavor robust statistical methods like those in Wilcox for some reason). The BARRA GEM model and competitors use fundamentally derived factors and while this makes them somewhat more complicated, it also makes their results more robust, and I *think* this ends up reducing portfolio turn-over in the MVP indexes (though, setting trading costs aside, I'm not convinced it performs as well; I'd have to get a lot more data and do a lot more experimentation to determine that.)

Assuming we use TSM,ITSM,TBM or break TSM into some standard components like small or value, and assuming we can estimate the required parameters to some reasonable level of accuracy, what is a typical suggested portfolio from this process?


1) This is an off-topic question for this thread since we are talking about alternative ways to weight these indexes, not how to optimize a portfolio of cap-weighted indexes. (Though, while I'm thinking about it, I'll point out that there's good research that e.g. simply omitting bonds with call risk from TBM improves returns. There are a lot of other documented anomalies as well. So to the extent that these alternative weighting methods work around the known anomalies, they should do better.)

2) There are a couple of ways to answer your question. The normal way to do it is to write down what you expect returns and covariances to be. (Instead of covariances you can use variances and correlations which give you the same information.) Then use portfolio mathematics to solve for the optimal sharpe ratio. (If this leaves you with returns that are too low, you can use leverage to increase both returns and risk. If it leaves you with risk that is too high, you move some of your money to cash and decrease your exposure to the portfolio.)

3) The more robust way to solve it (which is actually used by fund-of-funds hedge fund managers) is to assume that you don't know what relative returns will be but that covariances will stay relatively constant (accounting for the fact that in liquidity crises, lots of portfolio correlations go to 1, etc.) and then simply minimize volatility; i.e. you equalize your dollar exposure to each risk opportunity. To the extent that TBM and TSM are uncorrelated, this means you weight them inversely proportional to their volatilites.

4) I haven't run the numbers with these two funds, but IIRC, this method tells you to put ~30% in the S&P500 and ~70% in treasury bonds which works out to be pretty close to the historically optimal sharpe ratio. (And doing this historically would have probably gotten you closer to that optimum than the traditional method in #2 using long-run historical average returns. Method #2 really only seems to work better prospectively if you can predict a large relative bull or bear market in some asset class.) Using Jack Schwager's futures data for 1980 to 1995 (what I happen to have on hand), shows that historically this got you a Sharpe ratio of about 1.5 (that this ratio is so high is probably an artifact of the double bull market, that it is close to the best ratio you could have gotten in a given year is not). It returned only slightly less than the S&P500 over that time period and at substantially lower risk. (It also returned more than T-bonds at slightly lower risk.) If you use leverage to equalize the risk exposure, you need about 1.08x leverage to make the risk equal the risk of 100% T-bonds, in which case it nets you an extra ~75% return over the 15 year period vs. T-bonds (750% vs 675%) . If you want to equal the risk of stocks, you need about 1.38x leverage, and then you come out with an extra 100% returns (800% vs. 700%). Realistically, you'd pick something in-between. (N.B. I didn't account for differences between futures taxation and stock taxation when I did this. Also note that the primary reason for the higher cumulative returns of the mixed portfolio is that reduced volatility improves CAGR.)
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 2:27 pm

MCSquared wrote:You might be interested in this thread:


Rick Ferri wrote:A rose by any other name is still a rose.

Structured indexing = quant investing.

It's all marketing. It's all sales spin.

I'm not being critical of what DFA is doing. Just call it what it is. They are not following market-cap benchmarks, nor are they trying to mimic any part of the market. What DFA does is select securities with rather sophisticated multi-factor screens, trade securities using momentum strategies, and employs an eclectic securities weighing strategy. None of this is bad, but it's not indexing either. It's quantitative investing! Even more so than what Robb Arnott has done with RAFI indexes, BTW.


I disagree with Ferri's quote above, though I share his concern that the DFA funds may be over-hyped by some people.

1) Market-cap weighting is only passive if you make certain assumptions that we know to not be true. Under other assumptions, then various alternative indexes become the passive investment. The reason market-cap weighting is popular has more to do with the fact that it is low cost, relatively robust, and so forth, and less to do with the fact that it is theoretically "correct".

2) Quant funds have high turn-over and focus on arbitraging mispricing phenomena. What DFA does is more quantitative than simple market cap investing, but that doesn't make them a quant fund. In particular, quant funds use a lot of stochastic calculus from physics, but what DFA is doing is using financial mathematics based on the best academic studies. He has a better argument that the RAFI indexes are active strategies since they aren't transparent, supported by substantial academic evidence, etc.

3) Taken at face value, Ferri's post implies that tilting towards small and value (as he is reported to do) is also a "quant strategy" and that's just an absurd conclusion (which is the only reason DFA got brought up to begin with). Ferri himself agrees that small and value tilts are passive strategies in the thread you linked.

4) The bottom line on the DFA funds themselves is that there are multiple ways to implement an index tracking fund, and DFA makes different trade-offs than Vanguard. Investors should understand what these trade-offs are and pick their funds accordingly. (But this is moot for purposes of this thread.)
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 2:35 pm

steve r wrote:That said, an equal weight S&P500 underperformed the S&P500 in the 1990s. This chart compares low volatility strategy and fundamentally weighted indexes 1991-2011.


I just want to point out that the "low volatility strategy" used here is not the same as the volatility minimizing strategy I've been talking about. The S&P500 low volatility index just measures the performance of the 100 lowest volatility stocks in the S&P500 when they are weighted inverse to volatility. It doesn't actually run a factor model and weight them to minimize portfolio volatility. (There's a pretty dramatic difference between the two methods because, as I alluded to above, inverse volatility weighting only works if the assets are uncorrelated, and stocks tend to be highly correlated.)
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Re: Equal weighting or market cap weighting?

Postby Rick Ferri » Wed Jan 23, 2013 2:52 pm

Akiva wrote:The bottom line on the DFA funds themselves is that there are multiple ways to implement an index tracking fund, and DFA makes different trade-offs than Vanguard. Investors should understand what these trade-offs are and pick their funds accordingly. (But this is moot for purposes of this thread.)


It seems to me the first test to determine if a fund is an index fund ought to be if the fund follows an index. DFA funds do not follow indexes. Consequently, they are not index funds. The next best description would be a asset class fund. But DFA does not use all investible securities within an asset class, so that doesn't fit either. The third description for DFA funds would be quantitative, which means they use some type of screening model. That fits DFA.

BTW, where did this idea come from that said the required characteristic of a quant fund is that it must have high turnover of securities and use mathematics from physics to pick constituants? That's something someone made-up. A quant fund only has to have somewhat sophisticated buy and sell screens, which describes exactly what DFA does.

DFA is quant, and David Booth agrees.

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Re: Equal weighting or market cap weighting?

Postby steve r » Wed Jan 23, 2013 3:23 pm

Akiva wrote:
steve r wrote:That said, an equal weight S&P500 underperformed the S&P500 in the 1990s. This chart compares low volatility strategy and fundamentally weighted indexes 1991-2011.


I just want to point out that the "low volatility strategy" used here is not the same as the volatility minimizing strategy I've been talking about. The S&P500 low volatility index just measures the performance of the 100 lowest volatility stocks in the S&P500 when they are weighted inverse to volatility.


I gathered that - thus I added the chart sources.

Akiva wrote:... It doesn't actually run a factor model and weight them to minimize portfolio volatility ...


Is there is an easy way (EFT/Index fund) to invest in this?
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Re: Equal weighting or market cap weighting?

Postby Rodc » Wed Jan 23, 2013 3:39 pm

Akiva,

FWIW: Almost nothing in your last post is anything new to me, it is just basic math. The concern would be in all the assumptions you apply the math too.

But it misses the point I was trying to get at, so I will try again.

I had an early mentor that counseled: all great innovations are disruptive.

A new technology that allows someone to do the same job more efficiently is good, but not great. To be great a new technology it has to fundamentally change the way people work and live.

For example we spend way too much time and energy here debating ways of calculating max safe withdrawal rates, and all methods seem to fundamentally give the same basic result within some modest margin of error. So none are great innovations that topple the simplicity of the Trinity study. They may be modest incremental improvements, but nothing to get excited about. This seems to be true of 99.44% of arguments between academics: the stakes are so low all there is the fight.

So, I’m trying to understand the significance of minimum variance portfolio construction to an individual investor, who is likely very different from a hedge fund (would not lever up a minor advantage, interested in using straightforward long only mutual funds, etc.)

If min variance methods tell someone interested in investing in basic index funds that they can minimize variance with about a 70% treasury/ 30% stock portfolio, within some modest margin of error the same thing we learn from looking at historical results, that is interesting, but not a particularly valuable result. It validates in a sense what history already told us and that is good, but does not make most individuals a better investor.

A common around here portfolio for someone who does not want to tilt small and value might be 35/25/40 TSM/ITSM/TBM. I am not arguing this is great, just saying it seems in the mainstream. If one believes in tilting small and value (which for the record is what I do), then a roughly equivalent risk portfolio might split the stocks 50/50 Large cap blend and small cap value, and increase the bonds to 50% to balance taking a little more risk on the stock side. The question would then be what would such an investor end up with using min variance methods applied to the same building blocks, say TSM, large cap blend, small cap value (US and international) and TBM, and what is the expected performance difference?

The answer might be:

(1) You can’t get a comparable portfolio because it will end up with 70% TBM (used with TSM) or 80% TBM ( used with small and value tilt). And in practice you would not lever up because you can't do that in your 401K, costs are prohibitive, fear of margin call. That would be interesting.

(2) Or the answer might be something not all that far from the mainstream portfolios, maybe plus or minus 5% here or there. Interesting, but not very useful.

(3) Or the answer might be something wildly different, which would really be the most interesting. And then the follow up is what is the expected level of advantage?

I’m just hoping for a sense of which answer is closest to your expectations.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 3:43 pm

This DFA thing is a huge distraction from the main discussion. The signal is being lost in the noise. Perhaps a recap will be helpful:

Basically someone asked about alternative ways of constituting an index (such as "fundamentally" or "equally weighted"). After some back and forth it was pointed out that the reason equal weighting does better is because it has different factor loadings in the Fama-French model than market cap and thus has higher expected returns. That same person then compared the DFA small cap fund to some other small cap fund and pointed out that similarly, the differences in returns between those funds was accounted for by differences in factor loadings.

Then someone else objected that the DFA funds were "quant funds" and were thus "active" and that this wasn't a fair comparison. I then foolishly objected to the use of the term "quant fund" because there's a difference between a fund that uses a quantitative strategy (like DFA does) and the hedge funds that do "quantitative investment" like the Renaissance Technologies' Medallion Fund. No one thinks that what DFA does is in any way comparable to what Renaissance does and while it may be a misnomer, the latter is considered the prototypical "quant fund". It and funds like it have a bunch of characteristics that differentiate what they are doing from other sorts of active funds (which confusingly may also use different kinds of quantitative strategies and still not be called "quant funds").

In retrospect making this objection was a mistake because it contributed to derailing this thread. Still, I stand by my point which was that you shouldn't confuse what DFA is doing with what the hedge funds that are commonly called "quant funds" do (as the person who made the objection seemed to do). Furthermore, while DFA is different from Vanguard, it isn't fair to rule out the analysis in question because DFA funds don't try to beat the market as much as efficiently capture exposure to risk factors. And even if their goal was to beat the market with active management, you could still analyze the return differences in terms of factor loadings and reach the same basic conclusion that the person who brought it up was trying to make.

Anyway, in reply to what you wrote:

Rick Ferri wrote:
Akiva wrote:The bottom line on the DFA funds themselves is that there are multiple ways to implement an index tracking fund, and DFA makes different trade-offs than Vanguard. Investors should understand what these trade-offs are and pick their funds accordingly. (But this is moot for purposes of this thread.)


It seems to me the first test to determine if a fund is an index fund ought to be if the fund follows an index. DFA funds do not follow indexes. Consequently, they are not index funds.


Correct me if I'm wrong, but my understanding is that, e.g., the total weight a stock gets in one of their core funds is determined by some weighted mixture of the three Fama-French factor portfolios (so it's just a weighted average of the weights it gets in each of the three "indexes").

The next best description would be a asset class fund. But DFA does not use all investible securities within an asset class, so that doesn't fit either.


Well, AFAIK, Vanguard doesn't use literally every possible stock that constitutes an index either, they track a statistically representative sample of the actual index as a way of keeping costs down. (And they do a very good job of this.) My understanding is that DFA accepts more risk of tracking error to reduce trading and other costs.

The third description for DFA funds would be quantitative, which means they use some type of screening model. That fits DFA.


I understand that they don't aggressively reconstitute their funds as the indexes change, but my impression was that this was just a function of trading based on the fund's cash in-flows and out-flows rather than some attempt to actively get a better fill than the current market price.

Maybe I'm wrong about all of this. You've actually been to their events and probably know more about how the funds work than I do, but the above is my current understanding of what they do.

BTW, where did this idea come from that said the required characteristic of a quant fund is that it must have high turnover of securities and use mathematics from physics to pick constituants? That's something someone made-up. A quant fund only has to have somewhat sophisticated buy and sell screens, which describes exactly what DFA does.

DFA is quant, and David Booth agrees.


As I said above, my point was that DFA wasn't "quant" in the same way that Renaissance is "quant" (which is what the person I was replying to implied) because it didn't share any of the characteristics of the funds that are considered to be in the same style as that fund.

Furthermore it is a mistake to say that you can't use the Fama-French model to compare the returns of an active fund and a passive fund. To the extent that the differences in return are caused by different factor loadings, you know that manager skill wasn't involved, simply risk taking.

Anyway, in an attempt to get back on topic:
steve r wrote:Is there is an easy way (EFT/Index fund) to invest in this?


I'll answer your question, but as a preface, in my first post, way up top, I said, "I think that as a practical matter market-cap weighting generally makes sense." Of course you can deviate from pure market cap weighting to account for things like small cap and value premiums, various market anomalies, etc., but in general most investors want a market cap weighted index as their core fund.

Now, simply for the purposes of information, I pointed out that there were some perceived disadvantages to market-cap based funds, and that out of all the research on possible alternatives, I thought the minimum volatility portfolio idea had the best academic support because it falls out of the standard arguments for market cap weighting by suitably altering your assumptions in realistic, plausible ways and because the idea behind it seems mathematically sound. So if you are going to play with any of the things being discussed in the thread, this is probably the one you'd prefer.

Now, in answer to your question, until recently, there were only a couple of active funds in this space, but iShares recently created a couple that track the relevant MSCI indexes (ACWV, EFAV, EEMV, and USMV).
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Re: Equal weighting or market cap weighting?

Postby Rodc » Wed Jan 23, 2013 4:16 pm

The iShares are interesting. Very inexpensive. Very concentrated. Very short history.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 4:24 pm

Rodc wrote:For example we spend way too much time and energy here debating ways of calculating max safe withdrawal rates, and all methods seem to fundamentally give the same basic result within some modest margin of error. So none are great innovations that topple the simplicity of the Trinity study. They may be modest incremental improvements, but nothing to get excited about. This seems to be true of 99.44% of arguments between academics: the stakes are so low all there is the fight.


In fairness, none of the ideas that I'm talking about have minor significance.

So, I’m trying to understand the significance of minimum variance portfolio construction to an individual investor, who is likely very different from a hedge fund (would not lever up a minor advantage, interested in using straightforward long only mutual funds, etc.)


Well, *if* the advocates of this method are right, then you can get exposure to the risks that the stock market compensates with 30-40% less volatility. That means that your overall portfolio will have substantially lower volatility, substantially higher returns, or (likely) both. (At least over long-ish time horizons. In the short term, you could have a lot of "tracking error" against a market cap index.)

If min variance methods tell someone interested in investing in basic index funds that they can minimize variance with about a 70% treasury/ 30% stock portfolio, within some modest margin of error the same thing we learn from looking at historical results, that is interesting, but not a particularly valuable result. It validates in a sense what history already told us and that is good, but does not make most individuals a better investor.


Well, that was just my example of applying the math, but even here the results aren't insignificant, the reduced variance and higher CAGR are large. The only reason to deviate from this would be if you couldn't hit your return targets with this allocation and couldn't use leverage to fix it. Otherwise you'd be lowering your Sharpe ratio needlessly. (I realize that retail investors don't have access to leverage in the way that large institutions do, but I'm more comfortable giving examples from my area of expertise. Ferri and Swedroe are better to talk to about how to navigate the additional constraints smaller investors face.)

A common around here portfolio for someone who does not want to tilt small and value might be 35/25/40 TSM/ITSM/TBM. I am not arguing this is great, just saying it seems in the mainstream. If one believes in tilting small and value (which for the record is what I do), then a roughly equivalent risk portfolio might split the stocks 50/50 Large cap blend and small cap value, and increase the bonds to 50% to balance taking a little more risk on the stock side. The question would then be what would such an investor end up with using min variance methods applied to the same building blocks, say TSM, large cap blend, small cap value (US and international) and TBM, and what is the expected performance difference?


I understood this to be your question originally, but I didn't answer it directly because it was off topic for this thread and because I don't have the information that would be needed to run those numbers for you readily available. Still, I gave you a simpler example to extrapolate from. Similarly, in some other thread about the "Permanent Portfolio", I ran the numbers for someone and concluded that instead of 25/25/50 stocks/gold/fixed income, that the rational a priori allocation would have been 25/15/60 which incidentally turns out to have produced better returns with less risk (and falls extremely close to the results of post-hoc numerical optimization). As for your question, I can't do the math in my head or with a calculator once the correlations get non-trivial, so what you are asking for is a lot more work...

In any event, this thread is talking about alternative ways to weight an index of stocks, not about ways to decide on allocations between asset classes in a portfolio. (Though you are correct to say that the concepts and the math do not differ.) If you want to do this yourself and aren't familiar with the matrix algebra, you can probably get an answer anyway by simply using the "Solver" plug-in to Excel.

(1) You can’t get a comparable portfolio because it will end up with 70% TBM (used with TSM) or 80% TBM ( used with small and value tilt). And in practice you would not lever up because you can't do that in your 401K, costs are prohibitive, fear of margin call. That would be interesting.

(2) Or the answer might be something not all that far from the mainstream portfolios, maybe plus or minus 5% here or there. Interesting, but not very useful.

(3) Or the answer might be something wildly different, which would really be the most interesting. And then the follow up is what is the expected level of advantage?

I’m just hoping for a sense of which answer is closest to your expectations.


In general, I think the inability to go with a slightly levered conservative portfolio is an impediment that retail investors have to face. For a variety of reasons, you are often faced with having to accept a much worse sharpe ratio in return for a slightly better return. That's unfortunate.

Still, I think that the actual differences are smaller than you think because increasing your variance to increase arithmetic return does not always help your CAGR as much as you'd think. In terms of CAGR, you are accepting a lot of extra volatility for only a slightly higher gain. You should be sure that this is what you want. (That 25/15/60 portfolio used as an example above did extremely well historically despite its small allocation to stocks and it's not just an artifact of including gold. People are often more aggressive than they have to be.)

The iShares are interesting. Very inexpensive. Very concentrated. Very short history.


If you have access to a Bloomberg or Reuters terminal, you can pull up the history of the index it tracks and get more data. I think this is an interesting idea, but the jury is still out on whether it is right or not.
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Re: Equal weighting or market cap weighting?

Postby Barry Barnitz » Wed Jan 23, 2013 4:39 pm

Hi:

As it happens, I am currently working on a page dealing with Low Volatility index returns (MSCI, S&P, and Russell). As for investing options, iShares has four etfs tracking MSCI indexes, and Powershares has two etfs tracking S&P indexes. No one to my knowledge is providing index trackers for the Russell indexes.

You may want to note that the two linked articles have comments from Gus Sauter (indexuniverse article) and a John Spence article expressing Vanguard's interest in possibly adding Low Volatility index funds.

I am not sure I can accurately parse the methodologies behind the three index providers. (Anyone who wishes to help out on this page is more than welcome. If you are not currently signed up with the wiki, simply ask and access will be granted.)

Low Volatility Index returns - Bogleheads

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Re: Equal weighting or market cap weighting?

Postby steve r » Wed Jan 23, 2013 4:49 pm

Akiva wrote:
steve r wrote:Is there is an easy way (EFT/Index fund) to invest in this?


... So if (emphasis added) you are going to play with any of the things being discussed in the thread, this is probably the one you'd prefer.

Now, in answer to your question, until recently, there were only a couple of active funds in this space, but iShares recently created a couple that track the relevant MSCI indexes (ACWV, EFAV, EEMV, and USMV).


Thanks. I decided to add some EW index a few months back and am doing so shortly (after pending backdoor Roth). I think I will pick ACWV instead of EWRI. (The bulk of my investments are cap weighted 403b and was looking for something different, I also wanted a touch more international exposure in my Roth.) I am not a cap weighted purist, but I have not bought into the FF model either (the idea that certain sizes and value exposure will systematically outperform seems to counter EMH enough for me not to be a firm enough believer thus would personally be unable to stay the course - I have read enough discussions on this).

Rodc wrote:The iShares are interesting. Very inexpensive. Very concentrated. Very short history.


I am curious about the concentrated comment? It seems like it has a lot of sectors. Between 0.87 and 1.56 percent holdings for the largest 25 holding each. with 13.82 in top ten. 265 holdings in many countries and sectors. I am curious if I am missing something? (Clearly more concentrated than EWRI).

---
The emerging market one (EEMV) is also interesting. I am somewhat surprised in tilts growth per M*. Also. the expenses are scheduled to really come up next year on this one. Need to think / learn more.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 5:00 pm

Barry Barnitz wrote:Hi:

As it happens, I am currently working on a page dealing with Low Volatility index returns (MSCI, S&P, and Russell). As for investing options, iShares has four etfs tracking MSCI indexes, and Powershares has two etfs tracking S&P indexes. No one to my knowledge is providing index trackers for the Russell indexes.

You may want to note that the two linked articles have comments from Gus Sauter (indexuniverse article) and a John Spence article expressing Vanguard's interest in possibly adding Low Volatility index funds.

I am not sure I can accurately parse the methodologies behind the three index providers. (Anyone who wishes to help out on this page is more than welcome. If you are not currently signed up with the wiki, simply ask and access will be granted.)

Low Volatility Index returns - Bogleheads

regards.


Thanks for that information.

1) The first thing I'd note is that the MSCI indexes are constructed completely differently from the S&P and Russell ones. They really aren't comparable, and probably shouldn't go by the same name.

2) Re: methodology. The S&P and Russell ones basically take a list of stocks and add the N lowest volatility ones to the index where N is a certain number for the S&P and N is a % of the underlying index's market cap for the Russell. (This is in contrast to the original academic literature which *dropped* the N highest...) The MSCI one uses a risk factor model to adjust the weights on the stocks in the index such that it keeps roughly "market" risk exposure, but minimizes the expected volatility and then drops all the stocks with weights below a threshold.

3) MSCI has returns for their index going back at least 10 years, but I don't know how to get them for you without violating data licensing agreements. Maybe you could ask them nicely?

4) I think adding a column with the regular S&P 500 returns and volatility to each of those charts would be helpful for purposes of comparison.

steve r wrote:Thanks. I decided to add some EW index a few months back and am doing so shortly (after pending backdoor Roth). I think I will pick ACWV instead of EWRI. (The bulk of my investments are cap weighted 403b and was looking for something different, I also wanted a touch more international exposure in my Roth.) I am not a cap weighted purist, but I have not bought into the FF model either (the idea that certain sizes and value exposure will systematically outperform seems to counter EMH enough for me not to be a firm enough believer thus would personally be unable to stay the course - I have read enough discussions on this).


Just make sure you understand what the performance characteristics are -- it lags the market in up years and does better in down years.
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Re: Equal weighting or market cap weighting?

Postby steve r » Wed Jan 23, 2013 5:09 pm

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Re: Equal weighting or market cap weighting?

Postby Rodc » Wed Jan 23, 2013 7:35 pm

Well, that was just my example of applying the math, but even here the results aren't insignificant,


If the results are completely known already the method results in no significant new information; we all knew min variance stocks/bonds portfolio was historically about 30/70.

And yes I have strayed from one topic to a related topic; conversations are like that.

The more I think about this the more nonsensical it seems to be.

If one is building a diversified portfolio of stocks and bonds and one ignores expected returns and only looks at variance that completely ignores the rather important fact that stocks have a much higher expected return than bonds. That makes no sense at all. Might be valuable for a hedge fund that is willing to take on leverage, though may well blow up in their face, but is of no value to anyone here.

If one applies this, like the iShares funds to only a collection of say a couple hundred stocks it makes sense, especially if one sticks to large caps, to assume they have the same expected return so you can ignore expected returns. But then you must estimate expected variance (risk) of each individual company going forward (and correlation), like somehow this is a constant, like markets don't change and like this is not swamped by noise. Boy does that sound like a shady business. I might buy you have a hope, sort of or in a relative sense, to estimate the future variance of a large well defined sector (say stocks vs bonds, or large stocks vs small), but of individual companies? No way does that make sense.

*******************

As noted the MSCI indexes may go back 10 years, but so what? I can data mine all sorts of things and publish the things that worked for a short time, and yes 10 years is short when data mining, and bury the things that didn't. See me in 10 years and if these ETFs are going strong I'll buy you a nice dinner. I think the odds are in my favor.

This seems to not pass any common sense test. IMHO.

But for anyone who thinks this does make sense, I wish you luck, maybe I'm just a fuddy duddy.
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Re: Equal weighting or market cap weighting?

Postby Akiva » Wed Jan 23, 2013 7:51 pm

Rodc wrote:
Well, that was just my example of applying the math, but even here the results aren't insignificant,


If the results are completely known already the method results in no significant new information; we all knew min variance stocks/bonds portfolio was historically about 30/70.


It's not just min vol. It's also the highest sharpe ratio. And if you are rational, that's what you should care about.

And yes I have strayed from one topic to a related topic; conversations are like that.

The more I think about this the more nonsensical it seems to be.

If one is building a diversified portfolio of stocks and bonds and one ignores expected returns and only looks at variance that completely ignores the rather important fact that stocks have a much higher expected return than bonds. That makes no sense at all.


All you are saying is that you can't reliably predict what the returns are going to be over the time horizon that you plan to use for rebalancing. (And this is true. Stocks return more than bonds over a very long period of time, but they don't return more than bonds *every year*.)

Furthermore, part of the reason it works is because CAGR is a function of both returns and volatility and you can move volatility a lot more easily than you can more returns, so as a general rule, the highest CAGR is "close" to the minimum volatility portfolio.

Might be valuable for a hedge fund that is willing to take on leverage, though may well blow up in their face, but is of no value to anyone here.


Well, it highlights the costs of more aggressive allocations, which is worthwhile. And in point of fact, a moderately leveraged 30/70 allocation is substantially less risky than an unleveraged allocation that goes much heavier into stocks. So if it blows up in your face, then the heavier stock allocation would have blown up even more...

If one applies this, like the iShares funds to only a collection of say a couple hundred stocks it makes sense, especially if one sticks to large caps, to assume they have the same expected return so you can ignore expected returns.


Given that that's the original context we were talking about, things seem fine.

But then you must estimate expected variance (risk) of each individual company going forward, like somehow this is a constant, like markets don't change and like this is not swamped by noise. Boy does that sound like a shady business. I might buy you have a hope, sort of or in a relative sense, to estimate the future variance of a large well defined sector (say stocks vs bonds, or large stocks vs small), but of individual companies? No way does that make sense.


As much as you want to deny it, you can reliably predict covariances using a factor model. This has long been established.

*******************

As noted the MSCI indexes may go back 10 years, but so what? I can data mine all sorts of things and publish the things that worked for a short time, and yes 10 years is short when data mining, and bury the things that didn't. See me in 10 years and if these ETFs are going strong I'll buy you a nice dinner. I think the odds are in my favor.


I don't know if the ETF will stick around because people are probably only going to be interested in it for as long as they remember how volatile the stock market can get, which means that they'll dump it when it lags the market during the next major bull swing.

But as for the idea itself, this is at least grounded in serious academic scholarship. (Not "data mining" and other gimmicks.) So it is reliable to the extent that you find the research credible. I think there is some good evidence, but that the jury is still out. Thus what I said above holds: if you are going to play around with alternative weightings, this one deserves consideration probably much more than equal weighting and fundamental weighting.

This seems to not pass any common sense test. IMHO.


As I pointed out above, this is more sensible than lots of other things being suggested in this thread.
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Re: Equal weighting or market cap weighting?

Postby steve r » Thu Jan 24, 2013 8:38 pm

Akiva,

I am curious how bonds play into a lazy portfolio with variance minimization.

With the newest Simba data (1972-2012) a TSM or Total international Index would need roughly 1/3 bonds or ITT to get a one third reduction in standard deviation.

I am well aware that the variance minimization with underperform in boom markets. But so too will my current portfolio (which, incidently, also tries to minimize risk with diversification and low historic correlations of indexed assets). The only real concern I have is a "possible" disappearing ETF. The fact that ACWV - my favorite in terms of holdings - has higher bid ask spread. A short term expense ratio cap of .20 is nice, and long term actual expenses around .34 is tollerable.

Pulled no triggers yet.

Thoughts
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Re: Equal weighting or market cap weighting?

Postby Akiva » Sun Jan 27, 2013 4:03 pm

steve r wrote:Akiva,

I am curious how bonds play into a lazy portfolio with variance minimization.


Well, let's assume that the theory is right and that ACWV gives you roughly the same returns for about 65% of the volatility, back of the book calculations imply that you can put about 5% more in stocks than you otherwise would without markedly changing your risk. (The % is so small because stocks are already much more volatile than bonds.)

It may be worth pointing out that this effect may not amount to much in a retail investor's portfolio. I recently looked into the possibility of using VIX futures to reduce the volatility of a stock portfolio (and thereby allow you to increase your stock allocation for the same risk). Using monthly data between 1996 and 2012, the VIX had -70% correlation with VTSMX and almost 4x the volatility (and zero nominal returns). A mix of 85% VTSMX and 15% VIX futures had a 40% lower standard deviation of returns and a 50% higher sharpe ratio. Similar to above, this lets you increase your stock allocation by about 5%, and in a stock/bond portfolio, it improves your returns and decreases your volatility, but the impact is so slight that the sharpe ratio is only about 7% higher, and over a 20 year period, this works out to an extra 2.5% total return if you don't increase leverage. OTOH if you add 5% leverage so that your volatilities are equal, this works out to an extra 25% total return over a 20 year period.

Furthermore, I've been using a 30/70 portfolio as a comparison. But if you are willing to take the risks of the 60/40 portfolio that people think of as standard around here, then you can take on 150% leverage (for 250% total exposure) to get the risk with the VIX futures to equal THAT portfolio's risk. This is then the difference between a 14% and 6.4% CAGR which over 20 years is the difference between 13x and 2.5x your starting wealth. (Levering the 30/70 portfolio ~1.9x to equalize the risks, gives you an annual CAGR of 12.3% and 9x your starting wealth over 20 years.)

So, if these min-vol funds took off and it became easy to get options and futures on them, then you could do some interesting things with your portfolio because the lower volatility would allow you to take take on a lot more market exposure for the equivalent risk, which would translate into much higher returns. But I'm not sure how many people on this forum would be willing to do that sort of thing to begin with.
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Re: Equal weighting or market cap weighting?

Postby steve r » Mon Jan 28, 2013 8:05 pm

Akiva wrote:
steve r wrote:Akiva,

So, if these min-vol funds took off and it became easy to get options and futures on them, then you could do some interesting things with your portfolio because the lower volatility would allow you to take take on a lot more market exposure for the equivalent risk, which would translate into much higher returns. But I'm not sure how many people on this forum would be willing to do that sort of thing to begin with.


Not many.

I know insurance companies are piling into these things. Barry states Vanguard is consider making one. I wonder about being last to the party. I think if I am doing this to lower/minimize volatility that should not be a problem. Future returns may be different. But heck, I found papers back to 1926 suggesting the low vol method (SPLV) works very well indeed, particularly for large stocks!

On bond holdings, it also depends on your outlook on bonds. Using the Simba data and returns for the Min Vol and Low Vol etfs found on fact sheet of underlying indexes, you seem to be able to buy more stocks than 5% if your diversifying asset is t-bills. I tested with t-bills to offset the fact that my testing period is less than ideal (because treasuries exhibited stronger negative correlations over the last ten years than it had previously).

I am sold on the low vol or min vol concept ... am now debating/thinking how ...

The factsheets of the indexes (S&P, MSCI) suggest the low vol method has shown stronger returns ... but the testing period is way to short.

Backtested data on graphs of factsheets on indexes (attached) …. Nothing too precise in this analysis. Factsheets have annual data so I could do more.

Return on SPLV (lot of utilities) much better than USMV (one doubled, other up 50%), not sure if this is due to superior index or holding a lot of utilities at the right time. (1999 to 2011-12). I suspect more to do with holdings, but am not sure as of yet.

Comparing the current holdings of the two SPLV is 28 percent Consumer Defensive and 30 percent utilities versus 17.8 and 8.4 percent respectively in USMV.

Furthermore, EFAV (min volatility with optimization) nearly tippled since Nov 2001 … IDLV (low volatility) much more than tripled.

Both have about the same standard deviation of returns over the last ten to 15 years for both methods (11 to 12 range).

Comparing the holdings – consumer defensive is 20.65 / 17.72 in IDLV/EFAV respectively. Utilities are both under 8. IDLV is 18.6 percent in North America (none isn US) EFAV has zero in North America.

They both have standard deviations of 13ish

Based on performance – the low volatility method of choice appears to be simply holding the least volatile stocks based on history (no optimization). Ten year or so of data ain’t a lot.

SPLV lost 8 percent in 1999 – that would be hard to take I suspect. USMV was up 7 ish

That said, I like ACWV the most ... I like coordinating my U.S. and ex-US holdings, I like the max holding rules for various sectors/countries ... it looks more diversified. I suspect declining interest rates really helped utilities and consumer defensive stocks over the last ten plus years and that explains performance differences. ACWV also mirrors what I am trying to do with my index funds (maximize diversification by paying some attention to asset correlations).

On both method's I like the fact that based on current faith in the CAPM, it is unlikely to be overly widely adapted.

I ordered Falkenstein's book.

:happy In any event ... thanks for pointing this emerging asset class out to me.
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Re: Equal weighting or market cap weighting?

Postby Barry Barnitz » Mon Jan 28, 2013 8:37 pm

Hi all:

I have fleshed out the wiki page : Low Volatility Index returns - Bogleheads.

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