Isn't cap weighting less diversified than equal weighting?

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CULater
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Isn't cap weighting less diversified than equal weighting?

Post by CULater » Wed Sep 12, 2018 3:04 pm

From a diversification standpoint, isn't cap weighting actually less diversified than equal weighting? Why shouldn't we be investing in equal weighted funds based on better diversification of stock holdings?

iShares MSCE USA Equal Weighted ETF Sector Weights as of 9/11/18

Information Technology 16.40
Consumer Discretionary 14.92
Industrials 14.39
Financials 14.38
Health Care 11.10
Real Estate 5.99
Energy 5.94
Consumer Staples 5.55
Utilities 5.24
Materials 4.76
Telecommunications I0.97
Cash and/or Derivatives 0.22

iShares USA Total Market ETF Sector Weights as of 9/11/18

Information Technology 24.96
Financials 14.23
Health Care 14.18
Consumer Discretionary 13.13
Industrials 10.39
Consumer Staples 6.10
Energy 5.53
Real Estate 3.61
Materials 2.90
Utilities 2.82
Telecommunications 1.79
Cash and/or Derivative 0.37

It would appear that cap weighting devotes about 25% to IT, and only 11% to real estate, materials, utilities and telecom combined; while equal weighting has about 16% in IT and about 27% in real estate, materials. utilities and telecom. Similar weights for the other sectors. Which is better diversified?
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Tamalak » Wed Sep 12, 2018 3:14 pm

Who's deciding what the categories are? I could make a separate category for my niece's lemonade stand and suddenly it makes sense to give that as much money as the entire health care industry (which will be all the more profitable after people drink her lemonade :twisted: )

If one industry has 3x the stuff going on and makes 3x the profit as another, wouldn't it make sense to invest 3x the money in it if you wanted to spread it around equally?

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Re: Isn't cap weighting less diversified than equal weighting?

Post by CaliJim » Wed Sep 12, 2018 3:14 pm

How do you define "diversification"?

Equal weighting results in higher trading costs (more turnover), and results in a greater percentage of ownership of smaller companies.

If you want more "diversification", maybe you should look into slicing and dicing (diversification) across factors (large, value, small, momentum, credit risk) , not sectors.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by JoMoney » Wed Sep 12, 2018 3:15 pm

Cap weighting weights the stronger less risky stocks heavier than riskier stocks. In aggregate a broad market cap-weighted index holds the markets aggregate level of "risk".
Weighting in another fashion would change the level of risk, equal weighting would hold more of the smaller riskier stocks, theoreticly increasing the level of risk in the portfolio.

Some people have the idea that "diversification" is simply holding more individual stocks, and that more is better without regard to the risk it adds to the portfolio. I don't believe that is the case.

There are lots of ways you can change the level of risk in a portfolio, if your expectation is to garner above average returns from doing so, you would need a proportionate number of people willing to hold a less-risky less-returny portfolio. What the best measure of "risk" is can be disputed, and there are various models like CAPM and Fama-French Three Factor model... but the market in aggregate is the aggregate and where the center point of optimal risk/return is may change over time.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Cartographer » Wed Sep 12, 2018 4:45 pm

I think about it this way: if equal weighting was strictly better than market-cap weighting, then what would rational people do? They would equal weight. But this means, relative to market size, more money is flowing into the smaller companies. The result is that the market share of smaller companies would increase. This will keep going until the market weights approach equal, or else the positive effect of equal weighting disappears.

Therefore, no allocation scheme can be strictly better than market cap weighting. My understanding is that some version of this statement was formally proved by William Sharpe.

Of course, you can beat the market in terms of returns, but this means you must be taking on more risk. This is exactly what happens when you equal weight.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by nisiprius » Wed Sep 12, 2018 5:17 pm

Define "diversification" first and then we can talk about it.

I ought to stop at the snappy sound bite, but we also have to ask why we diversify and what we expect to get out of it.

We also have to compare and contrast equal weighting (which to me is both goofy, illogical, and very difficult and expensive to implement), versus adding a small-cap or a small-cap value tilt, which is much less problematical.

Data point #1. If the idea is crisis protection through "not putting all your eggs in one basket," then notice that in 2008-2009 fund, a cap-weighted S&P 500 fund, VTIAX, fell 53%, while an equal-weighted S&P 500 fund, RSP (orange) fell noticeably more--58%.

Source

Image

Data point #2. Since inception, RSP has had higher return, but has had higher risk by every measure than VFIAX. As a result, its Sharpe ratio, a measure of risk-adjusted reward, was about the same--very slight lower. In other words, there was no diversification benefit. It simply provided more return in exchange for more risk.

Source[url]. Data point #3. This is tricky becaus ... 100]Source
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Re: Isn't cap weighting less diversified than equal weighting?

Post by CULater » Wed Sep 12, 2018 10:39 pm

Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Wed Sep 12, 2018 10:51 pm

CULater wrote:
Wed Sep 12, 2018 10:39 pm
Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
I, for one, am inclined to agree with you. Putting a large portion of one's 'bet' on a handful of the world's largest companies does not, at least on the surface, appear to be as diversified as buying a more or less equal stake in all the publicly traded companies you can or at least the S&P 500. It's hard for me to wrap my mind around the argument that putting over 200 times as much money in Apple as Brighthouse Financial (BHF, firm 500 in the S&P) is more diversified than an equal weighting. It's also difficult for me to get around the argument that market cap weighting isn't just a popularity contest. I'm not saying that it's not effective, only that I have a hard seeing it as the most effective means of indexing.

I believe it was Meb Faber who said that in markets around the globe, the firm with the highest market cap tends to lag behind the rest of the market by around 5% annually.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by HEDGEFUNDIE » Wed Sep 12, 2018 10:53 pm

CULater wrote:
Wed Sep 12, 2018 10:39 pm
Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
Diversification is key, but the latest academic research has shown that diversification across industry sectors doesn’t do much for you (most sectors move together). Diversification across factors is key: growth, value, momentum, volatility, size.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by CaliJim » Wed Sep 12, 2018 10:55 pm

$1000 on Apple is not the same as $1000 on some tiny micro-cap.

In the first case you are getting ~0.00000001% ownership, and in the second case you are getting 0.01% ownership. That isn't 'diversification', that is tilting towards micro-caps.

"Putting the same amount on each opportunity" needs to consider that some opportunities are smaller, and have much different risks, than others.

One wants diversity across a multitude of risks: size risk, value risk, growth risk, momentum risk, credit risk, geographic risk, industry risk, technology risk, natural disaster risk, etc.

Looking at it via the 'sector' lens is short sighted.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Wed Sep 12, 2018 10:59 pm

If one buys the whole stock market, he necessarily owns it in a cap weighted form.
If one buys half of the whole stock market, should he put one and a half billion dollars on some microcap which capitalizes 20 millions at present to be equal weighted ?

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Re: Isn't cap weighting less diversified than equal weighting?

Post by CULater » Wed Sep 12, 2018 11:00 pm

HEDGEFUNDIE wrote:
Wed Sep 12, 2018 10:53 pm
CULater wrote:
Wed Sep 12, 2018 10:39 pm
Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
Diversification is key, but the latest academic research has shown that diversification across industry sectors doesn’t do much for you (most sectors move together). Diversification across factors is key: growth, value, momentum, volatility, size.
Point of view. But isn't EW also more diversified across factors than CW?
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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Wed Sep 12, 2018 11:01 pm

CaliJim wrote:
Wed Sep 12, 2018 10:55 pm
$1000 on Apple is not the same as $1000 on some tiny micro-cap.

In the first case you are getting ~0.00000001% ownership, and in the second case you are getting 0.01% ownership. That isn't 'diversification', that is tilting towards micro-caps.

"Putting the same amount on each opportunity" needs to consider that some opportunities are smaller, much smaller, than others.....
You can't identify what a tilt is until you've identified what 'flat' (i.e. no tilt) is. For many, no tilt means TSM as defined by market capitalization, but that's certainly not the only way to define the TSM.

One could just as easily argue that putting 200 times as much money in firm #1 in the S&P 500 over firm #500 isn't as diversified as an equal amount in both.
Thesaints wrote:
Wed Sep 12, 2018 10:59 pm
If one buys the whole stock market, he necessarily owns it in a cap weighted form.
He could buy an equal dollar amount of stock in every company in the whole stock market. And that would not be cap weighted.
Last edited by willthrill81 on Wed Sep 12, 2018 11:02 pm, edited 1 time in total.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by HEDGEFUNDIE » Wed Sep 12, 2018 11:05 pm

CULater wrote:
Wed Sep 12, 2018 11:00 pm
HEDGEFUNDIE wrote:
Wed Sep 12, 2018 10:53 pm
CULater wrote:
Wed Sep 12, 2018 10:39 pm
Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
Diversification is key, but the latest academic research has shown that diversification across industry sectors doesn’t do much for you (most sectors move together). Diversification across factors is key: growth, value, momentum, volatility, size.
Point of view. But isn't EW also more diversified across factors than CW?
Well it’s a “point of view” that has won its adherents the Nobel prize, and is being taught as part of the finance curriculum at the top MBA programs.

And no, neither EW nor CW diversifies across factors, other than purely accidentally for short periods of time.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by privatefarmer » Wed Sep 12, 2018 11:29 pm

Cartographer wrote:
Wed Sep 12, 2018 4:45 pm
I think about it this way: if equal weighting was strictly better than market-cap weighting, then what would rational people do? They would equal weight. But this means, relative to market size, more money is flowing into the smaller companies. The result is that the market share of smaller companies would increase. This will keep going until the market weights approach equal, or else the positive effect of equal weighting disappears.

Therefore, no allocation scheme can be strictly better than market cap weighting. My understanding is that some version of this statement was formally proved by William Sharpe.

Of course, you can beat the market in terms of returns, but this means you must be taking on more risk. This is exactly what happens when you equal weight.
BINGO. this is exactly right.

another way I look at it : cap-weighting is the most diversified if you are trying to spread out your money equally across all corporate EARNINGS, risk-adjusted. Apple is expected to take in far more $$$$ in earnings going forward than XYZ company, thus Apple costs a lot more to own/has a much larger market cap. This is rational. If you adjust for expected risk, cap-weighting equally spreads out your money in a way that allows the maximum diversity amongst CORPORATE EARNINGS which ultimately is all we should care about.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by StrangePenguin » Wed Sep 12, 2018 11:33 pm

As others pointed out, it doesn't make sense to weight small companies as much as a big ones. If you take the view that the fundamental reason to own a stock is to own a slice of the future profits generated by that company, then one might argue that a more fundamental weighting than market cap is the company's slice of total corporate profits. And sure enough -- there is an ETF (at least one) that takes an approach like this! It is called EPS: https://www.wisdomtree.com/etfs/equity/eps
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Wed Sep 12, 2018 11:37 pm

willthrill81 wrote:
Wed Sep 12, 2018 11:01 pm
He could buy an equal dollar amount of stock in every company in the whole stock market. And that would not be cap weighted.
Then he would not own the entire 30 trillions worth of stock market but only maybe a few hundred billions.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by CaliJim » Thu Sep 13, 2018 12:08 am

willthrill81 wrote:
Wed Sep 12, 2018 11:01 pm
You can't identify what a tilt is until you've identified what 'flat' (i.e. no tilt) is.
Flat is beta = 1; the cap weighted index. Tilt is more exposure to small and value.

So, here is what investopedia says about measuring diversification...without really defining it:
https://www.investopedia.com/ask/answer ... s-need.asp
And a Seeking Alpha article too:
https://seekingalpha.com/article/131260 ... sification
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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Thu Sep 13, 2018 12:11 am

CaliJim wrote:
Thu Sep 13, 2018 12:08 am
willthrill81 wrote:
Wed Sep 12, 2018 11:01 pm
You can't identify what a tilt is until you've identified what 'flat' (i.e. no tilt) is.
Flat is beta = 1; the cap weighted index. Tilt is more exposure to small and value.

So, here is what investopedia says about measuring diversification...without really defining it:
https://www.investopedia.com/ask/answer ... s-need.asp
Defining 'flat' as the cap weighted index is kind of a tautology.

This entire argument depends on how one defines 'the market'. Most define it in terms of 'market capitalization', and I'll be the first to say that there are some strong theoretical arguments in favor of that conceptualization. But I'll also be quick to point out that it's far from the only way to define the market.

That article, much like most of the discussions in favor of market cap weighting, is based on the modern portfolio theory. Without getting into the weeds and derailing the thread, I'll just say that it's only a theory, much like the efficient market hypothesis is just a hypothesis.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by nisiprius » Thu Sep 13, 2018 6:35 am

An investment in the (usual, cap-weighted) S&P 500 is fairly close to being the same as an investment in the cap-weighted total market, because it includes about 80% of the market by cap weight. If the goal is to mimic the market portfolio, an S&P 500 fund comes reasonably close. It's 80% of the way to the ideal goal. And if you want to come closer, you can pick between at least dozen or so "broad market" and "total market" funds and ETFs that will get you to up to more than 99%.

An investment in RSP, an ETF tracking the equal-weighted S&P 500, is not an equal-weighted investment in the stock market. It's not even close. A $10,000 investment in the equal-weighted S&P 500 is a decision to invest $20 each into 500 stocks, and zero, zip, nothing into 3,100 other stocks. It is covering only 14% of the total market, equal-weighted.

And there is no feasible way to close that 86% gap; I'll get to that shortly.

If you want an equal weighted strategy, that means you have decided that you want to put a dollar into Sealed Air Corporation for every dollar you put into ExxonMobil. You do not want to discriminate at all based on company size. But if you do not want to discriminate at all, then why do you want to put a dollar into Sealed Air Corporation, yet not a penny into Summer Infant, Incorporated? They're both stocks, aren't they?

I don't see any logical way to adopt an "equal weighted" strategy that doesn't try to equal weight the whole 3,600-stock market--or, at least, the vast majority of it by count. Maybe 3,500. Maybe three thousand. Not five hundred.

Now, point #1, there's no good way to do this. The only product I'm aware of that holds small cap stocks and has "equal weight" in its name is EQWS, the--I'm going to use scare quotes--Invesco Russell 2000 "Equal Weight" ETF. But if you look at it, you'll quickly discover that it does not invest in the stocks of the Russell 2000 with equal weight on each. Rather, it invests in an index called the "Russell 2000 Equal Weight" index, and this index is so far from being equal weighted that, well... look into it for yourself.

So, no, you can't simply invest 14% into RSP and 86% into EQWS and hold the market, equally weighted.

The second problem with equal weighting the market is that there isn't enough to go around. There really is a "what if everybody indexed" problem. The market capitalization of Summer Infant is $32 million. If you create an index fund in which it is 1/3,100th of the total, in order to meet the rules for the fund to be called "diversified," the fund cannot own more than $3.2 million of Summer Infant. Therefore, since it is equal weighted, it will own $3.2 million of each of the 3,100 stocks in the market, or a grand total of about $10 billion. Since the topic of this thread is "diversification," I assume we want to be "diversified" as defined by the Investment Company Act of 1940.

The size of the Vanguard Total Stock Market Index Fund is already seventy times that. Heck, the Schwab S&P 500 index fund is three times that. The iShares MSCI EAFE ETF (international stock index) is seven times that. Even if we are willing to say "the Fund is not consider diversified" in our literature, we still cannot reach the size of the big cap-weighted stock funds. The market would literally run out of Summer Infant stock long before that happened.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Lauretta » Thu Sep 13, 2018 7:40 am

Yes by definition market cap weighting is highly concentrated in the large stocks.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by rkhusky » Thu Sep 13, 2018 7:44 am

The standard equal weighting scheme uses the artificial boundary of company names. What you really want is equal weighting of market share, which is what cap weighting gives you.

Here is an example: Apple produces a number of products, let's say it is 10. If Apple was broken up into 10 different companies, one for each product, would you want to increase your stake in Apple products by a factor of 10, all with equal weight? Are iPods of equal value to iPhones, which are equal to iMacs, which are equal to iTunes? How does the fact that in one case all the products are under one company structure versus the other case, where the 10 have their own company structures, affect how much you want invested in the products? Wouldn't it be more logical to invest in each of the 10 companies in proportion to their market share, whose sum would be approximately equal to the market share of Apple as it currently stands?

Cap-weighted investing is insensitive to mergers and spin-offs and acquisitions. You don't need to buy or sell when they occur.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by rkhusky » Thu Sep 13, 2018 7:47 am

Lauretta wrote:
Thu Sep 13, 2018 7:40 am
Yes by definition market cap weighting is highly concentrated in the large stocks.
It is not by definition. It is just the way things are right now. And I'm not even sure I would characterize it as highly concentrated. One would have to define what "large" means. If all companies had the same market share, you would have equal weighting in a cap-weighted index.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by vineviz » Thu Sep 13, 2018 8:42 am

I'd say the closest thing to a consensus definition that exists for "diversification" is "the practice of spreading one's money across different investments with the aim of reducing risk".

One thing that people often fail to understand is that modern portfolio theory does generally aim to reduce risk (and therefore deliver a diversified portfolio) but instead aims to deliver a mean-variance optimized portfolio (i.e. one that maximizes risk-adjusted return). Mean-variance optimization is one of the key underlying theoretical premises for a market-cap weighted portfolio, and while such portfolio has many advantages it's not necessarily the most diversified portfolio (no matter how many assets it contains).

There are a number of different ways that academics and practitioners have used (and still use) to maximize diversification. A short list would include:
  • naive diversification: putting equal amounts of money on each asset or asset class
  • risk parity: putting equal amounts of risk on each asset or asset class
  • maximum diversification ratio: maximizes the number of independent sources of risk in a portfolio
  • minimum variance: minimizes the volatility of the portfolio
  • minimize tail risk: allocating risk in a way that reduces the expected impact of very large negative events
Although naive diversification works surprisingly well from a diversification standpoint, it (like market-cap weighting) does not NECESSARILY produce the most diversified stock portfolio. Putting equal weight on Netflix and NextEra Energy, Inc. ignores the fact that the former is MUCH riskier than the latter, so equal weight still leaves the risk highly concentrated.

Practically speaking, though, stocks tend to be highly correlated AND the reasonable exception is that all stocks will tend to have similar risk-adjusted returns in the future. Given those to facts, it turns out that within the stock portion of the portfolio the diversification benefits of naive diversification (aka equal weights) tend to be relatively small once you have a modest number of stocks in the fund. Because the costs of an equal weight stock portfolio are MUCH higher than the costs of a market cap weighted portfolio, the former is generally preferred over the latter.

IMHO, if the goal is to increase portfolio diversification over a pure market-cap weighted portfolio then it's much more efficient to break down stocks into a few relatively uncorrelated sub-asset class index funds (e.g. US large cap growth, US small cap value, and emerging markets) and use a diversification optimization process for spreading risk between those funds. You could do the same thing with factors, and use the same process to allocate between stocks and bonds.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by nisiprius » Thu Sep 13, 2018 9:33 am

Lauretta wrote:
Thu Sep 13, 2018 7:40 am
Yes by definition market cap weighting is highly concentrated in the large stocks.
No, "by definition" it is no such thing.

Indeed, market cap weighting, by definition, puts the most dollars in the same stocks that the market puts the most dollars into. However, to call that a "concentration" is spin.

Seawater is 96.5% water and 3.5% dissolved salts. If you fill an aquarium with seawater, you will be filling it mostly with water. Would anybody describe that as "highly concentrated in water?" It isn't, it's simply natural seawater. Market cap weighting is the natural composition of the stock market. Depending on your purposes, you might not want that, just as, depending on your purposes, you might not want seawater.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Lauretta » Thu Sep 13, 2018 9:54 am

nisiprius wrote:
Thu Sep 13, 2018 9:33 am
Lauretta wrote:
Thu Sep 13, 2018 7:40 am
Yes by definition market cap weighting is highly concentrated in the large stocks.
No, "by definition" it is no such thing.

Indeed, market cap weighting, by definition, puts the most dollars in the same stocks that the market puts the most dollars into. However, to call that a "concentration" is spin.

Seawater is 96.5% water and 3.5% dissolved salts. If you fill an aquarium with seawater, you will be filling it mostly with water. Would anybody describe that as "highly concentrated in water?" It isn't, it's simply natural seawater. Market cap weighting is the natural composition of the stock market. Depending on your purposes, you might not want that, just as, depending on your purposes, you might not want seawater.
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by nisiprius » Thu Sep 13, 2018 10:10 am

Lauretta wrote:
Thu Sep 13, 2018 9:54 am
Nisiprius wrote:Seawater is 96.5% water and 3.5% dissolved salts. If you fill an aquarium with seawater, you will be filling it mostly with water. Would anybody describe that as "highly concentrated in water?" It isn't, it's simply natural seawater. Market cap weighting is the natural composition of the stock market. Depending on your purposes, you might not want that, just as, depending on your purposes, you might not want seawater.
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
Fine, but by calling the market composition "concentrated," you have decided to measure it by your personal standard of what it "should be." I don't think you should use what I have personally chosen for myself as the standard by which other peoples' allocations should be described. Objective people ought to be able to agree: the Leaning Tower leans. The plumb line doesn't.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by rkhusky » Thu Sep 13, 2018 11:31 am

Lauretta wrote:
Thu Sep 13, 2018 9:54 am
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
If you have two stocks with equal expected risk-adjusted return, why would the market substantially choose one over the other? Who is calculating the expected risk and return?

If the stocks are efficiently priced by the market, then their current prices are the correct prices. And their current market share is the correct market share.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by neurosphere » Thu Sep 13, 2018 11:43 am

CaliJim wrote:
Wed Sep 12, 2018 10:55 pm
$1000 on Apple is not the same as $1000 on some tiny micro-cap.

In the first case you are getting ~0.00000001% ownership, and in the second case you are getting 0.01% ownership.
I think this is the most straightforward answer I've seen describing cap weighting. It's purchasing the same percentage ownership of every stock in that index.

And that also is not a bad way to define "no-tilt". Just define "neutral" or tilt-less as an equal-percent ownership. Seems pretty logical and practical to me. And that's certainly diversified. Every stock gets the same percentage, and no choosing winners. Now, if one feels smaller stocks do better than larger stocks over time, we can argue at length whether some other weighting strategy would be better than say, adding a cap-weighted mid/small/micro fund.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by CULater » Thu Sep 13, 2018 11:44 am

Comparing EUSA (equal weighted) to VTI (cap weighted):

% assets in top 10 1.8% 17.9%
% assets in top 15 2.7% 22.3%
% assets in top 50 8.7% 41.3%

About 40% of VTI is invested in 50 stocks, while only about 9% of EUSA is invested in the largest 50 stocks it holds. Which one is less diversified?
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Re: Isn't cap weighting less diversified than equal weighting?

Post by bloom2708 » Thu Sep 13, 2018 11:45 am

CULater wrote:
Wed Sep 12, 2018 10:39 pm
Well, everybody keeps yapping about how owning the entire U.S. market represents great diversification. If you own everything are maximally diversified. What exactly does that mean, anyway? Seems to me that if you own everything equally weighted, that's more diversified since you're putting an equal number of chips on each opportunity.
The Total US Market index is more diversified because it hold ~3,600 stocks. The S&P 500 holds ~500 of the largest stocks.

Market weighting means the "ever moving" market determines how much of the 3,600 stocks you own. If a smaller stock blows up and issues more shares and the price increases from $1 to $100, the market cap increases and the total market fund buys more of that stock because "the market" has deemed it more valuable by buying that and selling something else.

Let's say that stock #3,634 is "Bob's Bait Inc". It has 1,000 shares outstanding at $10. The market cap is $10,000. This is complete bunk, but you would not want to own the same amount of Bob's Bait as Apple. In reality, you couldn't own it as there are not enough shares outstanding.

Not a perfect example, but I'm sure someone will correct me. :wink:
Last edited by bloom2708 on Thu Sep 13, 2018 11:55 am, edited 2 times in total.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Thu Sep 13, 2018 11:53 am

nisiprius wrote:
Thu Sep 13, 2018 10:10 am
Lauretta wrote:
Thu Sep 13, 2018 9:54 am
Nisiprius wrote:Seawater is 96.5% water and 3.5% dissolved salts. If you fill an aquarium with seawater, you will be filling it mostly with water. Would anybody describe that as "highly concentrated in water?" It isn't, it's simply natural seawater. Market cap weighting is the natural composition of the stock market. Depending on your purposes, you might not want that, just as, depending on your purposes, you might not want seawater.
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
Fine, but by calling the market composition "concentrated," you have decided to measure it by your personal standard of what it "should be." I don't think you should use what I have personally chosen for myself as the standard by which other peoples' allocations should be described. Objective people ought to be able to agree: the Leaning Tower leans. The plumb line doesn't.
I fail to see how her example is redefining what market concentration is. Perhaps you can expound on what you mean by that. I've actually used the same example to illustrate how a global market cap weighting still results in about 50% of your risk being concentrated in one country. I fail to see how putting 50% of your 'chips' on one country is more diversified than not putting more than 5%, for instance, of your chips on any one country. The same seems true of market cap weighting versus equal weighting.

That being said, if we assumed that the EMH is accurate* and that the risk-adjusted returns for all stocks is the same, then it doesn't seem likely to me to make any significant difference in investors' risk-adjusted returns whether they use market cap weighting, equal weighting, or any other weighting scheme apart from the fees involved, which are admittedly higher with equal weighted funds than most market cap weighted funds.

*For the record, I am not a firm believer in the EMH.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Lauretta » Thu Sep 13, 2018 12:41 pm

willthrill81 wrote:
Thu Sep 13, 2018 11:53 am
nisiprius wrote:
Thu Sep 13, 2018 10:10 am
Lauretta wrote:
Thu Sep 13, 2018 9:54 am
Nisiprius wrote:Seawater is 96.5% water and 3.5% dissolved salts. If you fill an aquarium with seawater, you will be filling it mostly with water. Would anybody describe that as "highly concentrated in water?" It isn't, it's simply natural seawater. Market cap weighting is the natural composition of the stock market. Depending on your purposes, you might not want that, just as, depending on your purposes, you might not want seawater.
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
Fine, but by calling the market composition "concentrated," you have decided to measure it by your personal standard of what it "should be." I don't think you should use what I have personally chosen for myself as the standard by which other peoples' allocations should be described. Objective people ought to be able to agree: the Leaning Tower leans. The plumb line doesn't.
I fail to see how her example is redefining what market concentration is. Perhaps you can expound on what you mean by that. I've actually used the same example to illustrate how a global market cap weighting still results in about 50% of your risk being concentrated in one country. I fail to see how putting 50% of your 'chips' on one country is more diversified than not putting more than 5%, for instance, of your chips on any one country. The same seems true of market cap weighting versus equal weighting.

That being said, if we assumed that the EMH is accurate* and that the risk-adjusted returns for all stocks is the same, then it doesn't seem likely to me to make any significant difference in investors' risk-adjusted returns whether they use market cap weighting, equal weighting, or any other weighting scheme apart from the fees involved, which are admittedly higher with equal weighted funds than most market cap weighted funds.

*For the record, I am not a firm believer in the EMH.
yes fees are higher for EW; on the other hand if you have a stategy where you equally weight different geographical regions (US, Europe, Pacific+Japan and EM) you pay less than for having an MSCI world ETF, and you avoid concentrating 50% of your assets in the US, which to me as a European has additional currency risk. So that's roughly what I do. I use cheap market cap ETFs but equal weight broad geographical regions.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Lauretta » Thu Sep 13, 2018 12:46 pm

rkhusky wrote:
Thu Sep 13, 2018 11:31 am
Lauretta wrote:
Thu Sep 13, 2018 9:54 am
Imagine you have 2 stocks, ticker SALT and WATER. If both are efficiently prized so that neither is more likely to outperform the other (in terms of risk-adjusted expected return), I would 'bet' 50% of my money on each; even though 96.5% of total bets are put on water.
What determines my allocation of my own funds is the the probability of achieving a given risk-adjusted return (which should be the same for both stocks if the market is efficient). I am not interested in how much other people have invested in each of the stocks.
If you have two stocks with equal expected risk-adjusted return, why would the market substantially choose one over the other?
Because one firm is larger than the other. The market allocates more to Apple than to Axon (just chose these firms randomy) simply because Apple is a larger firm. Not because it believes that Apple will outperform Axon.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by nisiprius » Thu Sep 13, 2018 1:02 pm

(Shrug) Give me a good, accepted, consensus definition of "diversification," "risk," "concentration," and "tilt" and maybe we can get somewhere. Right now this thread has been pretty much talking past one another.

In 1982, AT&T broke up. As it happened, I personally owned 40 shares of AT&T at the time. I ended up with shares of stock in seven different companies. The market, as it happened, valued the shares of the seven new companies as worth almost precisely the same as the previous shares of AT&T.

Do you honestly believe that I was less diversified the day before the breakup than the day afterward?

Do you honestly believe that the day after the breakup I ought to have gone out and bought extra shares equal to six times what I had, in order to bring each of those seven companies to the same number of dollars I previously had in AT&T?
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Re: Isn't cap weighting less diversified than equal weighting?

Post by bloom2708 » Thu Sep 13, 2018 1:10 pm

Lauretta wrote:
Thu Sep 13, 2018 12:46 pm
Because one firm is larger than the other. The market allocates more to Apple than to Axon (just chose these firms randomy) simply because Apple is a larger firm. Not because it believes that Apple will outperform Axon.
The "index" knows nothing of "forward". It is a snapshot of what is. Apple has a big market cap. The "index" owns more of it. If Apple returns to the near bankrupt days of yorn, the "index" will own much less of it.

Nobody knows if Axon will out perform Apple over a week, month, year. The index only knows what is.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by MIretired » Thu Sep 13, 2018 1:23 pm

I tend to think that diversification, cap-weighting, and MPT are 3 different things. I honestly don't know why cap-weighting would be considered a natural result of MPT.
I think that in the most general way, rebalancing is the action that resets to equal weight, whereas cap weighting is to not rebalance at all.
But, I can question whether I should rebalance from the one that is outperforming into the laggard. Doesn't seem wise. I often here the refrain 'it is overvalued'. Doesn't the market determine that.
I could own 2 funds. The value half of the S&P, and the growth half. One or the other will have a larger share of my portfolio over time, and they may zig-zag in size like a braided rope. But, again, to rebalance these 2 probably is not an act of diversification in the general sense of reducing idiosyncratic risk, but some adjustment under some other theory, like expected performance or valuation risk adjustment.
And if you bought an equal weight of 500 stocks a long, long time ago, and did not rebalance, you'd now have a cap weighting.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by randomguy » Thu Sep 13, 2018 1:39 pm

nisiprius wrote:
Thu Sep 13, 2018 6:35 am
An investment in the (usual, cap-weighted) S&P 500 is fairly close to being the same as an investment in the cap-weighted total market, because it includes about 80% of the market by cap weight. If the goal is to mimic the market portfolio, an S&P 500 fund comes reasonably close. It's 80% of the way to the ideal goal. And if you want to come closer, you can pick between at least dozen or so "broad market" and "total market" funds and ETFs that will get you to up to more than 99%.

An investment in RSP, an ETF tracking the equal-weighted S&P 500, is not an equal-weighted investment in the stock market. It's not even close. A $10,000 investment in the equal-weighted S&P 500 is a decision to invest $20 each into 500 stocks, and zero, zip, nothing into 3,100 other stocks. It is covering only 14% of the total market, equal-weighted.

And there is no feasible way to close that 86% gap; I'll get to that shortly.

If you want an equal weighted strategy, that means you have decided that you want to put a dollar into Sealed Air Corporation for every dollar you put into ExxonMobil. You do not want to discriminate at all based on company size. But if you do not want to discriminate at all, then why do you want to put a dollar into Sealed Air Corporation, yet not a penny into Summer Infant, Incorporated? They're both stocks, aren't they?

I don't see any logical way to adopt an "equal weighted" strategy that doesn't try to equal weight the whole 3,600-stock market--or, at least, the vast majority of it by count. Maybe 3,500. Maybe three thousand. Not five hundred.

500 is plenty. The s&p500 and TSM track pretty closely. Those 3500 additional stocks are <20% of your money AND most of that money is in the next 500 stocks. I mean do you worry that TSM doesn't hold pink sheet stocks and therefore isn't holding the whole market?

The S&P 500 is pretty diversified with no company above 5%. Compare that to something like Finland when Noika was something like 60% of the market capitalization in the early 00s. When you have one company in one industry dominating so much it is easier to make arguements for things like equal weighting giving out diversification.

Equal weighting the S&P 500 has beaten TSM in back testing. Trading costs and the churning though tends to reduce the performance to a point where it makes zero sense

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Re: Isn't cap weighting less diversified than equal weighting?

Post by bertilak » Thu Sep 13, 2018 2:07 pm

bloom2708 wrote:
Thu Sep 13, 2018 1:10 pm
Nobody knows if Axon will out perform Apple over a week, month, year. The index only knows what is.
I think the Efficient Market Hypothesis (EMH) assumption is that what is, as measured by capitalization weight, represents all investors' combined consensus of what will be, i.e. the future value discounted by (I think) a riskless rate of return. So, maybe nobody knows but a consensus of investors do expect. If we can't know, the best we can go on expectations.

If you know better, and I assume some people do know better for some specific stocks, go for it! But, if you can't reliably, and in a timely fashion, chase down that knowledge I say go for the consensus, a cap weighted index fund.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Thu Sep 13, 2018 2:11 pm

bertilak wrote:
Thu Sep 13, 2018 2:07 pm
bloom2708 wrote:
Thu Sep 13, 2018 1:10 pm
Nobody knows if Axon will out perform Apple over a week, month, year. The index only knows what is.
I think the Efficient Market Hypothesis (EMH) assumption is that what is, as measured by capitalization weight, represents all investors' combined consensus of what will be, i.e. the future value discounted by (I think) a riskless rate of return. So, maybe nobody knows but a consensus of investors do expect. If we can't know, the best we can go on expectations.

If you know better, and I assume some people do know better for some specific stocks, go for it! But, if you can't reliably, and in a timely fashion, chase down that knowledge I say go for the consensus, a cap weighted index fund.
Absolutely!
The consensus might very well be wrong, but that doesn't mean that going against consensus is right. In fact, it can be argued that consistently going against consensus will be more wrong than right.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Thu Sep 13, 2018 2:31 pm

bertilak wrote:
Thu Sep 13, 2018 2:07 pm
bloom2708 wrote:
Thu Sep 13, 2018 1:10 pm
Nobody knows if Axon will out perform Apple over a week, month, year. The index only knows what is.
I think the Efficient Market Hypothesis (EMH) assumption is that what is, as measured by capitalization weight, represents all investors' combined consensus of what will be, i.e. the future value discounted by (I think) a riskless rate of return. So, maybe nobody knows but a consensus of investors do expect. If we can't know, the best we can go on expectations.
If you believe the EMH to be accurate 'enough', then yes.
bertilak wrote:
Thu Sep 13, 2018 2:07 pm
If you know better, and I assume some people do know better for some specific stocks, go for it! But, if you can't reliably, and in a timely fashion, chase down that knowledge I say go for the consensus, a cap weighted index fund.
I believe you're making a logic jump here. If the EMH is accurate, that alone is not an argument for cap weighting. If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns. Cap and equal weighting should be expected to have essentially identical risk-adjusted returns. Indeed, a comparison of RSP to VFINX shows that their Sharpe ratios are almost identical (.60 and .62, respectively).
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Thu Sep 13, 2018 2:47 pm

willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
I believe you're making a logic jump here. If the EMH is accurate, that alone is not an argument for cap weighting. If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns. Cap and equal weighting should be expected to have essentially identical risk-adjusted returns. Indeed, a comparison of RSP to VFINX shows that their Sharpe ratios are almost identical (.60 and .62, respectively).
Not really. Expected returns matche risk only after all extra risk has been diversified away.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Thu Sep 13, 2018 2:51 pm

Thesaints wrote:
Thu Sep 13, 2018 2:47 pm
willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
I believe you're making a logic jump here. If the EMH is accurate, that alone is not an argument for cap weighting. If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns. Cap and equal weighting should be expected to have essentially identical risk-adjusted returns. Indeed, a comparison of RSP to VFINX shows that their Sharpe ratios are almost identical (.60 and .62, respectively).
Not really. Expected returns matche risk only after all extra risk has been diversified away.
Would you please clarify this statement? The EMH implies that risk-adjusted returns should be very similar for all stocks.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Thu Sep 13, 2018 3:10 pm

willthrill81 wrote:
Thu Sep 13, 2018 2:51 pm
Would you please clarify this statement? The EMH implies that risk-adjusted returns should be very similar for all stocks.
Yes, but the risk you adjust to is only the non-diversifiable risk.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by CULater » Thu Sep 13, 2018 3:18 pm

So, isn't cap weighting a kind of closet "momentum" index? Stocks for which cap is growing more relative to others garner a larger and larger weight in the index. I guess that's why VTI is tilted a little more toward large growth in the style box and SPY even more so. Equal weight is kind of a "buy low, sell high" mean-reversion index. Stocks that have outgrown or fallen below their proper static weight are rebalanced to their proper weight and the index is not tilted toward growth. CW ought to do better than EW in a MOM equity regime, while EW ought to do better than CW in a VAL equity regime.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by Thesaints » Thu Sep 13, 2018 3:27 pm

Before going bust LEH and ENE capitalization decreased; it never cycled back.
If we knew the "proper static weight" I'd agree with you, but I'm afraid they may not exist.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by aristotelian » Thu Sep 13, 2018 3:30 pm

"Diversification" is subjective. Ultimately the debate is semantic. I am not sure there is an argument on either side.

Setting aside the diversification question, market cap is consistent with efficient markets. You are weighting shares of companies according to their market value. Equal weighting contradicts this. It says there is something that the market doesn't know. In this case, you aren't necessarily trying to beat the market return with the same risk, rather you are trying to reduce risk with the same return.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by Boglegrappler » Thu Sep 13, 2018 3:30 pm

another way I look at it : cap-weighting is the most diversified if you are trying to spread out your money equally across all corporate EARNINGS, risk-adjusted. Apple is expected to take in far more $$$$ in earnings going forward than XYZ company, thus Apple costs a lot more to own/has a much larger market cap. This is rational. If you adjust for expected risk, cap-weighting equally spreads out your money in a way that allows the maximum diversity amongst CORPORATE EARNINGS which ultimately is all we should care about.
The first sentence is quite close to the correct viewpoint, I believe. Actually cap-weighting spreads your investment proportionately to earnings, but as "adjusted" for risk and growth (because market cap gives effect to the P/E relationship, which is driven by projected individual company growth and individual company risk). A company that is a slow grower and earns 100MM annually may be valued at half the market cap of another company that (currently) earns the same 100MM, but is growing at twice the rate of the first one.

As an aside, the example of Aapl isn't the best one to use, since it trades below the market multiple, and mostly has for a number of years now. One reason the Apple stock price keeps rising is that the market long ago concluded that it was unlikely that they could keep up their growth record.....but the company has increased sales and earnings materially over recent years. AMZN, at about 180 P/E would be a better stock to use in that example, since its selling for close to 10x the market multiple.

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Re: Isn't cap weighting less diversified than equal weighting?

Post by willthrill81 » Thu Sep 13, 2018 4:40 pm

aristotelian wrote:
Thu Sep 13, 2018 3:30 pm
"Diversification" is subjective. Ultimately the debate is semantic. I am not sure there is an argument on either side.

Setting aside the diversification question, market cap is consistent with efficient markets. You are weighting shares of companies according to their market value. Equal weighting contradicts this. It says there is something that the market doesn't know. In this case, you aren't necessarily trying to beat the market return with the same risk, rather you are trying to reduce risk with the same return.
Again, if the EMH is correct, then any large holding of stocks should be expected to have the same risk-adjusted returns, whether that holding is centered around cap weighting, equal weighting, or any other scheme. The question then comes down to one of costs, and cap weighting is certainly less costly to implement, at least now.
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Re: Isn't cap weighting less diversified than equal weighting?

Post by bertilak » Thu Sep 13, 2018 4:44 pm

willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
bertilak wrote:
Thu Sep 13, 2018 2:07 pm
bloom2708 wrote:
Thu Sep 13, 2018 1:10 pm
Nobody knows if Axon will out perform Apple over a week, month, year. The index only knows what is.
I think the Efficient Market Hypothesis (EMH) assumption is that what is, as measured by capitalization weight, represents all investors' combined consensus of what will be, i.e. the future value discounted by (I think) a riskless rate of return. So, maybe nobody knows but a consensus of investors do expect. If we can't know, the best we can go on expectations.
If you believe the EMH to be accurate 'enough', then yes.
bertilak wrote:
Thu Sep 13, 2018 2:07 pm
If you know better, and I assume some people do know better for some specific stocks, go for it! But, if you can't reliably, and in a timely fashion, chase down that knowledge I say go for the consensus, a cap weighted index fund.
I believe you're making a logic jump here. If the EMH is accurate, that alone is not an argument for cap weighting. If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns. Cap and equal weighting should be expected to have essentially identical risk-adjusted returns. Indeed, a comparison of RSP to VFINX shows that their Sharpe ratios are almost identical (.60 and .62, respectively).
Re: Logic jump. You re probably right and probably also right that risk-adjustment was part of that jump. All stocks may be just as fairly priced but one can take on more or less risk by picking more or less risky stocks (if you can figure out which is which). If one only wants market risk, one needs to go for the whole market (or whole index).
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker, the Cowboy Poet

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