Isn't cap weighting less diversified than equal weighting?

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

Post by JoMoney » Thu Sep 13, 2018 5:54 pm

willthrill81 wrote:
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.
Whether EMH is correct or not, the market represents the dollar weighted aggregate opinion of the market participants.
If EMH is true, all the bets are fair, some are more risky then others, but there is no advantage to one side or the other just a trade of risk/return.
IF EMH is not true, people who don't know more or have above average access to information or trading positions are at a disadvantage.
https://web.archive.org/web/20170429061 ... ssive.html
... In other words, market efficiency protects the less-skilled investor from consistently making bad investments because all stocks are fairly priced. There is, on the other hand, no such protection in a market where stocks are routinely mispriced. The active investing majority that underperforms the index will tend to be the same year after year. Thus, the argument for indexing is even stronger for individual investors if the stock market is not efficient. The game of poker provides, in some respects, an instructive analogy. Poker is a zero sum game, similar to active investing compared to indexing, and poker combines luck and skill, consistent with the assumption of a less than perfectly efficient market. An old adage among professional poker players applies to those deciding to participate in the active investing game. "If you don't know who the mark is, get up and leave the table, because it's you."

About two-thirds of all active investors, whose only financial justification for being active is beating the index, must fail in that objective each year. Press reports that quote the failure rate as substantially higher or lower in any given year, either track only one category of investor, or do not properly measure all active management costs. The two-thirds failure rate among all active investors is as mathematically certain as the forecast that exactly half of the workforce will earn less than the median income. It may seem unfair, but it cannot be otherwise. No amount of hope and luck (if the market is efficient) or work and skill (if it is not) can change that fact. Each individual investor should confront the question "Am I in the top third of everyone who thinks they are?" and the unavoidable answer "Probably not."
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

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

Post by KyleAAA » Thu Sep 13, 2018 6:13 pm

Maybe in the sense that it would tend to have small and value factor tilts. But it would probably have negative quality factor exposure.

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

Post by JoMoney » Thu Sep 13, 2018 6:41 pm

KyleAAA wrote:
Thu Sep 13, 2018 6:13 pm
Maybe in the sense that it would tend to have small and value factor tilts. But it would probably have negative quality factor exposure.
In a "factor" paradigm, equal weighting would likely have negative momentum as well.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

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

Post by Cartographer » Thu Sep 13, 2018 6:47 pm

willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns.
I don't think this is true. Suppose all expected returns are equal, uncorrelated, and have identical variance, and all stock prices are currently the same. Then owning half the market vs the whole market would have identical expected returns, but the standard deviation of the half market portfolio would be 40% higher.

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

Post by Thesaints » Thu Sep 13, 2018 7:01 pm

Cartographer wrote:
Thu Sep 13, 2018 6:47 pm
willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns.
I don't think this is true. Suppose all expected returns are equal, uncorrelated, and have identical variance, and all stock prices are currently the same. Then owning half the market vs the whole market would have identical expected returns, but the standard deviation of the half market portfolio would be 40% higher.
Sure. But the theory actually says that risk normalized returns should be the same if you consider only the non-diversifiable risk.
In your example, the risk of half the market and of all the market would be the same.

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

Post by Cartographer » Thu Sep 13, 2018 7:08 pm

Thesaints wrote:
Thu Sep 13, 2018 7:01 pm
Cartographer wrote:
Thu Sep 13, 2018 6:47 pm
willthrill81 wrote:
Thu Sep 13, 2018 2:31 pm
If the EMH is accurate, then any large number of stock holding should be expected to have very similar risk-adjusted returns.
I don't think this is true. Suppose all expected returns are equal, uncorrelated, and have identical variance, and all stock prices are currently the same. Then owning half the market vs the whole market would have identical expected returns, but the standard deviation of the half market portfolio would be 40% higher.
Sure. But the theory actually says that risk normalized returns should be the same if you consider only the non-diversifiable risk.
In your example, the risk of half the market and of all the market would be the same.
Ok, but at the end of the day when selecting between two portfolios, all I really should care about is the overall risk and returns of the two portfolios. In the example above, they may have the same non-diversifiable risk, but the actual risks are quite different and clearly one portfolio is better than the other.

For the cap vs equal weighting debate: if the risk-adjusted returns of the two weightings are similar, my guess is that this is just a happy coincidence and not the result of some deep underlying theory.

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

Post by Thesaints » Thu Sep 13, 2018 7:15 pm

Cartographer wrote:
Thu Sep 13, 2018 7:08 pm
Ok, but at the end of the day when selecting between two portfolios, all I really should care about is the overall risk and returns of the two portfolios. In the example above, they may have the same non-diversifiable risk, but the actual risks are quite different and clearly one portfolio is better than the other.
Why do you say so ? IIRC on "A Random Walk..." there is a graph showing how adding up individual stocks from the S&P one gradually decreases total risk, until with around 30 stocks it reaches the non-diversifiable risk asymptote.
Of course those stocks are assumed not to be in any particular correlation with each other. i.e. it wouldn't be true if one, for example, used only financial stocks. In such case total risk would converge to a higher value, which could be further decreased by diversifying across different sectors.

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

Post by Phineas J. Whoopee » Thu Sep 13, 2018 7:25 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.
And as always, threads of this type devolve into arguments over the definition of the word diversification.

Here's a thought. It might or might not be helpful, but here it is:

1) Diversification in terms of investing is implicitly taken to be good.

2) People have different opinions on what is good in terms of investing.

3) Therefore, people have irreconcilable definitions of the word diversification.

We will never all agree on what is good when it comes to investing.

PJW

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

Post by Cartographer » Thu Sep 13, 2018 7:29 pm

Thesaints wrote:
Thu Sep 13, 2018 7:15 pm
Cartographer wrote:
Thu Sep 13, 2018 7:08 pm
Ok, but at the end of the day when selecting between two portfolios, all I really should care about is the overall risk and returns of the two portfolios. In the example above, they may have the same non-diversifiable risk, but the actual risks are quite different and clearly one portfolio is better than the other.
Why do you say so ? IIRC on "A Random Walk..." there is a graph showing how adding up individual stocks from the S&P one gradually decreases total risk, until with around 30 stocks it reaches the non-diversifiable risk asymptote.
Of course those stocks are assumed not to be in any particular correlation with each other. i.e. it wouldn't be true if one, for example, used only financial stocks. In such case total risk would converge to a higher value, which could be further decreased by diversifying across different sectors.
In practice, it may be true that 30 stocks is enough. However, in the example of a market of uncorrelated identical stocks, there is no asymptote. Every time I quadruple the number of stocks in my portfolio, I halve the standard deviation.

Also, I think there is some doubt about whether or not 30 stocks is truly enough in practice

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

Post by Thesaints » Thu Sep 13, 2018 7:36 pm

Cartographer wrote:
Thu Sep 13, 2018 7:29 pm
In practice, it may be true that 30 stocks is enough. However, in the example of a market of uncorrelated identical stocks, there is no asymptote. Every time I quadruple the number of stocks in my portfolio, I halve the standard deviation.
Only because you have assumed zero correlation between them, so that the asymptote is effectively zero: All risk can be diversified away !

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

Post by willthrill81 » Thu Sep 13, 2018 8:16 pm

Phineas J. Whoopee wrote:
Thu Sep 13, 2018 7:25 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.
And as always, threads of this type devolve into arguments over the definition of the word diversification.

Here's a thought. It might or might not be helpful, but here it is:

1) Diversification in terms of investing is implicitly taken to be good.

2) People have different opinions on what is good in terms of investing.

3) Therefore, people have irreconcilable definitions of the word diversification.

We will never all agree on what is good when it comes to investing.

PJW
:thumbsup

I entirely agree. I just wish the 'cap weighted' crowd was not so militant in their views that it's the only logical way to index a market.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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

Post by CULater » Fri Sep 14, 2018 6:14 am

The first live index fund was based on equal-weighting. This was changed to CW in 1976 not because it was better but because it was easier to implement back then. Now, not so much.
In 1969–1971, Wells Fargo Bank had worked from academic models to develop the principles and techniques leading to index investing. John A. McQuown and William L. Fouse pioneered the effort, which led to the construction of a $6 million index account for the pension fund of Samsonite Corporation. With a strategy based on an equal-weighted index of New York Stock Exchange equities
https://www.vanguard.com/bogle_site/lib/sp19970401.html
May you have the hindsight to know where you've been, The foresight to know where you're going, And the insight to know when you've gone too far. ~ Irish Blessing

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

Post by vineviz » Fri Sep 14, 2018 6:19 am

CULater wrote:
Fri Sep 14, 2018 6:14 am
The first live index fund was based on equal-weighting. This was changed to CW in 1976 not because it was better but because it was easier to implement back then. Now, not so much.
In 1969–1971, Wells Fargo Bank had worked from academic models to develop the principles and techniques leading to index investing. John A. McQuown and William L. Fouse pioneered the effort, which led to the construction of a $6 million index account for the pension fund of Samsonite Corporation. With a strategy based on an equal-weighted index of New York Stock Exchange equities
https://www.vanguard.com/bogle_site/lib/sp19970401.html
A cap weighted portfolio is demonstrably superior in at least one respect, which is lower management cost due to turnover.

Then the question becomes one of whether there are any incontrovertible disadvantages, and there don’t seem to be any.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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

Post by CULater » Fri Sep 14, 2018 9:26 am

One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
May you have the hindsight to know where you've been, The foresight to know where you're going, And the insight to know when you've gone too far. ~ Irish Blessing

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

Post by UpperNwGuy » Fri Sep 14, 2018 9:45 am

CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
General Electric and Sears have gone way down in price. Are you suggesting that we would want to buy those stocks? Are you suggesting that we should sell Apple and Alphabet?

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

Post by willthrill81 » Fri Sep 14, 2018 9:56 am

vineviz wrote:
Fri Sep 14, 2018 6:19 am
CULater wrote:
Fri Sep 14, 2018 6:14 am
The first live index fund was based on equal-weighting. This was changed to CW in 1976 not because it was better but because it was easier to implement back then. Now, not so much.
In 1969–1971, Wells Fargo Bank had worked from academic models to develop the principles and techniques leading to index investing. John A. McQuown and William L. Fouse pioneered the effort, which led to the construction of a $6 million index account for the pension fund of Samsonite Corporation. With a strategy based on an equal-weighted index of New York Stock Exchange equities
https://www.vanguard.com/bogle_site/lib/sp19970401.html
A cap weighted portfolio is demonstrably superior in at least one respect, which is lower management cost due to turnover.

Then the question becomes one of whether there are any incontrovertible disadvantages, and there don’t seem to be any.
One notable difference, not necessarily a dis/advantage for either, between EW and CW is that it can lead to big differences in sector weights.

Image

Similarly, as of the composition of that table, the FANG stocks represented 6.79% of the S&P 500 for CW but only .80% for EW.

But again, for an EMH believer, all of this shouldn't make a significant difference in risk-adjusted returns, although the greater exposure to smaller companies with EW should lead to both higher risk and returns, which is what has been the case over the lifespan of RSP.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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

Post by Cartographer » Fri Sep 14, 2018 10:08 am

CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
I've wondered the same thing. Here's my take (which could be totally wrong): the market in aggregate has a certain risk appetite. If your risk appetite is identical to the market, then you should just own exactly what the market owns, as it will be the optimal portfolio for that level of risk. In this case, you should never have to rebalance, as the market will maintain the risk exposure for you.

On the other hand, if your risk appetite is more or less, you will need to hold assets in different proportions, and the market will no longer maintain your risk level on its own. This will end up requiring you to rebalance occasionally. In theory, you would do this for individual stocks, but that is too difficult. However, it is feasible to rebalance across large asset classes, and maintain market cap weighting within each class. This is probably not the truly optimal portfolio for your risk level, but it will likely be as close as you can get without incurring high expenses.

Edit: few more things. Your index funds actually do rebalance between stock holdings when stocks are added or removed from an index. By their nature, bonds are being created and terminated all the time, much more than stocks. And unlike stocks, I think the bond market grows primarily by issuing new bonds. Therefore, the bond market will grow faster than the value of any bond fund. So even the market weighting of stocks and bonds would need to rebalance stocks into bonds in order to capture this growth.
Last edited by Cartographer on Fri Sep 14, 2018 10:20 am, edited 1 time in total.

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

Post by CULater » Fri Sep 14, 2018 10:15 am

UpperNwGuy wrote:
Fri Sep 14, 2018 9:45 am
CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
General Electric and Sears have gone way down in price. Are you suggesting that we would want to buy those stocks? Are you suggesting that we should sell Apple and Alphabet?
Isn't that the idea behind rebalancing? You sell some of what's gone up to buy some of what's gone down. If you knew the future you could do a lot better, but rebalancing is suggested for people who don't know what will happen.
May you have the hindsight to know where you've been, The foresight to know where you're going, And the insight to know when you've gone too far. ~ Irish Blessing

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

Post by Thesaints » Fri Sep 14, 2018 10:20 am

A cap-weighted index can be followed by any number of investors, for any any fraction of the total market cap. And those investors (active) who choose not to follow the index do so in aggregate. Hence the paradigm that active investors in aggregate cannot outperform the ibdex.

That is not true anymore with non cap weighted indexes. There is a limit to how much money can be invested that way and active investors can outperform the index in aggregate.

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

Post by willthrill81 » Fri Sep 14, 2018 10:21 am

Cartographer wrote:
Fri Sep 14, 2018 10:08 am
CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
I've wondered the same thing. Here's my take (which could be totally wrong): the market in aggregate has a certain risk appetite. If your risk appetite is identical to the market, then you should just own exactly what the market owns, as it will be the optimal portfolio for that level of risk. In this case, you should never have to rebalance, as the market will maintain the risk exposure for you.

On the other hand, if your risk appetite is more or less, you will need to hold assets in different proportions, and the market will no longer maintain your risk level on its own. This will end up requiring you to rebalance occasionally. In theory, you would do this for individual stocks, but that is too difficult. However, it is feasible to rebalance across large asset classes, and maintain market cap weighting within each class. This is probably not the truly optimal portfolio for your risk level, but it will likely be as close as you can get without incurring high expenses.
You're correct, and this idea is behind the operation of risk parity portfolios. They hold a high percentage of bonds but then ratchet up the stock risk through leverage.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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

Post by UpperNwGuy » Fri Sep 14, 2018 10:54 am

CULater wrote:
Fri Sep 14, 2018 10:15 am
UpperNwGuy wrote:
Fri Sep 14, 2018 9:45 am
CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
General Electric and Sears have gone way down in price. Are you suggesting that we would want to buy those stocks? Are you suggesting that we should sell Apple and Alphabet?
Isn't that the idea behind rebalancing? You sell some of what's gone up to buy some of what's gone down. If you knew the future you could do a lot better, but rebalancing is suggested for people who don't know what will happen.
I don't subscribe to the "nobody knows nothing" mantra that gets tossed around in this forum so frequently. There's a lot I don't know about the market, but I think I know enough about the long-term rise and fall of large corporations to know that it is highly unlikely that either General Electric or Sears will ever recover their lost glory. As I asked before, are you suggesting that we would want to buy those stocks?

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

Post by rkhusky » Fri Sep 14, 2018 12:24 pm

CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
In general, you don't need to manually rebalance a cap-weighted portfolio because it is most always in balance. The only time you would need to buy/sell is when a stock leaves or enters the index or a company buys back or issues shares.

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

Post by willthrill81 » Fri Sep 14, 2018 3:19 pm

UpperNwGuy wrote:
Fri Sep 14, 2018 10:54 am
CULater wrote:
Fri Sep 14, 2018 10:15 am
UpperNwGuy wrote:
Fri Sep 14, 2018 9:45 am
CULater wrote:
Fri Sep 14, 2018 9:26 am
One thing I don't understand, quite. Essentially, a cap-weighted fund mirrors buying the "market"; all the stocks in the "market" in proportion to their relative cap weights -- and then it just continues to own the "shares" that it started with forever in effect. No rebalancing. Stuff that goes way up in price is not sold; stuff that goes way down in price is not bought. I thought rebalancing was important to control risk. How come it's OK to not rebalance between stock holdings? Is this what you'd do if you owned individual stock holdings separately?
General Electric and Sears have gone way down in price. Are you suggesting that we would want to buy those stocks? Are you suggesting that we should sell Apple and Alphabet?
Isn't that the idea behind rebalancing? You sell some of what's gone up to buy some of what's gone down. If you knew the future you could do a lot better, but rebalancing is suggested for people who don't know what will happen.
I don't subscribe to the "nobody knows nothing" mantra that gets tossed around in this forum so frequently. There's a lot I don't know about the market, but I think I know enough about the long-term rise and fall of large corporations to know that it is highly unlikely that either General Electric or Sears will ever recover their lost glory. As I asked before, are you suggesting that we would want to buy those stocks?
For the record, Sears is no longer even remotely in the S&P 500. However, GE still is.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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