How Many Stocks Are Really Needed in Index Funds?

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Alexa9
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How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

[2018 thread updated in 2022 --admin LadyGeek]

How many stocks are needed in an Index Fund to track Vanguard Total Stock Market Fund fairly closely? It is essentially a large cap fund since it is weighted by market cap. VTI boasts 3,600 stocks but is that really necessary? Are you getting your money's worth from the expense ratio?

I would guess the top 50-100 stocks by market cap would closely replicate VTI.

The top 1% of earners earn a majority of the money so I was curious if large cap companies perform similarly.

https://revenuesandprofits.com/top-50-u ... ket-value/

"Apple was in news recently because its market cap crossed the $800 billion mark. Apple is number one company right now in terms of market valuation. We were wondering how other companies rank on market valuation. So, we did a quick research on the market valuations of S&P 500 companies. The S&P 500 stock market index, maintained by S&P Dow Jones Indices, consists of 500 large-cap companies traded on US stock exchanges.

We pulled out the list of S&P 500 companies from Wikipedia. Then, we pulled out the latest market cap (as of May 12, 2017) of each of the 500 companies using Google Finance function. Then, we sorted the list of S&P 500 companies by market cap. This gave us the ranking of the 500 companies by their market cap. Then, we used all this information to prepare the diagram below for top 50 US companies by market value.
One of the key insights from this exercise was that Top 10% of the S&P 500 companies hold nearly 50% of the total market cap. If we sort the companies by market cap, we find that the top 50 companies hold nearly half of the total market cap of S&P 500 companies. The combined market cap of top 50 companies is $10.7 trillion, whereas the total market cap of all 500 companies is $21.8 trillion."

The only scenario I would find this might be valuable at all is a high net worth person that wants a zero expense ratio. In a small cap fund, I somewhat understand the need for many stocks, but not in a large cap or total market fund.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Thesaints »

Since Vanguard can replicate the total stock market for a 0.04% expense rate, I'd say there is no good reason for trying to match the index by other methods.
Besides, excluding smaller cap stocks, with the idea of buying them if and when they become very large cap stocks is tax inefficient since it generates extra turnover.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by David Jay »

Alexa9 wrote: Thu Jan 04, 2018 4:28 pmAre you getting your money's worth from the expense ratio?
What does that mean? Total Stock is amongst the lowest expense ratios among mutual funds. It is the same as the SP 500 index fund.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by RadAudit »

The short answer is you need enough stocks to track the index very closely.

As I recall from years ago, the S&P 500 accounted for 80% of the total market. The other 3000 stocks got the next 20%. Don't know if those numbers still hold from when the total market had more than 5000 stocks.

My other guess is that with the money VG's total stock has, they have to put it somewhere so they put it where they can match the index as close as possible.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

David Jay wrote: Thu Jan 04, 2018 5:07 pm
Alexa9 wrote: Thu Jan 04, 2018 4:28 pmAre you getting your money's worth from the expense ratio?
What does that mean? Total Stock is amongst the lowest expense ratios among mutual funds. It is the same as the SP 500 index fund.
You could buy the 50 largest companies and perform very similarly (I am guessing) for no expense ratio. Might be worth it if you have a high net worth.
RadAudit wrote: Thu Jan 04, 2018 5:21 pm The short answer is you need enough stocks to track the index very closely.

As I recall from years ago, the S&P 500 accounted for 80% of the total market. The other 3000 stocks got the next 20%. Don't know if those numbers still hold from when the total market had more than 5000 stocks.

My other guess is that with the money VG's total stock has, they have to put it somewhere so they put it where they can match the index as close as possible.
But for the average investor, does it matter how closely you track it? How many stocks is good enough? I think after about 50 stocks you're going to track it pretty closely if you look at the top holdings:
http://portfolios.morningstar.com/fund/holdings?t=VTI
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Jeff Albertson »

See William Bernstein (2000), 'The 15-Stock Diversification Myth'
http://www.efficientfrontier.com/ef/900/15st.htm
The reason is simple: a grossly disproportionate fraction of the total return came from a very few "superstocks" like Dell Computer, which increased in value over 550 times. If you didn’t have one of the half-dozen or so of these in your portfolio, then you badly lagged the market.

So, yes, Virginia, you can eliminate nonsytematic portfolio risk, as defined by Modern Portfolio Theory, with a relatively few stocks. It’s just that nonsystematic risk is only a small part of the puzzle. Fifteen stocks is not enough. Thirty is not enough. Even 200 is not enough. The only way to truly minimize the risks of stock ownership is by owning the whole market.
Also see this more recent article
https://www.marketwatch.com/story/why-p ... nk=sfmw_tw
The best-performing 4% of listed stocks accounted for the entire lifetime dollar wealth creation of the U.S. stock market since 1926.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by David Jay »

Alexa9 wrote: Thu Jan 04, 2018 5:33 pm
David Jay wrote: Thu Jan 04, 2018 5:07 pm
Alexa9 wrote: Thu Jan 04, 2018 4:28 pmAre you getting your money's worth from the expense ratio?
What does that mean? Total Stock is amongst the lowest expense ratios among mutual funds. It is the same as the SP 500 index fund.
You could buy the 50 largest companies and perform very similarly (I am guessing) for no expense ratio. Might be worth it if you have a high net worth.
How do you maintain a portfolio of the 50 largest stocks with zero expenses?

And if you are a VHNW individual, you have people for that. More expenses.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by MarginalCost »

Standard & Poor Maintain a S&P 100 index (OEX) that's intended to track the MegaCaps in a similar manner as you describe, though with a little weight given to sector balance. It represents 63% of the S&P 500's market cap

Below is a comparison of the S&P 500 (Red) and the S&P 100 (Blue) from Yahoo finance:
Image

While they're definitely highly correlated, in the late 90s/early 00s the S&P 100 had clear outperformance, while more recently the S&P 500 has pulled ahead.

Size is one of the characteristics where we have a lot of evidence that there's a difference in how companies perform. When you have assets like stocks that don't tend to always follow the most convenient statistical properties, the importance of larger sample sizes increases.

Maybe you'd have an argument a few decades ago. But today, diversification is dirt cheap, and one of the only free lunches there is. I wouldn't pass it up without good reason.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

Jeff Albertson wrote: Thu Jan 04, 2018 5:35 pm See William Bernstein (2000), 'The 15-Stock Diversification Myth'
http://www.efficientfrontier.com/ef/900/15st.htm
The reason is simple: a grossly disproportionate fraction of the total return came from a very few "superstocks" like Dell Computer, which increased in value over 550 times. If you didn’t have one of the half-dozen or so of these in your portfolio, then you badly lagged the market.

So, yes, Virginia, you can eliminate nonsytematic portfolio risk, as defined by Modern Portfolio Theory, with a relatively few stocks. It’s just that nonsystematic risk is only a small part of the puzzle. Fifteen stocks is not enough. Thirty is not enough. Even 200 is not enough. The only way to truly minimize the risks of stock ownership is by owning the whole market.
Also see this more recent article
https://www.marketwatch.com/story/why-p ... nk=sfmw_tw
The best-performing 4% of listed stocks accounted for the entire lifetime dollar wealth creation of the U.S. stock market since 1926.
Those are good points BUT I still think you can replicate VTI fairly well with I'd say 50 stocks since 50 stocks make up half the market cap of the S&P500.
David Jay wrote: Thu Jan 04, 2018 5:38 pm
Alexa9 wrote: Thu Jan 04, 2018 5:33 pm
David Jay wrote: Thu Jan 04, 2018 5:07 pm
Alexa9 wrote: Thu Jan 04, 2018 4:28 pmAre you getting your money's worth from the expense ratio?
What does that mean? Total Stock is amongst the lowest expense ratios among mutual funds. It is the same as the SP 500 index fund.
You could buy the 50 largest companies and perform very similarly (I am guessing) for no expense ratio. Might be worth it if you have a high net worth.
How do you maintain a portfolio of the 50 largest stocks with zero expenses?

And if you are a VHNW individual, you have people for that. More expenses.
Very little rebalancing, just reinvest dividends. 100 Free Trades per year for Flagship Select. Let's say I don't want to give these brokerages a penny.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by David Jay »

But it's not the same stocks year after year. If it is a VHNW individual, this is not in a 401K or IRA, it is taxable. Every time a company falls out of the top 50 there are capital gains on the sale. What are the capital gains on a half-million dollar sale? Your whole "no expenses" meme is hopelessly wrong.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by patrick013 »

You could have 500 stocks per general market index. Large, medium,
and small cap. The S&P 1500 composite index is pretty close to that.
I like having a separate index investment for each, large, medium, and
small caps. The risk of letting in less than excellent companies is greater
when over 500 stocks per capsize is in those indexes. But.............

CRSP and FTSE don't follow that and have indexes with 1000's of stocks at
least that have earnings, some growth, etc..

Russell has a 3000 which is roughly twice the size of the S&P 1500. But they
all need earnings to succeed.
age in bonds, buy-and-hold, 10 year business cycle
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

MarginalCost wrote: Thu Jan 04, 2018 5:47 pm Standard & Poor Maintain a S&P 100 index (OEX) that's intended to track the MegaCaps in a similar manner as you describe, though with a little weight given to sector balance. It represents 63% of the S&P 500's market cap

Below is a comparison of the S&P 500 (Red) and the S&P 100 (Blue) from Yahoo finance:
Image

While they're definitely highly correlated, in the late 90s/early 00s the S&P 100 had clear outperformance, while more recently the S&P 500 has pulled ahead.

Size is one of the characteristics where we have a lot of evidence that there's a difference in how companies perform. When you have assets like stocks that don't tend to always follow the most convenient statistical properties, the importance of larger sample sizes increases.

Maybe you'd have an argument a few decades ago. But today, diversification is dirt cheap, and one of the only free lunches there is. I wouldn't pass it up without good reason.
Good info. Right, my point is that it wouldn't exactly mirror the Total Market, but be "good enough."
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by nisiprius »

The Vanguard Large-Cap Stock Index Fund, VLCAX, holds 596 stock. The Vanguard Mega Cap Index Fund, VMCTX, available as Institutional class or to ordinary investors an ETF (MGC) holds 275 stocks. Both are selected systematically and only on the basis of size (unlike the S&P 500).

I agree, over the time period that MGC has existed, there hasn't been much difference.

Source
Image

But I don't understand your point about "getting your money's worth," since in fact, Total Stock (Admiral shares) has an expense ratio of, 0.04%, VLCAX 0.06%, and MGC 0.07%. That is, for whatever reason, it costs a (tiny) amount more to get fewer stocks.

There's another issue here, although it didn't show up in the past 11 years. It's part and parcel of the burstiness and "misbehavior of markets." Although you say most of the return of the market comes from the biggest stocks, it may be more accurate to say that most of the return of the market comes from a very small number of very-high-performing "superstocks" which are not necessarily the biggest. As a result, if a group of people each decide to hold and small random sample of the market instead of the whole market, their performance will vary based on how many of these superstocks they happens to catch. Mathematically, the dispersion of their results will be larger that would be expected if the returns of stocks followed a well-behaved normal distribution.

William J. Bernstein wrote about this some years ago in an essay on The Fifteen-Stock Diversification Myth. He concluded:
So, yes, Virginia, you can eliminate nonsytematic portfolio risk, as defined by Modern Portfolio Theory, with a relatively few stocks. It’s just that nonsystematic risk is only a small part of the puzzle. Fifteen stocks is not enough. Thirty is not enough. Even 200 is not enough. The only way to truly minimize the risks of stock ownership is by owning the whole market.
In short, given the actual expense ratio of Vanguard Total Stock Market Index Fund, I don't think there are savings to be gained by holding fewer stocks, and Bernstein's article makes a good case that some risk is incurred... so why bother?
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by GibsonL6s »

If you had a 1 million dollars, the annual fee is $400. What is your time worth to research how many stocks it would take to replicate the index, make the trades, the cost of the commissions, the time to monitor the performance and then identify those stocks leading to under performance if the index you create doesn't work etc.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by nisiprius »

Aha. Here we go. You said "the 50 largest stocks."

XLG, the Guggenheim S&P 500 Top 50 ETF:
The S&P 500® Top 50 ETF Index measures the cap-weighted performance of 50 of the largest companies in the S&P 500® Index
Ummm... it says "50 of the largest," not "the 50 largest," but I don't want to fuss about that. It has an 0.20% expense ratio.

Do you feel that the difference between these two total return charts is negligible? If you wanted the total stock market (blue), would you be happy with the tracking error you got from holding only the 50 largest stocks (orange)?
Source
Image

Note: this is not the result of expense in XLG. The expenses are only 0.20% per year. If you figure that the difference in expenses is let's say, 0.20% of $25,000 times 6 years, then the total expenses of XLG would be $300. That means if XLG had zero expenses, you'd have had $31,638.13, and $27,527.62 + $300 = $27,827.62. In other words, over this particular time period, you had a total lag of $3,810 in XLG, of which only $300 is due to expenses and $3,510, over ten times is much, is due to the error in representing the whole market using only the 50 largest stocks.

Now, let's be clear. There might, probably are periods of time over which XLG beats the Total Market. Or, XLG might, probably does have a lower standard deviation so maybe a higher Sharpe ratio. The point is: it is obviously quite different from the total market.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Wagnerjb »

Alexa9 wrote: Thu Jan 04, 2018 4:28 pm The only scenario I would find this might be valuable at all is a high net worth person that wants a zero expense ratio. In a small cap fund, I somewhat understand the need for many stocks, but not in a large cap or total market fund.
I used a similar strategy for about 15 years before I retired. I used around 30 individual stocks to replicate the Large Cap index, and I used mutual funds for small cap and international stocks.

As a Flagship member, my occasional trades were free. But more important than the zero ER is the tax benefits available to such a strategy. You tax loss harvest the losers. You hold on to the winners, maybe gifting them or donating them as part of rebalancing. You keep the dividend yield low.

You can expect a higher pre-tax return than an index fund, since they are notoriously prone to front-running - and you are not tracking an index. You have less turnover than the index fund, since you don't add or delete a fund when it falls out of some index.

Lastly, you can customize the portfolio to be underweight in your particular industry. In my case, living in Houston and working in the energy industry, being underweight in energy helped to compensate for my energy-sensitive job, stock options, RSUs and house value.

This strategy isn't for 99.9% of the folks here. But it clearly fits the Bogleheads principles of low cost, diversification, tax management, low turnover and passive investing.

Best wishes.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

Wagnerjb wrote: Thu Jan 04, 2018 8:18 pm
Alexa9 wrote: Thu Jan 04, 2018 4:28 pm The only scenario I would find this might be valuable at all is a high net worth person that wants a zero expense ratio. In a small cap fund, I somewhat understand the need for many stocks, but not in a large cap or total market fund.
I used a similar strategy for about 15 years before I retired. I used around 30 individual stocks to replicate the Large Cap index, and I used mutual funds for small cap and international stocks.

As a Flagship member, my occasional trades were free. But more important than the zero ER is the tax benefits available to such a strategy. You tax loss harvest the losers. You hold on to the winners, maybe gifting them or donating them as part of rebalancing. You keep the dividend yield low.

You can expect a higher pre-tax return than an index fund, since they are notoriously prone to front-running - and you are not tracking an index. You have less turnover than the index fund, since you don't add or delete a fund when it falls out of some index.

Lastly, you can customize the portfolio to be underweight in your particular industry. In my case, living in Houston and working in the energy industry, being underweight in energy helped to compensate for my energy-sensitive job, stock options, RSUs and house value.

This strategy isn't for 99.9% of the folks here. But it clearly fits the Bogleheads principles of low cost, diversification, tax management, low turnover and passive investing.

Best wishes.
Thanks for the feedback. Good to know that this is an option. Not the simplest option, but it works and can even be better in some ways.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by bottlecap »

The Dow seems to work with 30.

I’d like to hear about this "no cost" investing.

If you are high worth, Any savings by investing yourself ( and there probably aren’t any) aren’t worth your trouble.

JT
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Thesaints »

Alexa9 wrote: Thu Jan 04, 2018 5:33 pm You could buy the 50 largest companies and perform very similarly (I am guessing) for no expense ratio. Might be worth it if you have a high net worth.
That's simply not true. The largest 5 companies essentially did not exist 35 years ago. I understand you would have included them in your portfolio once they entered the top 50, but then you would have to sell stocks of another 5 companies and that is horribly inefficient as taxes are involved.
Not to mention that due to the market vagaries, companies would continuously jostle each other around position 40-60 and you have the choice of frequently correcting your holdings, or risk to miss the next Amazon as it climbs the ranking.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by aristotelian »

David Jay wrote: Thu Jan 04, 2018 5:38 pm How do you maintain a portfolio of the 50 largest stocks with zero expenses?

And if you are a VHNW individual, you have people for that. More expenses.
With Vanguard Flagship Services ($2 trades) you could probably get expenses down to .001% with a $1M portfolio. This approach would also open up lots of opportunities for Tax Loss Harvesting. I would probably want 100 stocks rather than 50.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by nisiprius »

bottlecap wrote: Thu Jan 04, 2018 8:39 pm...The Dow seems to work with 30...
What, exactly, do you mean by that? The Alexa9's opening words were "How many stocks are needed in an Index Fund to track Vanguard Total Stock Market Fund fairly closely?" Are you arguing that the Dow "tracks Vanguard Total Stock Market Fund fairly closely?" I would say that of course it depends on what you mean by "fairly," but I would not go farther than saying "not all that badly" or "stocks are stocks, all stocks go up and down pretty much together, so the Dow works surprisingly well as an indicator despite so any things about it being wrong."

Naturally, when any two strategies differ, people will assert that one is better and some people would argue that blue chips, or the Dow, or the "Dogs of the Dow," or something like that, is better than the total market. But that's very different from saying you can track the total market accurately with just thirty stocks.

I would offer this illustration. DIA, the ETF that tracks the Dow, against VTI, which tracks a total market index. Does DIA track VTI "closely?"

Source

Image
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by bottlecap »

nisiprius wrote: Fri Jan 05, 2018 6:37 am
bottlecap wrote: Thu Jan 04, 2018 8:39 pm...The Dow seems to work with 30...
What, exactly, do you mean by that? The Alexa9's opening words were "How many stocks are needed in an Index Fund to track Vanguard Total Stock Market Fund fairly closely?" Are you arguing that the Dow "tracks Vanguard Total Stock Market Fund fairly closely?"
I’m glad I got your blood going. But you're not quite right.

Alexa9's “opening words” were “How many stocks are really needed in Index funds?”

I answered.

I try not to make things more complicated than they need to be. I don’t have enough time on my hands.

If you don’t believe me, see the chart I prepared below:










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Re: How Many Stocks Are Really Needed in Index Funds?

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Re: How Many Stocks Are Really Needed in Index Funds?

Post by RadAudit »

Alexa9 wrote: Thu Jan 04, 2018 5:33 pm But for the average investor, does it matter how closely you track it?
Tracking error is a real concern to a number of folks. The lower the tracking error the better, even for us very small investors.

My concern is that if I'm making projections for the amount of money I'm going to need to live on for the next ten+ years (which I do) and the amount of money that is coming in, I've got big enough problems estimating 10 year returns on stocks. (No offense meant to any professional estimators.) I really don't need the extra hassle of trying to figure in changes due to tracking error.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by nisiprius »

Alexa9 wrote:How many stocks are needed in an Index Fund to track Vanguard Total Stock Market Fund fairly closely? I would guess the top 50-100 stocks by market cap would closely replicate VTI.
The S&P 500® Top 50 Index has replicated it about this closely (blue, Total Stock; orange, Top 50):
Image
Alexa9 wrote:But for the average investor, does it matter how closely you track it?
I don't know. Probably not. How close is "close enough" for you?
How many stocks is good enough?
Many investors feel that fewer stocks is better, if you can choose a superior category (blue chips, dividend stocks, dividend growers, value stocks), or superior individual stocks. They claim that too many stocks results in "diworsification." But if what you want to do is track a total market index fairly closely, I don't see that you've made a case as to why roughly following the major features of the index by using fifty stocks at zero cost, is better than tracking that index almost perfectly at a cost of 0.04%.

Of course if you have the desire and the wherewithal to invest in the fifty stocks yourself, why not? It's certainly not crazy and I'd love to hear what you have to say about it in a few years.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Jeff Albertson »

For the same expected return, you are taking much more uncompensated risk. I don't understand why anyone would want to do that.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by malabargold »

For a site dedicated to the champion of low-cost broad index funds, it always amuses me how many people tilt/concentrate holdings or otherwise try to get an “edge” to achieve “ better than average” returns.
This incessant yearning (greed?) is precisely what leads people off the Boglish path.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Wagnerjb »

nisiprius wrote: Fri Jan 05, 2018 8:54 am
Alexa9 wrote:How many stocks are needed in an Index Fund to track Vanguard Total Stock Market Fund fairly closely? I would guess the top 50-100 stocks by market cap would closely replicate VTI.

Many investors feel that fewer stocks is better, if you can choose a superior category (blue chips, dividend stocks, dividend growers, value stocks), or superior individual stocks. They claim that too many stocks results in "diworsification." But if what you want to do is track a total market index fairly closely, I don't see that you've made a case as to why roughly following the major features of the index by using fifty stocks at zero cost, is better than tracking that index almost perfectly at a cost of 0.04%.
We need to be careful what benchmark we are using here. Alexa asked if the top 50-100 stocks would be an adequate proxy for the Total Stock Market and I emphatically say NO. That is because 50-100 large stocks leave out the small cap universe, where we have seen higher returns (and higher risk).

I suspect that the top 50-100 stocks would mirror the Large Cap index or the S&P500 quite well. But if an investor is looking to replicate the Total Stock Market, I don't think a portfolio of individual stocks makes sense here.

Best wishes.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by bgf »

this sounds like it should be a statistics question. ive never taken a single statistics course, so i could be way off here.

you could otherwise word the question as, how large must the sample be to have a very high degree of confidence (low margin of error) that the sample mean will equal the true population mean?

sample being your portfolio and population being the index.

i would imagine if we were dealing with a normal distribution, this would be a relatively straightforward problem to answer. you could probably come up with something like, the answer is ~315 stocks.

unfortunately, stock returns are not normally distributed. maybe this makes the question intractable maybe it doesn't. i dont know enough.

anyone educated enough to provide a statistical answer?
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by aristotelian »

Folks, what if the pseudo-index of individual stocks enables greater tax efficiency through harvesting of losses and gains? I would think that greater tax efficiency would easily make up for any small performance gap (and of course, there is the possibility that you could overperform).

To me, by far the biggest risk would be behavioral risk involved in watching individual stock positions.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Wagnerjb »

Alexa9 wrote: Thu Jan 04, 2018 5:33 pm
But for the average investor, does it matter how closely you track it? How many stocks is good enough? I think after about 50 stocks you're going to track it pretty closely if you look at the top holdings:
Tracking error is no big deal for investors who understand their investments and their strategy. Your idea of the top 50 stocks would undoubtedly have a small amount of tracking error in any one year, but likely match the appropriate benchmark over the years.

For a real life example, look at BRLIX. This is the Bridgeway Blue Chip 35 index fund. It holds 35 very large cap stocks. Over the past 10 years, it has matched the S&P500 which is about what you would expect. (You would actually expect slight underperformance given that the S&P500 has smaller stocks than just the top 35). But in any given year, BRLIX returns differ from the S&P by 3-5%. That is what is shown in this Surz/Price paper on small portfolios as well, on page 5.

http://ppca-inc.com/pdf/DiversByNumbers.pdf

Personally, with my 30 stock portfolio I experienced the same level of tracking error.

Many people cannot tolerate or understand tracking error, and for them a stock portfolio wouldn't be appropriate.

Best wishes.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

Vanguard is great and index funds are great but I'm starting to think that they are becoming too popular with the massive flood of assets going to them. I got to thinking how would I go about investing without index funds which I did before finding Bogleheads/Vanguard. My old strategy was to hold 20-30 mega cap stocks in various sectors. One company going belly up would mean a <5% loss in my portfolio. OTOH a company doing very well would mean a large increase in my portfolio. Is it as diversified or accurately track an S&P 500 fund? Not really, but is it "good enough?" I would think so. Backtesting the DJIA vs. S&P shows this pretty well. Are index funds really that magical?? Sure, buying 30 stocks is a little more leg work than VTI, but it's also passive if you're not easily tempted and has a few advantages. Tax loss harvesting, 0% ER, etc.
bgf wrote: Fri Jan 05, 2018 10:41 am this sounds like it should be a statistics question. ive never taken a single statistics course, so i could be way off here.
Yes I am curious if there are any stats people out there to help out.

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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Wagnerjb »

aristotelian wrote: Fri Jan 05, 2018 6:36 am
David Jay wrote: Thu Jan 04, 2018 5:38 pm How do you maintain a portfolio of the 50 largest stocks with zero expenses?

And if you are a VHNW individual, you have people for that. More expenses.
With Vanguard Flagship Services ($2 trades) you could probably get expenses down to .001% with a $1M portfolio. This approach would also open up lots of opportunities for Tax Loss Harvesting. I would probably want 100 stocks rather than 50.
The first 25 trades are free for Flagship members. But the tax management opportunities are by far the more compelling driver for such an individual stock strategy. The ER savings is exceedingly trivial. And yes....you need to use this investment strategy in a taxable account for it to make sense.

We have seen an entire industry develop over doing exactly this. Betterment and Wealthfront and other Robo Advisors are automating the tax loss harvesting aspect, demonstrating that there is enough value in this aspect to warrant their costs. Of course, there is more to tax management (lower dividend yield, gifting, donating, etc) but tax loss harvesting is maybe the most significant.

Best wishes.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by whodidntante »

Zero. You can get really close by using derivatives.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by finite_difference »

Long term, looks like Total Market beats S&P 500 by about 0.5%. While past performance is no guarantee of future results, the additional small cap exposure and diversification provided by the Total Market Fund may lead to some advantages.

~50 basis points is nothing to sneeze at :)
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by willthrill81 »

Alexa9 wrote: Thu Jan 04, 2018 5:33 pm You could buy the 50 largest companies and perform very similarly (I am guessing) for no expense ratio.
I doubt very much that you would get very similar performance from such a portfolio. The market-cap leader has underperformed the rest of the market by around 5% per year. Tilting a portfolio away from the most popular (in terms of market cap) companies has historically resulted in a boost of around 1% in returns.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by bottlecap »

Alexa9 wrote: Fri Jan 05, 2018 11:50 am Vanguard is great and index funds are great but I'm starting to think that they are becoming too popular with the massive flood of assets going to them. I got to thinking how would I go about investing without index funds which I did before finding Bogleheads/Vanguard.
Index funds are too popular, so to avoid their popularity, you will simply invest in the underlying assets that index funds do? I'm not sure what you think you will achieve.

If it's lower costs, great. But expect to spend a lot of time and mental energy deciding which stocks stay in and out of you "fund" and when you should rebalance.

It's quite frankly not worth most people's time. Especially wealthy people, whose time is typically quite valuable.

But the answer to your question is how closely do you want to track the index? Here is a summary of what EJ Elton and MJ Gruber report: http://www.firstadvisorscapital.com/p/how-many-holdings

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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Alexa9 »

So for anyone interested in the statistics:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

The Top 100 Holdings in VTI make up 53% of the fund
The Top 200 Holdings in VTI make up 67% of the fund
The Top 300 Holdings in VTI make up 75% of the fund
The Top 400 Holdings in VTI make up 80% of the fund
The Top 500 Holdings in VTI make up 83% of the fund

Even more surprising!:
The Bottom 1000 Holdings in VTI make up 0.2% of the fund
(Insignificant almost? Kind of my point of the thread: how many stocks are really needed? Although certainly a small cap could take off)
The Bottom 2000 Holdings in VTI make up 2% of the fund
The Bottom 3000 Holdings in VTI make up 13% of the fund (Good reason to tilt to small caps)
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by willthrill81 »

Alexa9 wrote: Fri Jan 05, 2018 1:48 pm So for anyone interested in the statistics:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

The Top 100 Holdings in VTI make up 53% of the fund
The Top 200 Holdings in VTI make up 67% of the fund
The Top 300 Holdings in VTI make up 75% of the fund
The Top 400 Holdings in VTI make up 80% of the fund
The Top 500 Holdings in VTI make up 83% of the fund

Even more surprising!:
The Bottom 1000 Holdings in VTI make up 0.2% of the fund
(Insignificant almost? Kind of my point of the thread: how many stocks are really needed? Although certainly a small cap could take off)
The Bottom 2000 Holdings in VTI make up 2% of the fund
The Bottom 3000 Holdings in VTI make up 13% of the fund (Good reason to tilt to small caps)
It seems that you're more interested in tilting toward mid-caps and small-caps. If so, then just buy index funds that cover those segments of the market instead of large-caps. Alternatively, you can get an equal weight S&P 500 ETF. Guggenheim has had one (RSP) since 2003, and from 2004-2017, it has outperformed Vanguard's S&P 500 market-cap weighted index fund (VFINX) by 1.12%, though it had a slightly bigger drawdown over that period (-55.58% vs. 50.97%).

I too have serious doubts about whether market-cap weighting is the optimal means of indexing in the real world.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by bgf »

Alexa9 wrote: Fri Jan 05, 2018 1:48 pm So for anyone interested in the statistics:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

The Top 100 Holdings in VTI make up 53% of the fund
The Top 200 Holdings in VTI make up 67% of the fund
The Top 300 Holdings in VTI make up 75% of the fund
The Top 400 Holdings in VTI make up 80% of the fund
The Top 500 Holdings in VTI make up 83% of the fund

Even more surprising!:
The Bottom 1000 Holdings in VTI make up 0.2% of the fund
(Insignificant almost? Kind of my point of the thread: how many stocks are really needed? Although certainly a small cap could take off)
The Bottom 2000 Holdings in VTI make up 2% of the fund
The Bottom 3000 Holdings in VTI make up 13% of the fund (Good reason to tilt to small caps)
i think there are a couple things to keep in mind. first, those numbers just tell you the relationship between a certain number of stocks and their percentage of overall market cap at this particular point in time.

tracking error due to sampling over the long term would, i think, show up most drastically when your portfolio happens to miss out on the most extreme outperformers over that period, stocks out on the 'fat tail' of the distribution.

for example, and cherry picking to illustrate a point, if you created a 20 stock portfolio 25 years ago that included both apple and amazon, your "tracking error" would be very large, as they massively outperformed the index over that period. this would be the best of tracking errors, but still an error.

similarly, if you created a 20 stock portfolio that did not include apple, amazon, microsoft, cisco, or berkshire, i'd be willing to bet that your portfolio underperformed against the index. those are only 5 stocks out of 500, just 1%, but they had an outsized impact on the overall market return, both because of their annualized return as well as their overall market cap. this is the 'fat tail' of the stock return distribution.

sampling relies on the assumption that the outliers have little effect on the mean and that generally, given a large enough sample, your data will cluster around the same mean as the population.

when you have outliers that have outsized effects, the assumption that your sample mean will converge to the population mean breaks down. at least, that is my understanding of it.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by selters »

The S&P 500 Top 50 index gets pretty close: http://us.spindices.com/indices/equity/sp-500-top-50
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Thesaints »

willthrill81 wrote: Fri Jan 05, 2018 2:01 pm I too have serious doubts about whether market-cap weighting is the optimal means of indexing in the real world.
If you could buy the entire stock market you would necessarily be market cap weighted.
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Re: How Many Stocks Are Really Needed in Index Funds?

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Re: How Many Stocks Are Really Needed in Index Funds?

Post by willthrill81 »

Thesaints wrote: Sat Jan 06, 2018 2:37 am
willthrill81 wrote: Fri Jan 05, 2018 2:01 pm I too have serious doubts about whether market-cap weighting is the optimal means of indexing in the real world.
If you could buy the entire stock market you would necessarily be market cap weighted.
Not at all. It is theoretically possible to equally weight every publicly traded company in the world. That is far from a market cap weighting. For instance, you can buy an ETF that equally weights all of the companies in the S&P 500 as opposed to market cap weighting them.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by PFInterest »

all of them.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Thesaints »

willthrill81 wrote: Sat Jan 06, 2018 10:37 am Not at all. It is theoretically possible to equally weight every publicly traded company in the world. That is far from a market cap weighting. For instance, you can buy an ETF that equally weights all of the companies in the S&P 500 as opposed to market cap weighting them.
Then you would not own the entire stock market. In fact, you would be owning only a small fraction of it. Precisely the value of the smallest listed company in the world multiplied by the number of listed companies, which as you can imagine is utterly negligible compared to the total value of all listed companies.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by Dottie57 »

Doesn't the index define the stocksthat should be owned?
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by nisiprius »

willthrill81 wrote: Sat Jan 06, 2018 10:37 am...Not at all. It is theoretically possible to equally weight every publicly traded company in the world. That is far from a market cap weighting. For instance, you can buy an ETF that equally weights all of the companies in the S&P 500 as opposed to market cap weighting them...
Maybe. However, you canNOT buy an ETF that equally weights the Russell 2000, let alone the Russell 3000 (total market more or less)

What? you might say. What about the EQWS PowerShares Russell 2000 Equal Weight Portfolio ETF? Sounds good, until you actually take a look at this ETF's holdings. They should all be close to 0.05%, right?
Holding, Weighting
Snyder's-Lance Inc (LNCE) 0.35%
Calavo Growers Inc (CVGW) 0.32%
Ingles Markets Inc (IMKTA) 0.31%
...
Guaranty Bancshares Inc (GNTY) 0.02%
eHealth Inc (EHTH) 0.02%
Alexander's Inc (ALX) 0.02%
Investors Title Co (ITIC) 0.02%
Arlington Asset Investment Corp (AI) 0.02%
National Western Life Group Inc (NWLI) 0.02%
The "equal-weighted" ETF actually weights some stocks more than 15 times as much as others. How come?

Well, in part it is because the "Russell 2000 Equal Weight Index" doesn't weight equally.

As far as I know, there is not any mutual fund or ETF that even has a name even faintly suggesting that it invests equally-weighted in the total market.

So if we cap-weighted index investors are fairly happy with the S&P 500, can't would-be equal-weighted investors be happy with the equal-weighted S&P 500? No, because by cap-weight, the S&P 500 is about 80% of the market, which is a pretty decent chunk; but by equal weight, the S&P 500 is only 1/8th of the market, and not any better or more representative than the other 7/8ths.
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Re: How Many Stocks Are Really Needed in Index Funds?

Post by willthrill81 »

Thesaints wrote: Sat Jan 06, 2018 2:01 pm
willthrill81 wrote: Sat Jan 06, 2018 10:37 am Not at all. It is theoretically possible to equally weight every publicly traded company in the world. That is far from a market cap weighting. For instance, you can buy an ETF that equally weights all of the companies in the S&P 500 as opposed to market cap weighting them.
Then you would not own the entire stock market. In fact, you would be owning only a small fraction of it. Precisely the value of the smallest listed company in the world multiplied by the number of listed companies, which as you can imagine is utterly negligible compared to the total value of all listed companies.
I said "theoretically possible," not currently feasible. I suspect that we'll see more and better equal weight ETFs going forward. Time will tell. The point is that market-cap weighting is not the only way to index a market.
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