A suggestion on minimum number of stocks to hold if randomly selecting companies.

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A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Anon9001 »

1 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 10% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 0.8% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 0.4% Increase in Probability to Out-perform Value-Weighted Market

10 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 39% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 2% Increase in Probability to Out-perform Value-Weighted Market

90 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 471% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 62% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 6% Increase in Probability to Out-perform Value-Weighted Market

According to these figures maximum diversification benefit in terms of probability of out-performing value weighted market ie capitalization weighted market return occurs at 25 stocks. I would add however that if you are picking random 25 stocks to do a quality screen and have good sector diversification. That should probably increase probability of out-performing capitalization weighted market by a moderate amount. Now you might ask where I got these figures?

Well from the Hendrik Bessembinder study that many link to here saying 96% of stocks under-perform treasury bills.

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Last edited by Anon9001 on Fri May 14, 2021 11:11 am, edited 3 times in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by tibbitts »

Anon9001 wrote: Thu May 13, 2021 9:28 am I would add however that if you are picking random 25 stocks to do a quality screen and have good sector diversification. That should probably increase probability of out-performing capitalization weighted market by a moderate amount.
If you use screens and require sector diversification you would no longer have 25 random stocks.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by HootingSloth »

Anon9001, could you explain a bit about what you see as the advantages of doing this? It is not hard to get exposure to over 11,000 stocks by just holding VTSAX and VTIAX. All the probabilities you list of outperforming the market are less than 50%. What do you think is happening in the other (presumably >50%) cases?
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

tibbitts wrote: Thu May 13, 2021 9:34 am If you use screens and require sector diversification you would no longer have 25 random stocks.
Good point but I am assuming the people who are interested in doing these concentrated portfolios are doing it to out-perform market and I am suggesting this quality screen and sector diversification to improve probabilities beyond the 45% chance you get by doing it randomly for 10 Year Horizon and 37% chance you get for 90 Year Horizon.
Last edited by Anon9001 on Thu May 13, 2021 9:43 am, edited 1 time in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by scout1 »

How much is the outperformance and how much is the underperformance when they occur?
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

HootingSloth wrote: Thu May 13, 2021 9:37 am Anon9001, could you explain a bit about what you see as the advantages of doing this? It is not hard to get exposure to over 11,000 stocks by just holding VTSAX and VTIAX. All the probabilities you list of outperforming the market are less than 50%. What do you think is happening in the other (presumably >50%) cases?
These are just random stock portfolio probabilities. I would not take them too seriously unless you are a die hard EMH fanatic who assumes a company with a high debt and company with low to zero debt have same risk of going to 0, also that you assume large and small companies have same risk of going to 0. I would assume that if you are doing a quality screen and sector diversification the probabilities go up to 50-50 chance which is pretty good. Now there is a down-side to owning 25 stock portfolios in that they tend to have high tracking error relative to market. If you are not capable of handling that than you should not do this.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by galeno »

I'd like to see the OP's attitude if and when he goes thru a multi year bear market like the 2000-2002 bear. The other 3 bears (1987, 2008, and 2020) were yawns for us. Before we became Bogleheads in 2006 we invested like the OP wants to do. For 11 years.

At the time we were using 12-16 stocks picked by a simple annual screen. From 1996-2005. Our 80/20 port: CAGR = 15.9%. GSD = 27.4%. vs 100% VTI: CAGR = 11.0%. GSD = 19.9%.

Looks good right? Well, rebalancing into 12-16 stocks in January 2001 and 2002 felt like we were throwing our money into a furnace. A nightmare I don't wish on anybody. When we finally reached our previous nominal portfolio high of 1999 we switched to Boglehead investing. And we went to 60/40.

Today we're at 50/50. A simple 2 fund port.
Last edited by galeno on Fri May 14, 2021 1:14 pm, edited 1 time in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Valuethinker »

galeno wrote: Thu May 13, 2021 1:45 pm I'd like to see the OP's attitude if and when he goes thru a multi year bear market like the 2000-2002 bear. The other 3 bears (1987, 2008, and 2020) were yawns for us. Before we became Bogleheads in 2006 we invested like the OP wants to do. For 11 years.
Probably worth reminding those of us who don't remember, that 1987 was not a bear market. It was, in essence, a 1 day correction. Just a brutal one.

Real bear markets? Try Emerging Markets. 1994 after Mexico nearly defaulted. 1997-98 in Asia, Russia, Brazil etc.

2008-09 I think it depended on your physical proximity to financial markets, in particular New York or London. I knew too many people who worked in financial services. Basically it was the end of the world - or the threatened end of the world. The colourful expression used by the British civil servants on the Friday to the Chanceller (Minister of Finance) was "If we don't do something (about RBS & HBOS) then by Monday morning there will be no money in the bank machines (ATMs)". That's not just colourful - I did know people who were withdrawing the maximum cash they could from ATMs, over that weekend. There was that smell of panic that you get - the moment before the rush for the exits.

Of course Greece and Iceland they literally did put restrictions on how much you could withdraw. A maximum of 60 Euros a day from bank machines in Greece; Iceland imposed foreign exchange controls. That was a few years later. And this all had real consequences - actual physical hunger became a thing again in some of the developed world's cities.
Today we're at 50/50. A simple 2 fund port.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

Reading Hendrink Bessinder study on Global markets and what I found is very interesting two markets ie Switzerland and Colombia have 47.5%, 50% of their individual stocks out-perform value-weighted market return for Lifetime Horizon for period January 1990-June 2020. If you are investing in these two markets you probably could do well with just 5 stocks. The Hendrink Bessidener study on Global markets unfortunately does not do a diversification comparison on probability to out-perform value weighted market like he did with the US study so we have to guess how much stocks are needed for Ex-US markets to not get disadvantaged by the positive skewness of individual stock returns. My local market (India) has 37% lower percentage of individual stocks that out-perform value-weighted market in comparison to US market for 1990-2020 so I assume that 35 stocks instead of 25 stocks should be enough especially when combined with sector diversification and quality screen. If your local stock market has a even lower percentage of individual stocks that out-perform value-weighted market than US market you should prefer to own minimum 50 stocks. Maybe even 100 stocks if not doing a quality screen and sector diversification.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by mffl »

The correct answer of course is one stock and a time machine.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by nisiprius »

Written 20 years ago, confirmed by more recent studies like Bessembinder's...

The Fifteen-Stock Diversification Myth
One of the most dangerous investment chestnuts is the idea that you can successfully diversify your portfolio with a relatively small number of stocks, the magic number usually being about 15....

...[Data and discussion]...

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.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

nisiprius wrote: Fri May 14, 2021 9:07 am Written 20 years ago, confirmed by more recent studies like Bessembinder's...
I am sorry if this comes off as a insult but I am genuinely curiously did you even read the post properly? I got these figures from Bessembinder's US paper. I already told you before also that Bernstien covered a period where extreme skewness of stock returns was there so please stop posting this article which is very flawed to me. And this skewness of stock returns is dependent on what country stock market you are invested into. If it is Switzerland, Columbia you can do okay with 5 stocks considering 47.5-50% of individual stocks there out-perform value-weighted market. Even in US markets where 36.5% of individual stocks out-perform value-weighted market for Lifetime Horizon for the period of 1990-2020 25 stocks capture majority of skewness premium. I would like it if the people here could actually read the post properly before commenting.
Last edited by Anon9001 on Fri May 14, 2021 2:06 pm, edited 4 times in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by mffl »

Anon9001 wrote: Fri May 14, 2021 9:12 am ... so please stop posting this rubbish to me. ... I would like it if the people here could actually read the post properly before commenting.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

nisiprius wrote: Fri May 14, 2021 9:07 am
I am just borrowing this image from you regarding LEXCX which only has 20 stocks from 1930s and I am confused how you can believe the Bernstein article regarding 15 stocks and look at LEXCX performance and not get confused regarding how close it is tracking the market if you believe the Bernstein article saying that you need 1 quadrillion stocks to match market return. This is real world evidence along with Bessembinder's US paper that is showing the Bernstein article is rubbish.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by gubernaculum »

Anon9001 wrote: Thu May 13, 2021 9:28 am 1 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 10% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 0.8% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 0.4% Increase in Probability to Out-perform Value-Weighted Market

10 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 39% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 2% Increase in Probability to Out-perform Value-Weighted Market

90 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 471% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 62% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 6% Increase in Probability to Out-perform Value-Weighted Market

According to these figures maximum diversification benefit in terms of probability of out-performing value weighted market ie capitalization weighted market return occurs at 25 stocks. I would add however that if you are picking random 25 stocks to do a quality screen and have good sector diversification. That should probably increase probability of out-performing capitalization weighted market by a moderate amount. Now you might ask where I got these figures? Well from the study that many link to here saying 96% of stocks under-perform treasury bills.

Image

You are likely correct as it is few stocks in the S&P500 that drive the gain, usually 5 on average. With 30 stocks you have an index. That is why I like WVENX, 60 or so stocks, has done great since 1929. My wife has one fund portfolio, 100% VWENX
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Schlabba »

Anon9001 wrote: Fri May 14, 2021 9:12 am
nisiprius wrote: Fri May 14, 2021 9:07 am Written 20 years ago, confirmed by more recent studies like Bessembinder's...
I am sorry if this comes off as a insult but I am genuinely curiously did you even read the post properly? I got these figures from Bessembinder's paper. I already told you before also that Bernstien covered a period where extreme skewness of stock returns was there so please stop posting this rubbish to me. And this skewness of stock returns is dependent on what country stock market you are invested into. If it is Switzerland, Columbia you can do okay with 5 stocks considering 47.5-50% of individual stocks there out-perform value-weighted market. Even in US markets where 36.5% of individual stocks out-perform value-weighted market for Lifetime Horizon 25 stocks capture majority of skewness premium. I would like it if the people here could actually read the post properly before commenting.
Suggesting a portfolio of 5 over a total world index fund is rubbish.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by 123 »

With an S&P500 or Total Stock Market fund or ETF you are pretty much guaranteed to get average market returns (less the expense ratio).

If you hold a sample of individual stocks there is no guarantee that you will ever get close to matching average market returns for any time period.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Northern Flicker »

Anon9001 wrote: Thu May 13, 2021 9:28 am 1 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 10% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 0.8% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 0.4% Increase in Probability to Out-perform Value-Weighted Market

10 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 39% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 3% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 2% Increase in Probability to Out-perform Value-Weighted Market

90 Year Horizon=

1 to 5 Stock Value Weighted Portfolio Improvement= 471% Increase in Probability to Out-perform Value-Weighted Market
5 to 25 Stock Value Weighted Portfolio Improvement= 62% Increase in Probability to Out-perform Value-Weighted Market
25 to 50 Stock Value Weighted Portfolio Improvement= 11% Increase in Probability to Out-perform Value-Weighted Market
50 to 100 Stock Value Weighted Portfolio Improvement= 6% Increase in Probability to Out-perform Value-Weighted Market

According to these figures maximum diversification benefit in terms of probability of out-performing value weighted market ie capitalization weighted market return occurs at 25 stocks. I would add however that if you are picking random 25 stocks to do a quality screen and have good sector diversification. That should probably increase probability of out-performing capitalization weighted market by a moderate amount. Now you might ask where I got these figures?

Well from the Hendrik Bessembinder study that many link to here saying 96% of stocks under-perform treasury bills.

Image
The posting is an incomplete analysis. The smaller the number of stocks also increases the probability of underperforming the market and increases it for each level of drawdown. For instance, the probability of the portfolio going to zero is much higher with 1-5 stocks than with a market portfolio, value weighted or otherwise.
My postings are my opinion, and never should be construed as a recommendation to buy, sell, or hold any particular investment.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by David Jay »

Anon9001 wrote: Fri May 14, 2021 9:12 am...so please stop posting this rubbish to me.
Not a great way to stimulate discussion...

Especially considering the analysis history of the individual who’s comment you called rubbish. Go read Nisiprius’ last, say, 10,000 posts.
Last edited by David Jay on Fri May 14, 2021 11:53 am, edited 1 time in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

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.....
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Northern Flicker »

Here is an article reporting work that found that a minimum of 60 stocks is required to diversify unsystematic risk away, and about 100 are required if you want to be confident in having done so:

http://eprints.utas.edu.au/17313/1/2013 ... cation.pdf
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

David Jay wrote: Fri May 14, 2021 11:47 am Especially considering the analysis history of the individual who’s comment you called rubbish. Go read Nisiprius’ last, say, 10,000 posts.
I did not call his comment rubbish. I called Bernstein's article regarding this issue rubbish. If you are to look at his article Bernstein says
The "market return" (all 500 stocks held in equal proportion) was 24.15%. This is considerably higher than the 18.94% return of the actual S&P for two reasons: First, the S&P is a cap-weighted, not an equal-weighted, portfolio. Second, and much more important, many of the stocks in the S&P on 11/30/99 were not in the index at the beginning of the period. The recently-added stocks obviously had much higher returns than the companies they replaced, upwardly biasing the entire series of returns"
He is comparing the 15 stock portfolios to the equal weight index which is having high returns due to the recently added stocks having much higher returns. This is flawed study. I pointed out this to Nisi before sometime back and he is still using this article so I was slightly frustrated with him.
Northern Flicker wrote: Fri May 14, 2021 12:31 pm Here is an article reporting work that found that a minimum of 60 stocks is required to diversify unsystematic risk away, and about 100 are required if you want to be confident in having done so:

http://eprints.utas.edu.au/17313/1/2013 ... cation.pdf
90% confidence for ES1 minimum 38-52 is necessary not 100 stocks. I am skimming the pdf though so I might have missed something.
To achieve the same level of risk reduction but with 90% confidence,
instead of on average, we find that portfolios aimed at diversifying extreme losses (e.g., ES1%)
are typically larger (US: 52; UK: 44; Japan: 50; Canada: 41; Australia: 38 stocks) than when
we use SD as our risk metric (US: 49; UK: 43; Japan: 39; Canada: 40; Australia: 38 stocks)
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by galeno »

KISS answer. Every 6 stocks cuts your non-systemic risk in half.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Northern Flicker »

Anon9001 wrote:
Northern Flicker wrote: Fri May 14, 2021 12:31 pm Here is an article reporting work that found that a minimum of 60 stocks is required to diversify unsystematic risk away, and about 100 are required if you want to be confident in having done so:

http://eprints.utas.edu.au/17313/1/2013 ... cation.pdf
90% confidence for ES1 minimum 38-52 is necessary not 100 stocks. I am skimming the pdf though so I might have missed something.
To achieve the same level of risk reduction but with 90% confidence,
instead of on average, we find that portfolios aimed at diversifying extreme losses (e.g., ES1%)
are typically larger (US: 52; UK: 44; Japan: 50; Canada: 41; Australia: 38 stocks) than when
we use SD as our risk metric (US: 49; UK: 43; Japan: 39; Canada: 40; Australia: 38 stocks)
90% confidence is not very strong confidence, particularly for risk management. 100 stocks worked in all of their similations, so that is the basis for the choice. When dealing with return, you can strategize around the average case. When protecting against risk, you should be looking at the worst case.
My postings are my opinion, and never should be construed as a recommendation to buy, sell, or hold any particular investment.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

Northern Flicker wrote: Fri May 14, 2021 12:31 pm 90% confidence is not suoer strong confidence. 100 stocks worked in all of their similations, so that is the basis for the choice. When desking with return, you can strategize around the average case. When protecting against risk, you should be looking at the worst case.
The pdf you linked is using Random stocks yet ES1 90% confidence is not requiring 100 stocks. Let's admit to ourselves a company with high debt and company with zero debt don't have same risk of going to 0, company which is small and company which is large don't have same risk of going to 0, Unprofitable companies and Profitable companies don't have same risk of going to 0. If you are doing a quality screen and sector diversification I am pretty sure ES1 100% confidence can be reached with even fewer than 100 companies. I hope this is not a controversial statement to make considering many here believe EMH is correct.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by LadyGeek »

The discussion is getting contentious. As a reminder, see: General Etiquette
At all times we must conduct ourselves in a respectful manner to other posters.
I also corrected a spelling error in the thread's title, from"randomlly" to "randomly".
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by scout1 »

Anon9001 wrote: Fri May 14, 2021 1:30 pm
Northern Flicker wrote: Fri May 14, 2021 12:31 pm 90% confidence is not suoer strong confidence. 100 stocks worked in all of their similations, so that is the basis for the choice. When desking with return, you can strategize around the average case. When protecting against risk, you should be looking at the worst case.
The pdf you linked is using Random stocks yet ES1 90% confidence is not requiring 100 stocks. Let's admit to ourselves a company with high debt and company with zero debt don't have same risk of going to 0, company which is small and company which is large don't have same risk of going to 0, Unprofitable companies and Profitable companies don't have same risk of going to 0. If you are doing a quality screen and sector diversification I am pretty sure ES1 100% confidence can be reached with even fewer than 100 companies. I hope this is not a controversial statement to make considering many here believe EMH is correct.
They have different risk profiles but they also have different return profiles which is the whole point. Doing a quality screen can just as much reduce your ability to outperform, leaving you stuck with high quality underperformers. Every active manager at a mutual fund says they screen for quality and 80% we know underperform which is fairly empirical evidence that we see every year.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Anon9001 »

I do think the area where diversification can help massively to increase the probability of beating the market is if the mean of the stocks are similar when going from 50 to 950 stocks as the more concentrated portfolios tend to have higher volatility and lower correlation to the market decreasing the probability of them beating the market if the means are similar for diversified portfolios. The problem is except for Low Beta stocks the means for diversified portfolios are not similar to means of concentrated portfolios meaning there is a limited benefit to diversifying beyond 25-50 stocks in terms of improving probability to out-perform market. This means that if a investor want to invest in only Low Beta stocks I would recommend wide diversification of even 1000 companies because the means are not different for low beta stocks when going from concentrated portfolio to diversified portfolio of Low Beta stocks so you get big boost in probability to out-perform market by adding more low beta stocks. I learned about this from AlphaArchitecht article that RovenSkyfoll posted in SCV thread.
scout1 wrote: Fri May 14, 2021 1:53 pm They have different risk profiles but they also have different return profiles which is the whole point. Doing a quality screen can just as much reduce your ability to outperform, leaving you stuck with high quality underperformers. Every active manager at a mutual fund says they screen for quality and 80% we know underperform which is fairly empirical evidence that we see every year.
I would like for you to look at Quality factor. Cliff Asness said it's extremely robust as a factor but there is no risk story to it. So avoiding junk companies is sort of a free lunch if you will. Now I don't know why you are mentioning active managers in this discussion considering the average fees they charge is high and we tend to forgot that these active managers a not so small group of them closet index so that tends to drag down numbers.
Last edited by Anon9001 on Sat May 15, 2021 6:18 am, edited 2 times in total.
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Re: A suggestion on minimum number of stocks to hold if randomlly selecting companies.

Post by Northern Flicker »

Anon9001 wrote: Fri May 14, 2021 1:30 pm
Northern Flicker wrote: Fri May 14, 2021 12:31 pm 90% confidence is not super strong confidence. 100 stocks worked in all of their similations, so that is the basis for the choice. When desking with return, you can strategize around the average case. When protecting against risk, you should be looking at the worst case.
The pdf you linked is using Random stocks yet ES1 90% confidence is not requiring 100 stocks. Let's admit to ourselves a company with high debt and company with zero debt don't have same risk of going to 0, company which is small and company which is large don't have same risk of going to 0, Unprofitable companies and Profitable companies don't have same risk of going to 0. If you are doing a quality screen and sector diversification I am pretty sure ES1 100% confidence can be reached with even fewer than 100 companies. I hope this is not a controversial statement to make considering many here believe EMH is correct.
Why should I accept a 90% confidence interval for diversifying away unsystematic risk when it doesn't cost anything to diversify it away with full confidence?
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by mffl »

How is this any different than any other discussion on active management? Costs aside, any approach you take is equally likely to outperform or underperform the market. Sure, the distribution of outcomes is different, but the average outcome is still the same as the market, and the outlier outperformance is exactly offset by outlier underperformance.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by galeno »

The COSTS are why we are Bogleheads. More so for non-US investors.
mffl wrote: Fri May 14, 2021 2:58 pm How is this any different than any other discussion on active management? Costs aside, any approach you take is equally likely to outperform or underperform the market. Sure, the distribution of outcomes is different, but the average outcome is still the same as the market, and the outlier outperformance is exactly offset by outlier underperformance.
KISS & STC.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by mffl »

galeno wrote: Sat May 15, 2021 2:28 pm The COSTS are why we are Bogleheads. More so for non-US investors.
mffl wrote: Fri May 14, 2021 2:58 pm How is this any different than any other discussion on active management? Costs aside, any approach you take is equally likely to outperform or underperform the market. Sure, the distribution of outcomes is different, but the average outcome is still the same as the market, and the outlier outperformance is exactly offset by outlier underperformance.
Agreed on that, of course. I'm not saying this is a good idea, quite the opposite. I don't see how it's a good idea even if costs are zero.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by HootingSloth »

mffl wrote: Wed May 19, 2021 4:18 pm
galeno wrote: Sat May 15, 2021 2:28 pm The COSTS are why we are Bogleheads. More so for non-US investors.
mffl wrote: Fri May 14, 2021 2:58 pm How is this any different than any other discussion on active management? Costs aside, any approach you take is equally likely to outperform or underperform the market. Sure, the distribution of outcomes is different, but the average outcome is still the same as the market, and the outlier outperformance is exactly offset by outlier underperformance.
Agreed on that, of course. I'm not saying this is a good idea, quite the opposite. I don't see how it's a good idea even if costs are zero.
I would find it helpful if the OP could state clearly, without diverting onto some other topic, what he sees as the most important benefit of this approach. Or if anyone else has an idea. We have been talking about potential downsides, but I have not been able to understand what the upside is supposed to be. Just that there is some (<50%) chance of overperforming the market? Can't this also be achieved by playing roulette instead? Or is the idea that it is difficult for some non-US investors to find appropriate equivalents of the low-cost total market funds that US investors have access to? Something else?
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by galeno »

@HootingSloth

The OP writes many "interesting" posts. I think he's a newbe who is having difficulties with the concept of "KISS & STC".

Regarding your other questions. Our retirement port: 50% VWRD + 45% AGGG + 5% USD CASH. Simplicity is bliss.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Thesaints »

The figures do not seem correct:
With one stock one would have "10% increase in probability of outperforming the index over 1 year, 39% increase in probability of outperforming the index over 10 years, and 471% increase in probability of outperforming the index over 90 years"

Of course, the probability of outperforming the market by picking a single stock goes down as the time interval gets longer. So the underlined part cannot mean that.
What does it mean ? "Increase" with respect to what ?
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by muffins14 »

It seems like a totally unnecessary risk to take, to pick 5 stocks and hope for outperformance. Why not just tilt to small value?

Good luck with your 5 stocks, it would be great to note them here and follow up on performance vs benchmarks
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Thesaints »

muffins14 wrote: Wed May 19, 2021 10:41 pm It seems like a totally unnecessary risk to take, to pick 5 stocks and hope for outperformance. Why not just tilt to small value?
You can make a lot more money with the right 5 stocks.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by muffins14 »

Sure, and what’s the probability of getting the right 5 when your method is random selection?

What’s the expectation value of that outcome?
What’s the dispersion of outcomes under that strategy?
What’s the probability that you underperform the market?
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Anon9001 »

Thesaints wrote: Wed May 19, 2021 9:54 pm The figures do not seem correct:
With one stock one would have "10% increase in probability of outperforming the index over 1 year, 39% increase in probability of outperforming the index over 10 years, and 471% increase in probability of outperforming the index over 90 years"

Of course, the probability of outperforming the market by picking a single stock goes down as the time interval gets longer. So the underlined part cannot mean that.
What does it mean ? "Increase" with respect to what ?
I took a vacation from this site because I have been too addicted to it but now I am back so I will answer what you are talking about. This percentage increase in probability of out-performing market is from going from picking 1 random stock to picking 5 random stocks (value-weighted) for 1 Year,10 Year and 90 Year Horizons. It is interesting even for 90 Year Horizons that most of the skewness premium (ie increase in probability of out-performing market if picking stocks randomly) can be captured by owning 25 stocks for US stock market even though only 4% of individual stocks out-perform value-weighted market for 90 Year Horizon.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by nisiprius »

I apologize for being slow in getting your point.

I still feel that Bessembinder's "the best-performing four percent of listed companies explain the net gain for the entire U.S. stock market since 1926" is indeed a confirmation of Bernstein's "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."

But I do take your point that the performance history of LEXCX and even the DJIA suggests that Bernstein's position that you truly need the total market is overstated. Certainly, the performance of the S&P 500 is close enough to the total market, presumably because by the time some small stock becomes big enough to matter, it will be big enough to enter the S&P 500.

Yes, I need to think some more about what LEXCX teaches us.

I'm not convinced that there's any particular virtue in randomizing stock choices.

I think what LEXCX and the Dow suggest is that it is important to mirror cap-weighting, and that perhaps what is going on is that the largest companies are big enough to be averaging within themselves a suite of positively-skewed activities.

So the question of course is whether this is a practical question, because for a US investor anyway it is so cheap and easy to just buy the whole market whether you need to or not.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by dumbmoney »

There's a world of difference between picking 30 stocks at random (which are likely to be all small/micro-caps) and picking 30 mega-cap, representative stocks (like the Dow). The former really is under-diversified. The latter is acceptable though not ideal.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Anon9001 »

nisiprius wrote: Sat May 22, 2021 5:19 pm So the question of course is whether this is a practical question, because for a US investor anyway it is so cheap and easy to just buy the whole market whether you need to or not.
:sharebeer +1 for being able to change your mind. It is rare for someone on the Internet to change their mind. The Bessembinder study while showing only 4% percent of stocks out-perform market show that only 25 random stocks even for 90 Year Horizon is enough to capture majority of skewness premium. This is probably due to value-weighting (ie capitalization weighting) of the 5,25,50,100 random stock portfolios as that avoids a small-cap tilt (of equal-weighting) where skewness is a issue. If you are picking 5-25 random small-caps than it's highly likely you are going to lose your money and probably 90% of them under-perform value-weighted market due to majority of small-caps being junk companies. Having a market portfolio tends to have a lower positive skew relative to a 5-25 stock portfolio so if person is having a substantial positive skew (consistent small losses rare huge gains) preference than they should not own the market. This in fact what the Bessembinder study is saying. Image
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Thesaints »

muffins14 wrote: Thu May 20, 2021 7:21 am Sure, and what’s the probability of getting the right 5 when your method is random selection?
Is a lot higher than the probability of outperforming the market by selecting all the 504 companies in the index, which is zero.

I'm not saying selecting 1 (or 5 stocks) is a good way to invest. I'm only saying that if one wants (or needs !) to outperform the market that is the way to go.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by Thesaints »

Anon9001 wrote: Sat May 22, 2021 8:46 am
Thesaints wrote: Wed May 19, 2021 9:54 pm The figures do not seem correct:
With one stock one would have "10% increase in probability of outperforming the index over 1 year, 39% increase in probability of outperforming the index over 10 years, and 471% increase in probability of outperforming the index over 90 years"

Of course, the probability of outperforming the market by picking a single stock goes down as the time interval gets longer. So the underlined part cannot mean that.
What does it mean ? "Increase" with respect to what ?
I took a vacation from this site because I have been too addicted to it but now I am back so I will answer what you are talking about. This percentage increase in probability of out-performing market is from going from picking 1 random stock to picking 5 random stocks (value-weighted) for 1 Year,10 Year and 90 Year Horizons. It is interesting even for 90 Year Horizons that most of the skewness premium (ie increase in probability of out-performing market if picking stocks randomly) can be captured by owning 25 stocks for US stock market even though only 4% of individual stocks out-perform value-weighted market for 90 Year Horizon.
It still feels wrong. Increasing the number of stocks picked should decrease the probability of outperforming the index.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by HootingSloth »

Anon9001 wrote: Sun May 23, 2021 1:03 am Having a market portfolio tends to have a lower positive skew relative to a 5-25 stock portfolio so if person is having a substantial positive skew (consistent small losses rare huge gains) preference than they should not own the market.
Thanks, Anon9001. I think this answers my question. The desired upside here is matching with a utility function that values buying "lottery tickets." I think you will find that most Bogleheads do not have this kind of preference, which is one reason you will encounter a lot of skepticism if this is your preference and you do not state it quite clearly.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by HootingSloth »

Anon9001 wrote: Sun May 23, 2021 1:03 am Having a market portfolio tends to have a lower positive skew relative to a 5-25 stock portfolio so if person is having a substantial positive skew (consistent small losses rare huge gains) preference than they should not own the market.
Thanks, Anon9001. I think this answers my question. The desired upside here is matching with a utility function that values buying "lottery tickets." I think you will find that most Bogleheads do not have this kind of preference, which is one reason you will encounter a lot of skepticism if this is your preference and you do not state it quite clearly.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by BeBH65 »

The investopedia article illusion-of-diversification has the follozing table:

Code: Select all

#stocks		1	15	30	60	Entire Market
StdDev		45.00%	16.50%	15.40%	15.20%	14.50%
R2		0.00	0.76	0.86	0.86	1.00
Track Error	45.0	8.1	6.2	5.3	0.0
a portfolio of even 60 stocks captures only 0.86 or 86% of the diversification of the market in question.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by CuriousTacos »

nisiprius wrote: Sat May 22, 2021 5:19 pm I apologize for being slow in getting your point.

I still feel that Bessembinder's "the best-performing four percent of listed companies explain the net gain for the entire U.S. stock market since 1926" is indeed a confirmation of Bernstein's "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."

But I do take your point that the performance history of LEXCX and even the DJIA suggests that Bernstein's position that you truly need the total market is overstated. Certainly, the performance of the S&P 500 is close enough to the total market, presumably because by the time some small stock becomes big enough to matter, it will be big enough to enter the S&P 500.

Yes, I need to think some more about what LEXCX teaches us.

I'm not convinced that there's any particular virtue in randomizing stock choices.

I think what LEXCX and the Dow suggest is that it is important to mirror cap-weighting, and that perhaps what is going on is that the largest companies are big enough to be averaging within themselves a suite of positively-skewed activities.

So the question of course is whether this is a practical question, because for a US investor anyway it is so cheap and easy to just buy the whole market whether you need to or not.
LEXCX and the DJIA could just be the product of survivorship bias though. And they aren't randomly selected nor static collections of companies.
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by muffins14 »

Thesaints wrote: Sun May 23, 2021 12:28 pm
muffins14 wrote: Thu May 20, 2021 7:21 am Sure, and what’s the probability of getting the right 5 when your method is random selection?
Is a lot higher than the probability of outperforming the market by selecting all the 504 companies in the index, which is zero.

I'm not saying selecting 1 (or 5 stocks) is a good way to invest. I'm only saying that if one wants (or needs !) to outperform the market that is the way to go.
It seems like in exchange for getting a small probability of outperforming the market, you’re getting a larger probability of under-performing the market. The trade off doesn’t make sense to me
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Re: A suggestion on minimum number of stocks to hold if randomly selecting companies.

Post by anil686 »

Anon9001 wrote: Sun May 23, 2021 1:03 am
nisiprius wrote: Sat May 22, 2021 5:19 pm So the question of course is whether this is a practical question, because for a US investor anyway it is so cheap and easy to just buy the whole market whether you need to or not.
:sharebeer +1 for being able to change your mind. It is rare for someone on the Internet to change their mind. The Bessembinder study while showing only 4% percent of stocks out-perform market show that only 25 random stocks even for 90 Year Horizon is enough to capture majority of skewness premium. This is probably due to value-weighting (ie capitalization weighting) of the 5,25,50,100 random stock portfolios as that avoids a small-cap tilt (of equal-weighting) where skewness is a issue. If you are picking 5-25 random small-caps than it's highly likely you are going to lose your money and probably 90% of them under-perform value-weighted market due to majority of small-caps being junk companies. Having a market portfolio tends to have a lower positive skew relative to a 5-25 stock portfolio so if person is having a substantial positive skew (consistent small losses rare huge gains) preference than they should not own the market. This in fact what the Bessembinder study is saying. Image
I agree with this - the problem is identifying in advance those stocks. I think what LEXCX tells us (and I am a big fan of the fund as was Bogle in his books), is that this strategy is not a bad strategy in that for an individual investor worried about taxes and costs, this strategy could reduce both. But Bogle wrote this at a time where he cited the average index fund was running an ER of 0.2% and used the tax costs of the average mutual fund. As those who hold broad market index funds now, the ER is under 0.05% (And actually less when you read the shareholder report for VG TSM which runs something like even with the index), and are more tax efficient than traditional mutual funds for VG b/c of the ETF share class or if one buys an ETF from another provider - can experience significant tax savings next to traditional index funds (TIF). Ultimately, LEXCX and picking 30 blue chip stocks at random over a variety of sectors of the economy will probably not underperform the market - but as in the case of LEXCX, will not outperform to any large degree the market either.

Which leads to the second part and third parts. The second is that behavioral errors cost investors a lot in general. Holding 30 blue chip stocks seems like it would be a good idea - the problem (as indicated by LEXCX) would be if Berkshire did not buy the railroads. In that case, LEXCX would not hold BRK stock. 30 years is a long time - Jeff Bezos already says he does not expect Amazon to be there in 30 years - I would bet he is right. Tracking error can be disconcerting and faith that a portfolio of 30 stocks which may be 18 in 30 years, could be difficult to stomach.

Part 3 is that many of us invest for us and our spouse and our heirs. Complexity of managing a portfolio may be easy for the OP - perfect. It may not be for the spouse or the heirs. If they hire an advisor to help them manage the portfolio (let's say at 1% a year), that would likely be too much of a hurdle for LEXCX to pass the total market. The simplicity of just a couple of funds or one balanced fund is attractive because it is easy to explain, easy to understand and *easier* to manage.

Nothing wrong with selecting a portfolio of 30 stocks - and yes you would have an opportunity to outperform the market - but that outperformance will likely be small and filled with tracking error as well as complexity. So I get what you are saying, but total market funds are virtually without cost now and are tax efficient - I am not sure why you would take the risk of underperforming the market over any time period (meaning with tracking error)....
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