### Author Topic: Likelihood of beating the market vs # of stocks invested in  (Read 1639 times)

• Bristles
• Posts: 268
• Age: 39
• Location: Halifax, NS
##### Likelihood of beating the market vs # of stocks invested in
« on: April 24, 2018, 07:11:11 AM »
I was wondering if there exist any data sets of all companies and their returns over the last 30 years or so? Further, if anyone has run the numbers of what your returns and variance would be with 1, 2, 3, 10, 100... all the way up to the total number of stocks?

I briefly searched, found this for the Russel 3000: http://business.nasdaq.com/media/The_Capitalism_Distribution_Blackstar_Funds_tcm5044-42315.pdf

and it says that 36% of stocks outperformed the market, and includes a histogram for distribution of returns. This makes sense given a Pareto distribution.

So for instance in this case, with a 1 stock portfolio, your EV would be market return, the range would be -100% to +10,000% or something, and the likelihood of beating the market would be 36%.

Next, look at the 3000*2999 possibilities of an equally weighted 2 stock portfolio, and make a histogram of that. In that case you would expect the tails to contract (best case is top two companies, which by definition would be less likely, and less total return than top 1), and likelihood of beating the market to go up.

Finally continue with all this all the way up with bigger and bigger portfolio to an index fund where you match returns.

Towards the middle I assume this would be computationally almost impossible because with a 3000 choose 1500 I guess you get 1.791967E+901 combinations, so a numerical method approach where you just pick a bunch of random data sets until you get something stable would be the only approach.

What I was thinking though, is that towards the top end, a random 2999 stock portfolio would be *more* likely than not to beat the market, because the one random stock you didn't pick, has a 64% chance of under performing the market.

Is this reasoning sound? Do such data sets or such analyses exist?

#### ChpBstrd

• Walrus Stache
• Posts: 5118
• Location: A poor and backward Southern state known as minimum wage country
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #1 on: April 24, 2018, 09:54:04 AM »
Look up Modern Portfolio Theory. MPT posits there is a risk/reward tradeoff and that portfolios can fall below a line known as the "efficient frontier" where you get the maximum amount of reward given the level of risk you are taking. A portfolio with one or two stocks would be much riskier than a portfolio with, say, 30 stocks, because an adverse event affecting one of your companies won't wipe out your 30 stock portfolio, but such a routine occurrance might wipe out your 1 or 2 stock portfolio. Diversification reduces the variance of returns, and a metric of a stock's volatility, known as beta, is calculated amd used as a proxy for risk.

Portfolios might fall far below the efficient frontier. This would be the case for a portfolio with just a handful of stocks, where the (rationally calculated) expected return is the market average return, but the risk is higher than a more diversified portfolio with the same expected return.

#### secondcor521

• Magnum Stache
• Posts: 4879
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• Location: Boise, Idaho
• Big cattle, no hat.
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #2 on: April 24, 2018, 10:50:58 AM »
Towards the middle I assume this would be computationally almost impossible because with a 3000 choose 1500 I guess you get 1.791967E+901 combinations, so a numerical method approach where you just pick a bunch of random data sets until you get something stable would be the only approach.

What I was thinking though, is that towards the top end, a random 2999 stock portfolio would be *more* likely than not to beat the market, because the one random stock you didn't pick, has a 64% chance of under performing the market.

Is this reasoning sound? Do such data sets or such analyses exist?

Maybe and I doubt it.

There is part of the efficient market hypothesis that says that inefficiencies in the market can exist as long as the costs and risk and time associated with capitalizing on that inefficiency are greater than the inefficiency itself.  It's sort of like knowing that the gas station in the next town over has gas that sells for 2 cents cheaper than where you are.  Yes, it is cheaper, but to get there you'd burn up your savings driving to the next town, not to mention the portion of your smartphone contract you paid to access the web to check GasBuddy.com to know about the price discrepancy in the first place.

In the case you describe, the under-performance is not likely to be very much.  Also, avoiding under-performance on 1/3000th of a portfolio is going to be a rounding error in terms of the overall portfolio performance - i.e., you might be avoiding a 0.000001% drag on performance.  On the other side, you'd have to maintain a portfolio of 2,999 stocks for 30 years, making sure not to buy that 3,000th stock, and dealing with issues of mergers, acquisitions, and divestitures (what happens if the 3,000th company buys one of your 2,999 stocks?  Or if they merge with one of the 2,999?  Or if they divest and create stock number 3,001?).  The cost to maintaining that portfolio is more than a little bit of money.

So I think it's possible in theory, but in practice I think the costs outweigh the benefits.

(A related example would be socially conscious investments, which try to avoid things like cigarette manufacturers, gun manufacturers, alcohol businesses.  My understanding is that these types of mutual funds tend to have higher-than-average expenses and lower-than-average returns.)

#### frugal_c

• Bristles
• Posts: 300
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #3 on: April 24, 2018, 01:05:35 PM »
What I was thinking though, is that towards the top end, a random 2999 stock portfolio would be *more* likely than not to beat the market, because the one random stock you didn't pick, has a 64% chance of under performing the market.

Is this reasoning sound? Do such data sets or such analyses exist?

There is a flaw in this logic.  Yes, each stock only has a 36% change of out-performing the market but when they do out-perform it can be by considerably margins.  It's easier to think about this with a larger pool of stocks.  If you excluded 100 stocks instead of just 1, yes roughly 64 would under-perform but the 36 that out-perform should do so by a sufficient margin that it evens out to the market return.

• Handlebar Stache
• Posts: 2299
• One Does Not Simply Work Into Mordor
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #4 on: April 24, 2018, 03:08:31 PM »
No, because you had no knowledge of whether the stock you picked was a winner or a loser. Therefore it wouldn't affect the expected return, you would just have 1 less stock. If you extend your logic you would not own any stocks, because most of them will under perform the market. (A variation of what frugal_c said I think.)

#### bdbrooks

• Posts: 62
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #5 on: April 24, 2018, 03:18:38 PM »
https://alphaarchitect.com/2014/09/09/how-many-stocks-should-you-own-the-costs-and-benefits-of-diversification/

Here is a link to alpha architect. They do some great research. They invest systematically based on factors. So they don't want to diversify too much, but they need to diversify enough. This at least tells you where they are coming from.

To save some of you the trouble, it takes about 20-50 stocks to eliminate most of the Idiosyncratic Risk (risk you can eliminate by diversifying).

#### MustacheAndaHalf

• Walrus Stache
• Posts: 5977
##### Re: Likelihood of beating the market vs # of stocks invested in
« Reply #6 on: April 25, 2018, 09:05:26 AM »
While I favor index investing, the best case I've seen for active management is made by C Thomas Howard.  I believe he was a finance professor who then became a portfolio manager.  He claims that the first 10 picks of active managers beat the market, and the picks after that trail the market.  Since profit is proportional to assets under management, the goal is actually to avoid scaring investors rather than beating the market.  Being close to a benchmark tends to get rewarded, while running a fund with only a few stocks gets penalized.  I'm not entirely convinced, but I find his explanations more plausible than most active managers.
https://blogs.cfainstitute.org/investor/author/cthomashoward/