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Is There an Optimal Number of Stocks to Own?

By Mike Adams

SUBJECT LINE: Is there an optimal number of stocks to own?

“I could improve your ultimate financial welfare by giving you a ticket with only 20 slots in it, so that you had 20 punches — representing all the investments that you got to make in a lifetime. And once you’d punch through the card, you couldn’t make any more investments at all.1”

  • Warren Buffett speaking to MBA students 1998.

How do money managers decide how many stocks to own in their portfolios? There are tons of mutual funds that own several hundred stocks. Is that a good number? How do they decide?

We believe there is an optimal number of stocks to own. To maximize the performance of your portfolio the optimal number is four (4) stocks! Does that surprise you?

Mike Adams got his undergraduate degree in math at Oregon State University before going on to Carnegie Institute of Technology (now Carnegie Mellon University). Beginning as a stockbroker in 1986 and transitioning to managing client portfolios, that was the question that Adams ruminated on for several years. There were no studies. Warren Buffett had chosen just five (5) stocks for his portfolio in the early years.

Drawing on his background in math Adams came up with an approach in 1990 through mathematical game theory which surprisingly did not vary much from what Warren Buffett stated.

Imagine a game with five players. Each has a different risk level for his stake. The game has an edge: each time a player wins, he wins $2. Each time a player loses, he loses $1. Principle 1 is to seek stocks with twice the upside as compared to the downside. Principle 1 also dispels the conventional wisdom that an investor needs to be right 66% of the time. It shows being right 50% of the time if stocks are correctly picked will result in making money. (

There are 100 plays. Player One will bet $1 each time for every one of the 100 plays. The first time the player wins, they will have $102. Next time the player bets and loses. The player has $101. Work that out for 100 plays and the player has the expected ending value of $150.

Player 2 decides to play not a set amount, but a set percentage. For this player 10% is the bet. For the first bet the player sets out $10 (10%). The player wins and has $120. Now the player bets $12 (10% of $120). The player loses the $12 and now has $108. When this player finishes 100 rounds of betting Player 2 has $4,700!

The sequence of wins and losses makes no difference. Math is commutative: axb=bxa. If Player 2 loses the first bet of $10, their holding would be $90. If the player bets $9 (10% of $90) and wins, the player would have $108.

Player 3 bets 25% of their holdings. The expected return after 100 plays is $36,100!!

But the expected value does not continue going up. 25% is the maximum.

Here is the table for the five players:

Player   Bets                     Expected Return

   1             $  1                          $      150        

   2             10%                         $   4,700

   3             25%                         $ 36,100

   4             40%                         $   4,700

   5             51%                         $        36



What this means is this: concentrated portfolios should, in theory, do better than highly diversified portfolios.

Prior to 2000 there was only one study published in 1978 that showed portfolios with a limited number of stocks did better than highly diversified portfolios. When Adams came up with the game theory approach, he had not read the 1978 study.

Since 2000 there have been several hundred studies that validate the Adams Financial Concepts approach of developing portfolios with a very limited number of stocks.

Mark Twain was probably right when he said for investors the right approach is to put all of your eggs in one basket and watch the basket.  That is the reason we believe our clients get better returns than the average financial advisor (


 Comment:  This conclusion is based on mathematical game theory. To maximize gain, the optimum number of securities, assuming a 2 to 1 reward- risk ration and a 50-50 chance of winning and losing, is four securities. However, this is only one factor in determining the number of securities in a portfolio. 

Formula is as follows: E = {P(1+b-2b2)}n/2, where              

E= expected value              

P=beginning principal              

b=percent bet each time              

n=number of plays 

Article Written By:

Mike Adams, President & Principal

Adams Financial Concepts LTD

1001 Fourth Ave, Suite 4330, Seattle WA 98011

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