Sunday, March 6, 2011

Proof that capital markets are NOT efficient

This is an exercise that I've stolen from Warren Buffett. It's entitled "The super investors of Graham-and-Doddsville."

Let's imagine we have 5,000,000 monkeys all taking part in a coin toss contest. The rules? Each monkey is paired with another and they flip a coin. The one to guess it correctly moves on to round 2 where it will face another monkey who also guessed correctly in round 1. This continues for 20 rounds where all the remaining monkeys are the final winners.

Since in each pairing, 1 monkey wins and 1 monkey loses (eliminated) we will end up with 1/2 the # of monkeys in each successive round. We also know that a coin toss gives you a 50% chance of guessing correctly.

Round 1: 5,000,000 monkeys remain
Round 2: 2,500,000 monkeys remain
Round 3: 1,250,000 monkeys remain
.
.
.
Round 14: 610 monkeys remain
Round 15: 305 monkeys remain
Final winners: 153 monkeys (do me a favour and forget that we can't have 1/2 monkeys .. just assume the numbers work out well)

So what are the odds of being one of the 153 final winners? Probability of 0.00305% (0.5^15). Basically extremely low odds. Think of this as a metaphor for investors now. Academics say that yes, there will be some major winners (such as Warren Buffett), but it's just a very low probability and entirely luck.

But what would you think if I told you that 100 of the 153 winning monkeys all came from the same zoo and had the same trainer? You would think that had something to do with them all winning! You would think they actually had better odds than the 0.00305% probability. Well this is what Warren Buffett argues is the case with value investors. Of the "unlikely" group of investors that consistently beat the market averages, a large majority of them are value investors following the principles of Benjamin Graham. Buffett goes on to show the records of several such investors/friends who all use value investing but have significantly different looking portfolios, but they all beat the market consistently.

How can the efficient market hypothesis hold water in light of this argument? "Buffett's argument has never, to my knowledge, been addressed by the efficient-market theorists; they evidently prefer to continue to prove in theory what was refuted in practice" - Seth Klarman

For more information, check out this WikiPedia page. I haven't checked the numbers given there to confirm they are correct but you get the point of the article.

11 comments:

  1. So pretty much the majority of investors that strike it rich are because of some advantage of using a specific principle? Some smart monkeys.

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  2. Hm, I think it depends on what you mean with "efficient". There are more than one meaning
    Baxxmans

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  3. Interesting, Buffet is an investing genius(well duh!)

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  4. If capital markets are efficient, there will not be bubbles or market crashes.

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  5. Baxxman, it is true that the gods of academic finance (why do we listen to those who do nothing but theorize in academia never entering the real world, over those who are walking the walk day in and day out?) claim there are 3 basic levels of efficiency. However, the basic claim in all of them is that "abnormal" (above average) returns will not be generated. The only thing that is different among their definitions is the information set that is included (e.g. at the semi-strong form it includes all publicly available information, at the strong form it includes everything from the other levels PLUS inside information).

    Regardless of which form you claim the capital market is in, the evidence given shows that a majority of the winners are winning consistently and are all using a similar winning approach.

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  6. I completely understand this. It's sort of like having a high performing character in an MMO...everyone wants to copy your build because it's successful and outperforms everything else in the game.

    then the nerfbat happens..

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  7. Very interesting read, it's funny that they can outperform everyone by following a simple principle.

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  8. Buffett is a smart man. Probably the only investor, whose advice is worth a damn.

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  9. I think this is really good to know, but doesn't exactly garner confidence in the suppose it economic recovery going on.

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  10. I love your take on these things. And while I dont understand THAT much of financing, i got to give it you Buffet here. Great view of capital markets

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