While I think The Intelligent Investor is a worthwhile book, I think it got it wrong for the very reasons I mentioned above.
Anyway, I'm not making any argument here for how the market works, other than pointing out that saying that half of fund managers do worse than the median does not imply that they are unskilled or not providing value. Nor am I saying that they do provide value, but rather the original theory is both flawed and insufficient to make a conclusion.
In games of skill, past results certainly give expectations of future results. Going back to the hockey analogy, I would expect the top 10% of performers over five years (determined by some metric) would as a whole outperform a random sample of 10% of the league in a sixth year. Madoff is a bad example here - he was breaking the law, but nobody knew. If you catch a top sports player doping, it doesn't suddenly mean that the game is a game of chance, or that all of the top performers are cheaters (although repeatedly catching cheaters may indicate systematic problems) - rather it means that someone cheated to fake performance. They were playing a different game, but nobody knew.
Going back to the original point, if you want to determine whether something is a game of chance or skill, you have to fix the prior.
Let's say we had coin flipping tournaments, and people were claiming that it's a game of skill. Looking at past statistics, some people seemed to perform far better than the expected 50-50 split. You however claim that coin flipping is just a game of chance. How do you prove it? You look at results for some period of time, say five years. Take the "winners" from that group - say the top 20% of performers. Under the hypothesis that it's a game of skill, these should be a selection of the most skilled people.
Now track their results for a sixth year. If it was a game of skill, the expectation would be that as a whole, these individuals would continue to perform at a high level. However, as a game of chance, you would expect performance to be completely random among these high performers - and by doing this, you can determine whether coin flipping is a game of chance or skill.
Anyway, I'm not making any argument here for how the market works, other than pointing out that saying that half of fund managers do worse than the median does not imply that they are unskilled or not providing value. Nor am I saying that they do provide value, but rather the original theory is both flawed and insufficient to make a conclusion.
In games of skill, past results certainly give expectations of future results. Going back to the hockey analogy, I would expect the top 10% of performers over five years (determined by some metric) would as a whole outperform a random sample of 10% of the league in a sixth year. Madoff is a bad example here - he was breaking the law, but nobody knew. If you catch a top sports player doping, it doesn't suddenly mean that the game is a game of chance, or that all of the top performers are cheaters (although repeatedly catching cheaters may indicate systematic problems) - rather it means that someone cheated to fake performance. They were playing a different game, but nobody knew.
Going back to the original point, if you want to determine whether something is a game of chance or skill, you have to fix the prior.
Let's say we had coin flipping tournaments, and people were claiming that it's a game of skill. Looking at past statistics, some people seemed to perform far better than the expected 50-50 split. You however claim that coin flipping is just a game of chance. How do you prove it? You look at results for some period of time, say five years. Take the "winners" from that group - say the top 20% of performers. Under the hypothesis that it's a game of skill, these should be a selection of the most skilled people.
Now track their results for a sixth year. If it was a game of skill, the expectation would be that as a whole, these individuals would continue to perform at a high level. However, as a game of chance, you would expect performance to be completely random among these high performers - and by doing this, you can determine whether coin flipping is a game of chance or skill.