> For 100 stock fund managers buying and selling stocks, statistics tells us that 50 of them will do better than the market averages (and 50 will do worse).
If you're going to simplify things, take out the numbers because the numbers are wrong.
For example, let's suppose that there are six companies you can invest in, and six managers who each invest in one company. One company grows 600%, and the other five declare bankruptcy. Average growth is 16%, but only 1 in 6 managers beat the average.
The other thing that's wrong is that you use the term "statistics" where you mean "probability theory". Probability theory describes how many managers you'd expect to beat the average. Statistics describes how you'd test this.
> If you're going to simplify things, take out the numbers because the numbers are wrong.
The numbers are exactly right. The problem lies with your example in which businesses either grow without bound or go bankrupt. In the real world, and typically, half of investors do better, and half do worse, than the market average.
> The other thing that's wrong is that you use the term "statistics" where you mean "probability theory".
Since one forms the foundation of the other, that's a distinction without a difference, especially when conversing with people who think there are secrets of the winners. The ideas are very simple, and specifying which aspect of statistics gives the most detail is hardly worth specifying.
Quote: "As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data."
You're mistaken on both counts, even though your top-level point is essentially correct.
On the first count, you're mistaken because there's no reason to assume that the distribution is symmetric. This doesn't damage your point, but as klodoph says, your actual example numbers are not necessarily representative. You'll note that this minor mistake in your comment has attracted a legion of minor corrections, all of them correct, all of them missing (or at least ignoring) your most-important point.
On the second count, that's like saying that math is the foundation of computing, and so the two are indistinguishable. klodolph is correct that the two are different, and it doesn't affect your point at all, so you should acknowledge the minor correction and stick to the relevant point.
More generally, did you notice that your top-level comment was basically saying "Warren Buffet is wrong about this aspect of investing"? You could be right, but it's not likely. I believe the reason for this mistake is that you may have have misread this sample of Buffet's thinking (and your overall claims as I understand them may actually agree with and Buffet as I understand him).
(In my humble understanding) Buffet claims that there may or may not exist investors who have superior (or inferior) skill, but that in MOST cases the results are due to luck, and "skilled" investors are mostly indistinguishable from lucky investors. Although I have not seen you agree or disagree with this claim, I note that all of your arguments are consistent with this. Your arguments revolve around being unable to determine which are which, after the fact; so do Buffet's! I further note that it seems ludicrous to claim that there do not exist anti-skilled investors, and thus all other investors will be more skilled than the mean skill level, and that this probably won't matter, because luck will drown it all out.
My overall points here are:
* I agree with your high-level claims (as I understand them) about money-managers
* I believe Warren Buffet, in this letter to Katherine Graham, agrees with
your high-level claims
* nearly every commenter in these threads agrees with your high-level claims
* the comment by wheaties is a counter-example
* some of the minor details of your points are technically wrong or confusing,
in ways that invite nit-picking, but do not impact your actual argument
On the other hand, starting on page 15 (of 19), Buffet suggests (and advocates) an alternative (his #5) that is NOT fully respectful of the efficient market hypothesis. So your position is not Buffet's entire position (though I see from your Equities Myths page that you have noticed this, and you suggest that perhaps Buffet is nothing except lucky).
> On the first count, you're mistaken because there's no reason to assume that the distribution is symmetric.
First, I never said that, and second, that assumption isn't necessary -- the location of the mean won't change, and the mean is the thing you would need to beat, not the median. The reason is that market indices measure the mean (the sum of all the values divided by the count of values), not the median (the midpoint between the highest and lowest value).
> On the second count, that's like saying that math is the foundation of computing, and so the two are indistinguishable.
And? I invite you to argue that it's not so. Computers do what they do solely on mathematical and logical principles. Some would argue that that represents a drawback, hence experiments with things like fuzzy logic. But even fuzzy logic is deterministic and logical, it's just sometimes closer to messy reality. But all of computer science, and computer operations, are strictly logical.
> ... klodolph is correct that the two are different ...
Computer science and mathematics? Only someone unfamiliar with computer science would make that claim. Computer science is applied mathematics.
> ... so you should acknowledge the minor correction ...
Are you familiar with the idea that, if you make an argument, the burden is yours to produce evidence for it? Computer science is applied mathematics.
> Buffet suggests (and advocates) an alternative (his #5) that is NOT fully respectful of the efficient market hypothesis.
But that's not the topic. Whether the EMH is reflected in the real market or not, the issue is whether someone can consistently beat the market averages for reasons other than chance. These are separate, independent topics.
> Buffet claims that there may or may not exist investors who have superior (or inferior) skill, but that in MOST cases the results are due to luck, and "skilled" investors are mostly indistinguishable from lucky investors. Although I have not seen you agree or disagree with this claim ...
The reason I haven't either agreed or disagreed is because there's no way to establish it scientifically, with evidence. So I disagree that Buffett can make the case, and for the same reason, I can't make the case either. That leaves us with the null hypothesis -- without evidence, the thesis is assumed to be false.
> More generally, did you notice that your top-level comment was basically saying "Warren Buffet is wrong about this aspect of investing"?
If you invent quotes for people, we won't get anywhere. I can only say that Buffett can't make his case, and I have said that. That leaves us with the default scientific position -- the null hypothesis. Without evidence, an assumption that a thesis is false.
> ... some of the minor details of your points are technically wrong or confusing ...
Your simplification ruins the example because in the real world, as in lutusp's example, managers are investing in a portfolio of stocks, not 1 in 6 with a 1/6 chance of a 600% return.
There is a reason for market theory and the saying that you can't outperform the market in the long term: everything will average out.
Lutusp's example is perfectly adequate and theoretically sound
If you're going to simplify things, take out the numbers because the numbers are wrong.
For example, let's suppose that there are six companies you can invest in, and six managers who each invest in one company. One company grows 600%, and the other five declare bankruptcy. Average growth is 16%, but only 1 in 6 managers beat the average.
The other thing that's wrong is that you use the term "statistics" where you mean "probability theory". Probability theory describes how many managers you'd expect to beat the average. Statistics describes how you'd test this.