[lutusp]

> A better way to put it: what are the chances that over a 48-year timeframe, a random strategy will return ~20% annualized return compared to the market's ~10%?

Easily answered. Let's say that a 10% return is the mean return, and one standard deviation is 5% -- just an example, and these numbers aren't real (although they could be established by asking everyone what their returns are).

So a return of 20% or better represents two standard deviations above the norm, or 2.2% of the investing population (this is a one-tailed distribution). How many investors will achieve that result in a large population? 2.2%. In a pool of a million investors, that's 22,000 people.

> Buffett is an existence proof that investment is skill, not chance.

With all respect, it's more accurate to say that your view of probability is an existence proof that many people don't understand statistics. Let me ask you -- do you understand how science works? Scientists don't say what you just said, ever. They say that the probability that this outcome resulted from chance is p ("p-value"), referring to the probability that the result arose because of chance. (My 2.2% probability above is a p-value.)

When the LHC scientists announced that they believed they might have detected the Higgs boson, did they say that their measurement constituted an "existence proof" that the Higgs was real? No, because they were scientists addressing educated people, they expressed their result in terms of a p-value -- p was the probability that their result came about because of chance, not the hypothesized particle.

A chance result isn't the last possibility that a scientist considers, it's the first. And no one who has been educated claims that a result that might have arisen by chance constitutes an "existence proof".

[throwawaymsft]

I am not an expert in the scientific method, but know a P value of < .05 (in this case, 39/47 is more like .000001) is pretty strong evidence of the conclusion. Of course things can always be due to chance; I may not be a person, but a chimp randomly hitting keys.

At what point do you say "The hypothesis that a professional investor with a published strategy who returns the best-performing fund in history appears to not be based on chance?".

Do you really think 2% of investors (1 in 50!) achieve 20% compound growth over 48 years? Do you know how many billions that is? (Buffet started with $100k and grew it to the 9th biggest company in the world. Where are the thousands of other investing billionaires?)

Do you really think beating the market long-term is a simple 1-time standard deviation computation? (I thought it was impossible, now 50% of people will consistently beat the market long term by any margin?)

Per the cited article, from trained economists:

"Buffett’s success has become the focal point of the debate on market efficiency that continues to be at the heart of financial economics. Efficient market academics suggest that his success may simply be luck, the happy winner of a coin-flipping contest as articulated by Michael Jensen at a famous 1984 conference at Columbia Business School celebrating the 50th anniversary of the book by Graham and Dodd (1934). Tests of this argument via a statistical analysis of the extremity of Buffett’s performance cannot fully resolve the issue."

[lutusp]

> ... but know a P value of < .05 (in this case, 39/47 is more like .000001) is pretty strong evidence of the conclusion.

This is false, and the fact that it's false has been proven and accepted for years.

http://www.nature.com/news/scientific-method-statistical-err...

Quote: "P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume."

http://bigthink.com/neurobonkers/the-statistical-significanc...

Quote: "P<0.05 is the figure you will often find printed on an academic paper, that is commonly (mis)understood as indicating that the findings have a one in twenty chance of being incorrect."

Also, your effort to estimate the probability of 39/47 is seriously flawed -- it depends on the distribution of successes and failures within the list.

> At what point do you say "The hypothesis that a professional investor with a published strategy who returns the best-performing fund in history appears to not be based on chance?".

Have you been reading my replies? The answer is never. The scientists at the LHC have acquired a p-value of 5-sigma for their observation of the Higgs, meaning the probability that their apparent detection of the Higgs arose from chance is 2.8 * 10^-7 (the "p-value"), but guess what? They are never going to say, "We detected the Higgs." Only ignorant science journalists say things like that, in the same way that ignorant stock market journalists say, "So-and-so has a reliable method for beating the market."

> Do you really think beating the market long-term is a simple 1-time standard deviation computation?

Yes, that's exactly what it is, given adequate data. And if that cannot be done, then economics has earned its reputation as a non-science.

> Do you really think 2% of investors (1 in 50!) achieve 20% compound growth over 48 years?

That was a hypothetical example, don't try to use it as an argument.

> I thought it was impossible, now 50% of people will consistently beat the market long term by any margin?

You will need to try to edit your posts to make them comprehensible. If you're asserting this viewpoint, I can prove that, for a random market with random buys and sells, with millions of investors, (a) 50% will do better than the average (uncontroversial), and (b) many of them will become rich by chance alone -- not just do better than the average, but become very rich with a small initial stake. Details here:

http://arachnoid.com/equities_myths/index.html#Market_Model

> Per the cited article, from trained economists ...

What? You're invoking the authority of "trained economists" to bolster your viewpoint? First, economists aren't scientists, second, an appeal to authority is a logical error, and third, your choice of quotation supports my view, not yours.

But I ask you to examine your position, and I shall help you do this by way of a reductio ad absurdum. Let's say there's a system for improving on average market returns, that it's something other than a chance outcome, and that it can be defined, tested, and thereby proven to exist in a scientific sense -- that it can be raised above the level of cocktail chatter.

1: Thesis: There is a way to trade securities that can be assured to reliably improve on average market returns, by means other than chance. The method can be written down, and therefore it can be tested objectively.

2: If (1) is correct, then anyone could take the proven, defined method, apply it to the market on a large scale, and drain it of all its capital in a short time.

3: But, notwithstanding the certainty of human greed and simple curiosity, (2) has not happened, anywhere, ever.

4: Therefore (1) is false.

Why is that definitive? Because science cannot be just descriptions ("Warren Buffett has an equities track record"), it requires explanations ("This is why Warren Buffett has an equities track record"). If there is no explanation, there's no science, and there's no point in conversations like this one.

Anyone can describe something in the environment, but the only interesting ideas are those accompanies by a testable explanation, a theory that purports to explain some aspect of nature, a theory subject to empirical test. And the outcome is interesting whether the theory turns out to be true or false -- we learn just as much from false scientific theories as true scientific theories.

And this is a classic debate between someone who understands science, and someone who doesn't.

[gnaritas]

Jumping into the middle of this, while you're clearly up on your science and math, you're arguing against a straw man of your own making. No one is arguing that there's a defined testable method of consistently beating the market. They're arguing that what traders do is consistently find temporary inefficiencies in the market and arb them away and then move on looking for an advantage somewhere else. So no that doesn't mean believing profit can be consistently had means the market can be drained of equity. And obviously any published strategy will quickly stop working, this is well known and accepted by pretty much everyone.

The argument you need to address is whether it's possible for a person to consistently find new opportunities to arbitrage some inefficiency out of the market without relying on arguments that assume there's only one method and that it always works.

[throwawaymsft]

This is a debate between someone who is trying to force-fit reality into a scientific model and someone who isn't. You would like economists, they make many wonderfully simplifying assumptions to make the reasoning easier (like the efficient market hypothesis, perfectly well-informed, rational actors), which, unfortunately, are incorrect.

There's many things to say, but just consider that you believe beating the market over a 47-year time period comes down to a standard-deviation calculation where half will, half won't. Just ruminate on that. If you can't see the absurdity of it, I'm not sure what to say.