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.
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.
http://en.wikipedia.org/wiki/Probability_theory
Quote: "As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data."
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
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 ...
Locate one, but be prepared to offer evidence.
Email me if you actually care about replies. Either way, have a good evening.
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
--------------------------------------
I would like you to imagine a national coin-flipping contest. Let's assume we get 225 million Americans up tomorrow morning and we ask them all to wager a dollar. They go out in the morning at sunrise, and they all call the flip of a coin. If they call correctly, they win a dollar from those who called wrong. Each day the losers drop out, and on the subsequent day the stakes build as all previous winnings are put on the line. After ten flips on ten mornings, there will be approximately 220,000 people in the United States who have correctly called ten flips in a row. They each will have won a little over $1,000.
Now this group will probably start getting a little puffed up about this, human nature being what it is. They may try to be modest, but at cocktail parties they will occasionally admit to attractive members of the opposite sex what their technique is, and what marvelous insights they bring to the field of flipping.
Assuming that the winners are getting the appropriate rewards from the losers, in another ten days we will have 215 people who have successfully called their coin flips 20 times in a row and who, by this exercise, each have turned one dollar into a little over $1 million. $225 million would have been lost, $225 million would have been won.
By then, this group will really lose their heads. They will probably write books on "How I turned a Dollar into a Million in Twenty Days Working Thirty Seconds a Morning." Worse yet, they'll probably start jetting around the country attending seminars on efficient coin-flipping and tackling skeptical professors with, "If it can't be done, why are there 215 of us?"
Thanks for posting this -- it's first-rate. The fact that it corresponds exactly to my personal views can't be a factor, of course. :)
I read the entire article, and the problem is that it cannot distinguish between an effect and chance, and many have an incentive to call chance an effect. Also there's the announcement effect to consider -- once a player has a track record, people start reacting to his moves by buying the same stocks, after which the track record is no longer meaningful data.
The WSJ Dartboard Contest was a terrific test that could have shown a real effect, if there is one, and anyone who produced reliable returns would get a lot of free publicity. So there was a big incentive, but no one could show an effect. It was the closest thing to science I've seen, and it supported the null hypothesis.
50 will do better/worse than the MEDIAN of that GROUP OF 100 fund managers, not the market averages.
Oh, the managers will do worse than the market averages, because even if they avoid dumb moves, they will charge you for the privilege of managing your portfolio.
My original remark was meant to measure their performance before fees, as the WSJ Dartboard Contest did it (a contest in which the managers weren't able to keep up with market averages).
EDIT: for a symmetrical distribution, a distribution for which a classic Gaussian curve is appropriate, the median and the mean are the same.
haliax is pointing out that 100 fund managers may not be an unbiased sample. It's perfectly possible to find a biased sample of 100 individuals capable of beating the market (eg. a group of 100 insiders trading illegally).
EDIT: The "correct" thing to say is... "Based on evidence, fund managers do not outperform the market. Therefore, in a random sampling of 100 fund managers, we would expect 50 to underperform the market." This assumes (1) there is such evidence (likely?) and (2) that 100 is a sufficiently large sample to overcome the error bounds.
My point is that, of 100 typical managers, 50 will beat the averages. Not any specific set of 100 managers, just typical ones.
> ... and (2) that 100 is a sufficiently large sample to overcome the error bounds.
You're completely missing the point that it's not about any particular set of 100 managers -- they're just a representative sample meant to turn the results into convenient percentages.
A: "Take a random selection of 100 typical fund managers. Now ..."
B: "Wait! Which specific managers are you thinking of?"
A: "No, the 100 managers are meant to represent perfectly typical, average managers, and only to be able to use the number 100, in order to discuss the outcome in terms of percentages."
B: "Oh, umm, okay."
A: "How about I say 'Take a typical set of 1024 managers. Given that, 512 of them will beat the averages.'"
B: "Wait, where's my calculator? Is 512 half of 1024? Why are you trying to trip me up with oddball numbers?"
A: "Q.E.D."
> The "correct" thing to say is...
The correct thing to say is what I said.
Under those conditions... in a sampling of 100 "typical fund managers", more than half would still produce higher returns than the market.
You made an implicit assumption, which I believe is probably correct, that fund managers as a population are an unbiased sampling of the entire market -- ie. that their returns are the same as the market (or worse) -- but provided no evidence to back it up.
No, because we're comparing manager performance with market indices, like the DJIA, both of which include overall market growth.
The "average market" is measured by market indices, each of which tries to characterize a typical buy & hold portfolio. Thus, market indices ascend with overall market growth. That's what an average manager has to beat.
And the WSJ Dartboard Contest, which compares market indices with submitted manager performances, proves that managers cannot beat the market, even if their fees aren't included in the tallies.
> Under those conditions... in a sampling of 100 "typical fund managers", more than half would still produce higher returns than the market.
No, just half. not more, not less. Both the market indices and the managers would ride the ascending average value of the market as a whole. The only difference would be the theory being tested -- that some managers have special abilities that would give them an edge.
> You made an implicit assumption, which I believe is probably correct, that fund managers as a population are an unbiased sampling of the entire market -- ie. that their returns are the same as the market (or worse) -- but provided no evidence to back it up.
I keep proving my point with examples like the Dartboard Contest, and people keep ignoring the evidence. Don't you understand that submitters to the Dartboard Contest had every incentive to display their best performance -- a success would assure them of fame and wealth. But none of them could do it, over a period of years.
If you're looking to make money with the market, and you're not looking for a particularly high amount, and time is not an issue, an index fund is the way to go.
>statistics tells us that 50 of them will do better than the market averages (and 50 will do worse)
This is a common misunderstanding, but actually 50% will do better than the median not the average. Averages can be dominated by extreme events, so more than 50% can do better (or worse) depending on the skew.
Then we are discussing averages, in general. So, the common misconception would be:
-Averages are dominated by the median, and deviation from the mean is symmetric.-
If the market were skewed to the degree that a symmetrical normal distribution wasn't a realistic model, then (assuming a particular skew) beating the median would be child's play, but it also wouldn't produce returns different than the average portfolio -- that average portfolio that sits at or near the mean, not the median.
Another way to say this is that, if a skewed distribution peaked at some mean value M (the value on the curve that has a zero first derivative), and if there was a pathological, nonsymmetrical tail at the right or left that shifted the median value, the majority of portfolios would remain at the mean value in spite of the asymmetry.
This is like saying all personal relationships are limited to prostitutes. One can buy stocks directly, or invest in index mutual funds that don't have managers, for the reason that no management is required.
> Then track the winners. This will show whether it's a game of skill or chance.
But that's been done -- the WSJ Dartboard Contest showed that the experts don't do better than throwing darts at a list of stocks.
http://online.wsj.com/article/SB1000142412788732450470457841...
My point is that buying and holding an index fund, and relying on long-term market growth instead of phony expertise, is a much better approach to equity investment.
The market does not do better because there are fund managers, it does better if the underlying assets increase in value. All the other fluctuations are based on expectancies of those assets and arbitration.
It is entirely possible for 100% of fund managers to do below the market average, as fund managers dont own 100% of the market. It is also likely they have a losing bet against a market, as active fund managers employ resources in their operations, by trading and actively managing a portfolio, usually in the form of fees, and potential downsides on extra taxation as well.
Tracking "the winners" is the most fallacious and common attempt at gauging how good a fund manager or a stock is doing. Bernie Madoff was one of the winners for decades. Past results give no expectation to the future, which is so misleading given that the most common tool to show the value of a stock is a chart of how it did before, as opposed to how the company is doing (which require reading the statement).
I suggest reading "The Intelligent Investor". It is by far the best book on this topic out there , and it has enough layman terms and concepts that are very easy to understand once you expose yourself to them.
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.
To put it succinctly: On average fund managers reduce ROI.
As an alternative measurement, if you take the funds managed by most managers and look at the portfolio 1 year ago the fund would be better off with the previous year's portfolio. (This time mostly because of transaction costs)
Yes, a point I make in my article, but didn't make in my post. Fund managers are very difficult to justify.
From a scientific standpoint, that is false. You need to realize that it's not possible to show (prove, demonstrate) that such stories arise from anything but chance. A certain number of people are going to do very well because of chance, and some of those people are going to try to pose as experts.
But don't take my word for it -- instead, think. If there really was a surefire way to beat market averages, it wouldn't remain a secret for long, then everyone would practice it, then that "system" would become the norm -- the market average performance.
And if there really was a way to beat the market averages, if it was possible to make a huge sum of money systematically without risk or uncertainty, using a scheme other than chance, businesspeople (who are not fools) would refuse to raise capital using equities.
If you think hard enough, you will realize why there cannot be a deterministic, legal system to beat the market. There's always insider trading, but that's illegal for a reason.
> Just because most managers in assets and investment vehicles afforded by those whose worth is not of a sufficient level does not mean they do not exist.
They do not exist. I just proved it. If you didn't understand the above proof, read it again.
Furthermore, no is claiming that [i]anyone[/i] can "make huge sums of money systematically without risk," or that successful hedge funds that can turn 1 dollar into 1+r dollars can always turn 1e9 dollars into (1+r)e9 dollars, or even that there exists a single financial genius that can entirely eliminate risk.
What a collection of straw men you have succeeded in knocking down!
First, he didn't beat the market average 227 times in a row -- for most of those periods, he didn't lose money, but then a buy & hold investor also didn't lose money. A meaningful comparison would have to compare his outcomes with that for a buy & hold investor riding the ascending market value by holding a boring, geriatric index fund.
Second, I wish people would study probability theory and statistics before trying to have conversation like this one. A totally random computer-generated market, with random trades, produces a handful of very spectacular outcomes, by chance alone. The larger the investor pool, the greater the chance for a spectacular chance performance.
http://arachnoid.com/equities_myths/index.html#Market_Model
In the above market model, which is a computer market driven by random trades, no intelligence, essentially flipping coins, out of 100 investors, the best performance over 30 years is $233,000 from an initial stake of $10,000 (an average performance would be $51,800). And if you increase the investor pool to millions like in real life, you greatly increase the size of the most spectacular performances.
Now imagine that the best performer is a human being instead of a computer model. What are the chances that he will say, "Oh, I was just lucky." For one thing, he might not understand enough probability theory to even grasp that chance could explain the outcome. For another, he might want to set himself up as a financial expert and make more money exploiting other people's stupidity than he ever made in equities.
> I imagine consistently winning takes constant work and innovation.
Imagine anything you like. There are no secrets of the winners. Prove this false using scientific evidence. Prove that spectacular performances cannot result from the workings of chance, as my computer model proves.
> ... your arguments are incoherent ...
Only to someone who has his mind made up and who cannot evaluate evidence. Imagine a group of people flipping coins -- how many people need there be, flipping fair coins, for one of them to have a 50% chance to flip heads 20 times in a row? And what is the chance for the lucky winner to say, "Oh well, it was probably a chance outcome"?
answer: 2^20 = 1,048,576 people.
I'd also like to note the irony of your snarky comment about wishing that those who disagree with you ought to study some math, given the background of managers like Jim Simons.
Edit: > First, he didn't beat the market average 227 times in a row -- for most of those periods, he didn't lose money, but then a buy & hold investor also didn't lose money. A meaningful comparison would have to compare his outcomes with that for a buy & hold investor riding the ascending market value by holding a boring, geriatric index fund
The stock market rose by about 8 or 9% annually during that time. Dismissing his 227 positive months requires absurd contortions, like positing that his firm would invest in the stock market or t-bills for 11 months out of the year, and then make a series of large bets in the remaining month. Given that he made, I believe, 10k bets a year, the disparity in bet size must be massive to even come close to supporting your hypothesis.
What are you talking about? There is no evidence for the assumption, and the only reliable evidence stands against it, like the WSJ Dartboard Contest.
If a particular institution does better than the averages, the most likely explanation is chance, and no other explanation has anything resembling scientific evidence. And the Dartboard Contest demonstrates that, when called on to put up or shut up, the professionals weren't able to put up.
> The stock market rose by about 8 or 9% annually during that time. Dismissing his 227 positive months requires absurd contortions ...
No, it requires acknowledging that the market rose by 8 or 9% per annum, as you just pointed out. His performance needs to be compared to the market averages, not to a hypothetical flat market. I can see you're not getting this -- someone says, "I must be a stock genius, because I never saw zero or negative growth in my portfolio." Someone then deflatingly points out, "Neither did the average market, the holdings of retired, risk-averse investors in Ohio."
> ... to even come close to supporting your hypothesis.
It is not my hypothesis, it is the default assumption of people with scientific training -- if there is no evidence, there is no effect. And there is no evidence.
In a pool of ten million investors, a handful will show spectacular performance by chance alone -- this is a mathematical fact -- and those individuals would have to be saints to avoid assuming and claiming they're stock picking geniuses.
Occam's razor is a precept that says the simplest explanation tends to be the right one. The simplest explanation is that some investors come out ahead because of chance. This means the burden of evidence rests with those who would like to claim that stock market performances arise from "secrets of the winners".
That would be you.
Not if it's costly. By that I mean what if there is a market oracle that can pick tomorrows winners, but you have to pay X dollars to pull the crank and get the info.
In that case, it could be possible to "beat the market" in the sense that your stocks overperform, but you do not actually beat the market if you factor in the cost of the oracle.
Real world example: http://www.cnbc.com/id/100809395
>A closely watched consumer confidence number that routinely moves markets upon release is accessed by an elite group of traders, for a fee, a full two seconds before its official release, according to a document obtained by CNBC.
Another situation would be that you could overperform the market if you hired thousands of employees that analysed the markets, but not so much that you could pay their wages and still win.
It could also be the case that some people have a comparative advantage. Maybe they have certain skills that enable them to win were other people cannot.
> Real world example: http://www.cnbc.com/id/100809395
That's an announcement effect, not a method for beating the market. It exploits people's stupidity, not their intelligence. For a classic announcement effect, there are an equal number of winners and losers, and the average return is zero. In this specific example, some people get to buy the stocks in advance of the public announcement, then the public investors stupidly and dutifully buy stocks whose price has already peaked and is about to fall. It transfers money from uneducated investors to educated ones. If the uneducated investors realized what was being done to them, they would not invest and the system would collapse.
http://www.investopedia.com/terms/a/announcment-effect.asp
A typical announcement effect scam are online penny stock touters, who:
1. Buy a worthless stock.
2. Tout the stock online: "I just heard from my cousin that this stock is about to move!"
3. Wait for some idiots to invest in the stock.
4. Sell.
> It could also be the case that some people have a comparative advantage. Maybe they have certain skills that enable them to win were other people cannot.
Maybe Occam's razor says that it's all chance.
> I can't believe you aren't getting this.
Plenty of otherwise rationally minded people have a hard time reasoning about this stuff. If I had a dollar for every time someone suggested that you can beat the house by playing a Martingale... gosh! You'll have a much easier time persuading people if you don't insult them.
> Plenty of otherwise rationally minded people have a hard time reasoning about this stuff.
Rationality is what rationality does. There's a devious investment scam that, once explained, seems obvious, but most people fall for it unless forewarned. I call it the "Miracle Man" scam. Here it is:
http://arachnoid.com/equities_myths/index.html#Miracle_Man
I would like to live in a world where a scam like "Miracle Man" couldn't work, because people would say "It seems too good to be true, therefore chances are it's not true."
But that's not this world, not by any means.
And this is exactly what you "proved" could not happen
Following your example I can imagine that there is a mechanism (I wouldn't call it surefire) that can improve your odds. But that mechanism is difficult to acquire, difficult to transfer and not very scaleable. Therefore it is difficult for everybody to practice it. In fact some do it so badly that they end up loosing more than the average.
> If you think hard enough, you will realize why there cannot be a deterministic, legal system to beat the market.
I don't think anyone is arguing that there is a deterministic legal system to beat the market. Only that some people may be skilled enough to beat the market. edit:punctuation
Not difficult, impossible. It cannot be established scientifically. No control group, no meaningful controls.
> Following your example I can imagine that there is a mechanism (I wouldn't call it surefire) that can improve your odds.
And people who write worthless "secrets of the winners" books rely on this very assumption (and on the stupidity of the average investor). If such a thing existed, one of two things would happen:
1. It wouldn't remain secret for long, therefore everyone would practice it, therefore it would become the new average market performance. End result: no secret.
2. It would remain secret in perpetuity, the owner(s) of the secret would use it to either drain the market of its capital or foment public doubt about market fairness, as a result of which businesses would stop using the equities market to raise capital. End result: no market.
So the "secret" would either destroy the market, or the market would adjust to its existence in a way that everyone would have the same opportunity. Therefore there is no secret.
> I don't think anyone is arguing that there is a deterministic legal system to beat the market. Only that some people may be skilled enough to beat the market.
I hope you now see that this is impossible.
If this 'secret' could only be applied in small amounts, then the owner couldn't drain the market. Why do you think Buffett believes large funds can't outperform?
You assume any such 'secret' is infinitely scaleable. That's an incorrect assumption.
Insider trading is an advantage that exists but doesn't fall into your #1. Has it 'drained the market' or stopped businesses from using the stock market?
First, I never said or assumed that. Second, Human greed is, in fact, infinitely scaleable. But this is a silly debate -- obviously the most likely explanation for a spectacular market performance is chance.
> Insider trading is an advantage that exists but doesn't fall into your #1. Has it 'drained the market' or stopped businesses from using the stock market?
In a word, yes -- in a number of cases, companies try to buy themselves out of the stock market, for that and other reasons (like the tyranny of quarterly earnings reports and shortsighted boards of directors).
We're off on a tangent now. We've left the original topic. And the original topic was resolved by noting the WSJ Dartboard Contest, where managers had every incentive to show what they could accomplish, but instead they failed, spectacularly, in public, for years.
But this applies to any human endeavour! What's the secret to being successful in any field? Or rather, why aren't we all world-class concert pianists or martial artists or ballet dancers or whatever takes your fancy? Because knowing "the system" and practicing the system are very different things...
Sure, no problem with that. Case by case -- half the time it works, the other half the time it doesn't. Sum the outcomes and you have average performance, and you might as well have invested in an index fund and caught up on your reading.
Also, there are any number of convincing scams meant to distort one's thinking. My favorite is one I call "Miracle Man", in which a manager mails you six perfectly correct monthly predictions, all in advance of the real market they predict, then asks to take over your portfolio. Hard to believe, but it's a scam, it isn't real:
Yes, but with an appropriate degree of scientific skepticism, the "skill" assumption could actually be chance. And Occam's razor argues that chance is the more likely cause, not skill.
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). And a few of the managers will do very well indeed, but not because of skill. In fact, one can design a blind computer model that buys and sells stocks randomly, using pseudorandom numbers to make the decisions, and half the accounts will come out ahead of the averages, and a small number will do much better than the averages, just as in real life -- all because of chance.
More here: http://arachnoid.com/equities_myths