> 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.
Indeed, 50 may do worse than the market... but it's not because of a faulty appeal to "statistics."
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.
> haliax is pointing out that 100 fund managers may not be an unbiased sample.
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?"
Arg... Assume the entire population of fund managers, which is smaller than the population of the entire "market", has a mean return of 15%. Further, assume the market as a whole (superset including fund managers) has a mean return of 10%.
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.
> Further, assume the market as a whole (superset including fund managers) has a mean return of 10%. Under those conditions... in a sampling of 100 "typical fund managers", more than half would still produce higher returns than the market.
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.
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.