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Is outperformance versus an index a signal of managerial talent or the result of market randomness? The question is more than academic considering the size of the money management industry today. In Financial Derivatives: Pricing, Applications, and Mathematics Jamil Baz and George Chacko give a stylized answer to this question.

Consider a money manager whose portfolio value P and the index he is trying to beat (I) follow geometric Brownian motion
indexout01
where dWP and dWI are Wiener increments with correlation ρ. With F(P,I) = P/I = R denoting relative performance, one can build a new process Rt (by using Itô's lemma for the two-dimensional geometric Brownian motion (P,I)):
indexout02
The value of the process at time t is:
indexout03
By setting σP = 25%, σI = 15%, ρ = 90% and μP - μI = 3% the following table is obtained:
indexout04
If a portfolio manager outperforms the index by 3% per year on average and under the volatility and correlation conditions described above, it would take 300 years for this manager to outperform the index with 90% probability...
pauln meinte am 2. May, 23:05:
Careful, Michael, HedgeFundGuy's repuation is at stake... j/k 
HedgeFundGuy antwortete am 3. May, 00:11:
I can maintain the prior that my alpha is >0 for a couple decades before anyone can prove me wrong at the 5% level, even if my alpha=0! But then there's the fund convention to get the boot if you lose money over a calendar year. I need to work for a statistician. 
Mahalanobis antwortete am 3. May, 00:56:
I was talking about benchmark-huggers.
There is a non-linear relationship between the portfolio returns and the index returns in the hedge fund case, probably best approximated by a quadratic function. Hedge funds an negative returns... who told you such things? Somebody from the private equity industry? ;-D 
moominoid (guest) meinte am 20. Oct, 03:11:
Why not use daily data then? eom
Hedgehog (guest) antwortete am 20. Oct, 19:17:
Daily data is more noisy
Daily data wouldn't provide more information about the trend than monthly or annual data. The only way to estimate the trend more precisely is to increase the observation period.