Daarnet een interessant stukje gelezen in "
A Practical Guide to Risk Management"
(
Amazon.com: A Practical Guide to Risk Management eBook: Thomas S. Coleman: Kindle Store)
Onder beleggers wordt wel eens gediscussieerd hoe groot de kans is dat een beleggingsfonds 15 jaar lang de index klopt. Er wordt dan geopperd dat het wel heel onwaarschijnlijk is dat dit door toeval kan plaatsvinden. Wel, voor al diegenen die deze mening toegedaan zijn, hier een ontluisterend stuk uit dit boekje:
To appreciate how runs can mislead, consider observing 10 heads in a row
when flipping a coin. Having 10 in a row is unlikely, with a probability of 1 in
1,024 or 0.098 percent. Yet, if we flip a coin 200 times, there is a 17 percent
chance we will observe a run of either 10 heads or 10 tails.
Runs or streaks occur in real life, and we need to be very careful in
interpreting such streaks. As the example of 10 heads shows, unlikely events do
occur in a long-repeated process. A very practical example, highly relevant to
anyone interested in risk management, is that of Bill Miller, portfolio manager
of Legg Mason Value Trust Fund. Through the end of 2005, Bill Miller had
a streak of
15 years of beating the S&P 500, which is an extraordinary
accomplishment, but is it caused by skill or simply luck?
We will see that it
could easily be entirely because of luck.
The likelihood of a single fund beating the S&P 500 for 15 years in a row
is low. Say we choose one particular fund, and let us assume that the fund has
only a 50/50 chance of beating the index in a given year (so that no exceptional
skill is involved, only luck).
The probability of that fund beating the index for
the next 15 years is only 1 in 32,768 or 0.003 percent—very low.
But 0.003 percent is
not really the relevant probability. We did not select
the Value Trust Fund before the streak and follow just that one fund; we are
looking back and picking the one fund out of many that had a streak. The streak
may have been caused by exceptional skill, but it may also have been caused by
our looking backward and considering the one lucky fund that did exceptionally
well. Among many funds, one will always be particularly lucky, even if we could
not say beforehand which fund that would be.
When we look at many funds, how exceptional would it be to observe a streak
of 15 years? Say that only 1,000 funds exist (clearly an underestimate), that each
fund operates independently, and that each fund has a 50/50 chance of beating
the index in a particular year.
What would be the chance that, over 15 years, we
would see at least 1 of those 1,000 funds with a 15-year streak? It turns out to be
much higher than 1 in 32,768—roughly
1 in 30 or 3 percent.
Therefore,
observing a 15-year streak among a pool of funds is not quite so exceptional.
But we are not done yet. Commentators reported in 2003 (earlier in the
streak) that “no other fund has ever outperformed the market for a dozen
consecutive years over the last 40 years.” We really should consider the
probability that some fund had a 15-year streak during, say, the last 40 years.
What would be the chance of finding 1 fund out of a starting pool of 1,000 that
had a 15-year streak sometime in a 40-year period? This scenario gives extra
freedom because the streak could be at the beginning, middle, or end of the 40-
year period. It turns out that the probability is now much higher, around
33
percent. In other words, the probability of observing such a streak, purely caused
by chance, is high.
The point of this exercise is not to prove that Bill Miller has only average
skill. Possibly he has extraordinary skill, possibly not.
The point is that a 15-year
streak, exceptional as it sounds, does not prove that he has extraordinary skill.
We must critically evaluate the world and not be misled by runs, streaks, or other
quirks of nature. A streak like Bill Miller’s sounds extraordinary. But before we
get carried away and ascribe extraordinary skill to Bill Miller, we need to critically
evaluate how likely such a streak is due to pure chance. We have seen that it is
rather likely. Bill Miller may have exceptional skill, but the 15-year streak does
not, on its own, prove the point.
Als je de boeken van Taleb (of anderen die toeval/geluk beschrijven) gelezen hebt, dan is dit niets nieuws onder de zon. Maar voor de rest is dit denk ik wel een belangrijke basisles. Maak nooit de fout om langdurige goede prestaties in de beleggingswereld toe te schrijven aan vaardigheden en te denken dat een tijdsreeks van 10 -, 15-, 20 jaar geluk zou wegfilteren. Ja, voor een individueel fonds is de kans op zo'n reeks heel erg klein, maar de kans dat we zo'n 'bofkont' aantreffen in de totale pool van beleggingsfondsen is juist heel erg groot.
Hiij beschrijft het allemaal heel lineair. Hoger risico = hoger rendement.