Discerning skill from luck: I hope you have some time on your hands
Statisticians (and college freshmen) use a "t" statistic to determine the "statistical significance" of an outcome.
The same statistic can be used to tell if an investment's track record is attributable to skill instead of merely luck.
After some algebra, the formula looks like this:
N = (t x sd/mean)^2
N = number of sample data points
t = t statistic; 2.0 is considered statistically significant
sd = standard deviation
mean = average of what you are measuring
Let's assume we have an investment that has generated an eye-popping 5% alpha (excess return) with a standard deviation of 20%
(the average standard deviation of the market from 1926 through 2008).
How long would the manager have to generate this type of track record to be reasonably sure that it was the product of skill and not luck?
N = (2 * 20/5)^2 = 64
64 years.
If the excess return is 4% (still unheard of), N increases to 100 years.
If the standard deviation is 30% (reasonable given the high returns), N increases to 144 years.
Hence the required regulatory disclosure included (usually in micro-print) in every brokerage statement:
"Past performance is no indication of future results."
