Separating Manager Skill From Luck

Out of a thousand fund managers with zero real skill, flipping fair coins with their bets, some will still beat the market five years running just by chance — the same way some coin-flippers in a giant tournament will hit ten heads in a row. An allocator staring at one impressive track record cannot tell, from the return series alone, whether they are looking at genuine skill or the lucky survivor of a large crowd of random outcomes.

Turning a track record into a t-statistic

The standard tool is to treat a manager's average excess return as an estimate with uncertainty, not a fact, and ask how many standard errors it is from zero:

$$t = \frac{\bar{\alpha}}{SE(\bar{\alpha})} = \frac{\bar{\alpha}}{\sigma / \sqrt{n}}$$

In words: divide the average annual excess return by the standard error of that average, where the standard error shrinks as more years of data ($n$) accumulate. A large $t$-statistic means the average excess return is many standard errors from zero — hard to explain by chance alone. A small one means the same average could easily have come from a manager with zero true skill who simply got lucky.

Worked example

Two managers each ran for five years. Manager A averaged 4% annual excess return with a 6% standard deviation of that excess return. Manager B averaged 4% too, but with an 18% standard deviation.

$$t_A = \frac{4\%}{6\% / \sqrt{5}} = \frac{4\%}{2.68\%} \approx 1.49, \qquad t_B = \frac{4\%}{18\% / \sqrt{5}} = \frac{4\%}{8.05\%} \approx 0.50$$

Manager A's excess return is about 1.5 standard errors from zero — suggestive, though still short of the roughly 2.0 typically wanted for real confidence. Manager B's is only half a standard error away, indistinguishable from noise despite an identical headline return. The same average performance, viewed through consistency, tells two very different stories.

What this means in practice

This is why five-year track records are the industry's grudging minimum and why consultants weight consistency (a high information ratio) over headline return. It's also why manager selection is genuinely hard: even a true $t \approx 2$ track record still has roughly a 1-in-20 chance of being a lucky skill-less manager, and across thousands of funds being screened, some skill-less managers with exactly that profile are guaranteed to exist.