Four Years to Trust a Sharpe of 1.0

Some numbers you quote until you understand them, and then you stop. My Sharpe ratio is one of those numbers.

A Sharpe ratio is not a fact about a strategy. It is an estimate, computed from a sample of returns, and like any estimate it arrives with an error bar. The problem is that almost nobody prints the error bar next to the number, and once you work out how wide it is, most of what gets called a track record stops meaning very much.

The rule of thumb

Here is the approximation worth memorizing. The t-statistic on a Sharpe ratio, the thing that tells you whether it is distinguishable from zero, is roughly the Sharpe times the square root of the number of years of data. t is approximately SR times the square root of years.

Read a t of 2 as the usual bar for statistical significance and this says something uncomfortable. A strategy with a true annualized Sharpe of 1.0, which is a genuinely good strategy, needs four years of returns before its t-statistic clears 2. Four years to establish, at the loosest conventional bar, that the edge is not zero.

One year of a real edge

Run it for a single year. True Sharpe of 1.0, twelve months of returns, everything behaving. The point estimate lands somewhere near 1.0 if you are lucky, but the standard error is also near 1.0. A ninety-five percent confidence interval runs from roughly negative one to positive three.

Sit with that interval. A full year of a genuinely Sharpe-1.0 strategy cannot rule out that the true value is negative. It also cannot rule out that you are running a Sharpe-3 machine that belongs in a textbook. The year told you almost nothing you did not assume going in.

The error bar is wider than that

Everything above assumes returns are independent and identically distributed, drawn fresh each period from the same well-behaved bell curve. Strategy returns are not that. They autocorrelate, because positions persist and regimes cluster. They have fat tails, because the days that matter are the big ones. Andrew Lo worked out the fuller expression in his paper The Statistics of Sharpe Ratios, and both effects push the same way: the true standard error is larger than the tidy formula admits, sometimes much larger. The clean four-year number is the optimistic case, not the pessimistic one.

And the point estimate is biased up

Here is the part that turns a statistics lecture into a warning. The track record you are staring at is not a random draw. You are looking at it because it survived. You kept this strategy, funded this strategy, wrote a blog post about this strategy, precisely because its early returns looked good. That is selection, and selection conditions the sample on having already done well.

So the two errors do not cancel. The error bar is wider than the iid formula says, and the point estimate sitting in the middle of it is biased upward by the act of selection that made you look in the first place. You are reading a number that is too high, inside an interval that is too wide, and the process that surfaced the strategy for your attention guaranteed both at once.

The take

None of this means backtests are useless or that a good Sharpe is a lie. It means the number is soft in a specific, quantifiable way, and the softness does not shrink as fast as intuition expects. It shrinks like the square root of time, which is slow, and the slowness is the whole reason patience is not a virtue in this game but a requirement.

What I do with it is small. I stopped quoting a Sharpe with fewer than a couple of years behind it as though it were load-bearing. I treat any track record shorter than that as a hypothesis with a wide interval, not a result. And when a young strategy looks brilliant, I assume the number is flattering me, because the reason I am looking at it at all is that it already did.

Four years to trust a Sharpe of 1.0. Most of what I have is younger than that. So is most of what anyone shows you.