How Long Before Your P&L Means Anything

A new strategy makes money for six weeks straight. Is it good? The instinct is to say yes — the sign is right, and it's felt long enough that it seems like more than luck. It usually isn't. Because daily P&L is noisy, the amount of time required before you can statistically tell a real edge apart from a lucky streak is much longer than most traders' gut feel suggests, often by a factor of years, not weeks.

The arithmetic of why it's slow

Say a strategy has a true annualized Sharpe ratio of $S$. To be reasonably confident (roughly a 95 percent one-sided test) that the observed Sharpe is actually positive and not a noise artifact, you need approximately

$$T \approx \left(\frac{1.645}{S}\right)^2 \text{ years}$$

In words: the number of years of track record you need scales with the inverse square of the true Sharpe. A strategy with a genuinely good Sharpe of 1.0 needs roughly $(1.645/1)^2 \approx 2.7$ years before you can be reasonably sure it isn't noise. A more realistic Sharpe of 0.5 needs about $(1.645/0.5)^2 \approx 10.8$ years. Halving the Sharpe roughly quadruples the wait.

Worked example

Your new pairs strategy has run for two months (about 0.17 years) and shows an annualized Sharpe of 1.3 based on that short sample. Plugging into the formula the other way — solving for what Sharpe you'd need to already be significant at $T = 0.17$ — gives $S = 1.645/\sqrt{0.17} \approx 3.99$. Your observed Sharpe of 1.3 is nowhere near that bar. In plain terms: at two months of data, you would need an almost unheard-of Sharpe near 4 before the result stopped looking like it could be noise. A Sharpe of 1.3 over two months is consistent with a strategy that has no edge at all and simply got a good run.

Now suppose the same strategy runs for three years at a stable Sharpe near 1.3. The required Sharpe for significance at $T=3$ is $1.645/\sqrt{3} \approx 0.95$. The observed 1.3 clears that bar — three years in, you have real evidence, not just a good stretch.

What this means in practice

Don't size a strategy up sharply after a good first quarter, and don't kill one after a bad first quarter either — neither is long enough to be informative for anything but the most extreme Sharpe ratios. Desks that get this right treat early P&L as a soft signal, weighted alongside independent evidence: does the logic make sense, does the back-test hold out-of-sample, is the strategy's risk profile behaving as the model predicted. Live P&L becomes the dominant piece of evidence only after a year or more.