How many trades to prove your edge is real?

Question

Each of your trades has expected profit $\mu$ and standard deviation $\sigma$ , with a per-trade "Sharpe" of $s = \mu/\sigma = 0.05$ . Trades are roughly independent.

How many trades do you need before your cumulative P&L is statistically distinguishable from zero (say, a t-statistic of $2$ )?

Accepted Answer

After N independent trades, cumulative P&L has mean N\mu and standard deviation \sigma\sqrt{N} (means add, variances add). The t-statistic of your track record, how many standard errors the total sits above zero, is t = \frac{N\mu}{\sigma\sqrt{N}} = \sqrt{N}\,\frac{\mu}{\sigma} = \sqrt{N}\,s. So the significance of your edge grows only with the square root of the number of trades, scaled by your per-trade Sharpe. To reach t = 2 (roughly 95\% confidence the edge is real): \sqrt{N}\,s = 2 \;\Longrightarrow\; N = \frac{4}{s^2} = \frac{4}{0.05^2} = \frac{4}{0.0025} = 1{,}600 	ext{ trades.} You n…

How many trades to prove your edge is real?

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