How many trades to confirm a cents-per-share edge?

Question

A statistical-arbitrage signal nets an average of 10 cents per share, with a standard deviation of 40 cents across trades.

Roughly how many trades are needed before the average edge is statistically significant at the 5% level (t of about 2)? Assume trades are independent.

Accepted Answer

Set up the test. For N independent trades, the t-statistic for "the true edge is zero" is the per-trade Sharpe times the square root of the trade count: t = s{	ext{trade}}\sqrt{N}, \qquad s{	ext{trade}} = \frac{	ext{average edge}}{	ext{standard deviation}}. Evidence accumulates with the square root of the number of trades. Solve for the number of trades. Requiring t \geq 2: N \geq \left(\frac{2}{s{	ext{trade}}}ight)^2. The per-trade Sharpe is s{	ext{trade}} = 10/40 = 0.25, so N \geq \left(\frac{2}{0.25}ight)^2 = 8^2 = 64 	ext{ trades}. Interpretation. About 64 trades. A per-trade S…

How many trades to confirm a cents-per-share edge?

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