How many fills to validate a market maker's tick edge?

Question

A market maker captures an average of 1.5 ticks per fill, with a standard deviation of 5 ticks across fills.

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

Accepted Answer

Set up the test. For N independent fills, the t-statistic for "the true average edge is zero" is the per-fill Sharpe times the square root of the number of fills: t = s{	ext{fill}}\sqrt{N}, \qquad s{	ext{fill}} = \frac{	ext{average edge}}{	ext{standard deviation}}. Each fill contributes a bit of evidence, and the total evidence grows with the square root of the fill count. Solve for the number of fills. We want t \geq 2: N \geq \left(\frac{2}{s{	ext{fill}}}ight)^2. The per-fill Sharpe is s{	ext{fill}} = 1.5/5 = 0.30, so N \geq \left(\frac{2}{0.30}ight)^2 = (6.667)^2 = 44.4, which ro…

How many fills to validate a market maker's tick edge?

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