From a per-trade edge to an annualized Sharpe

Question

Each round-trip trade earns you, on average, $\mu = \$ 1.50 $with a standard deviation of$ \sigma = $40 $. You do about$ 800 $such trades per day,$ 252$ days a year, roughly independently.

What annualized Sharpe ratio does this per-trade edge imply?

Accepted Answer

The per-trade Sharpe is tiny: s = \frac{\mu}{\sigma} = \frac{1.50}{40} = 0.0375. On any single trade, the \40 of noise dwarfs the \1.50 edge, you'd never see the edge in one trade. But Sharpe aggregates with the square root of the number of independent trades. Over a year you do N = 800 	imes 252 = 201{,}600 	ext{ trades,} and the annualized Sharpe is S{	ext{ann}} = s\,\sqrt{N} = 0.0375 	imes \sqrt{201{,}600} = 0.0375 	imes 449 \approx 16.8. An annual Sharpe near 17 is enormous, the hallmark of a high-frequency market-making strategy. The magic isn't a big per-trade edge (it's minuscule)…

From a per-trade edge to an annualized Sharpe

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