A dollar edge per trade, 1000 trades a year: annual Sharpe?

Question

A desk nets an average profit of 12 dollars per trade, with a standard deviation of 200 dollars across trades, and it makes 1000 independent trades per year.

What annualized Sharpe ratio does this imply?

Accepted Answer

Build annual from per-trade. Over M independent trades, average profits add up and volatility grows by \sqrt{M}, so the annual Sharpe is the per-trade Sharpe times the square root of trades per year: SR{	ext{annual}} = \frac{m}{s}\sqrt{M} = s{	ext{trade}}\sqrt{M}. The dollar units cancel in m/s, so we can work directly with the raw dollar figures. Plug in the numbers. The per-trade Sharpe is s{	ext{trade}} = 12/200 = 0.06, and M = 1000: SR{	ext{annual}} = 0.06 	imes \sqrt{1000} = 0.06 	imes 31.62 \approx 1.90. Interpretation. A very small per-trade Sharpe of 0.06 still produces a health…

A dollar edge per trade, 1000 trades a year: annual Sharpe?

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