From a per-trade edge to an annual Sharpe ratio

Question

A tactic earns an average of 0.05% per trade, with a standard deviation of 0.50% across trades, and it makes 500 independent trades per year. What annualized Sharpe ratio does this imply?

Accepted Answer

Build the annual numbers from the per-trade numbers. Over a year of M independent trades, the average returns add up while the volatility grows by the square root of the count: - Annual average return = m 	imes M (means add), - Annual volatility = s 	imes \sqrt{M} (independent wiggles grow by \sqrt{M}). So the annual Sharpe is SR{	ext{annual}} = \frac{mM}{s\sqrt{M}} = \frac{m}{s}\sqrt{M} = s{	ext{trade}}\sqrt{M}, where s{	ext{trade}} = m/s is the per-trade Sharpe. In words: annual Sharpe = per-trade Sharpe times the square root of trades per year. Plug in the numbers. The per-trade Sharp…

From a per-trade edge to an annual Sharpe ratio

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