Excess return per unit of deviation in return.

Excess return per unit of deviation in return. Often confused with the simple mean / standard-deviation, a.k.a. signal-to-noise ratio.

A correct Sharpe ratio is defined with respect to a benchmark, against which its excess return can be computed.

In practice Sharpe ratio (SR) is annualized.

A very good reference is The Statistics of Sharpe Ratios, by Andrew W. Lo. It is explained in this paper

  • the link with the t-statistic: if a strategy has a Sharpe ratio or $S$ that is computed on $N$ days, then the t-stat of the strategy is $S/\sqrt{N}$
  • the correction that must be made if the strategy is not stationary to translate the SR computed on $N_1$ days to the one computed on $N_2$ days: obviously if the strategy is mean reverting at long time scale, the longer the window of computation, the lower the SR.
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