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Getting it down on `paper`

Calculating Sharpe Ratio

Let N = 250, the number of trading days in a year.
Let ROI[i] = the daily return :: close[i]/close[i-1] – 1
Let Reward = the expected daily return :: mean(ROI[1..N])
Let Risk = the standard deviation of daily returns :: std(ROI[1..N])
Sharpe = sqrt(N) * Reward / Risk
Sharpe = sqrt(N) * mean(ROI[1..N]) / stddev(ROI[1..N])
Sharpe = E[R-Rf]/sqrt(var(R-Rf))

Note: Risk-free rate is often LIBOR, and can be other metrics as well, but is often ignored for the purpose of calculating the Sharpe ratio.



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