The denominator of the Sharpe ratio is sample portfolio volatility, $\sigma_p$, which is the square root of portfolio variance based on the quadratic squared loss, L2. Alternatives for the denominator of the Sharpe ratio I know of are VaR and CVaR, which are downside risk measures, but how about robust loss functions like the L1/median loss or Huber loss that downweight outliers, how can they be computed into the Sharpe ratio as replacements to sample volatility? please provide formulas

  • $\begingroup$ Are you asking how to put those things in the denominator? I am guessing you are not. Instead, think about why the standard deviation appears in the Sharpe ratio. $\endgroup$ – steveo'america Feb 18 '20 at 21:04

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