The PortScenCVaRA.xlsx Model

Portfolio Optimization with the CVaR Risk Measure

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  CVaR differs from Sharpe Ratio or Omega ratio in that
the threshold is not specified but is a decision variable. 
One specifies only a target probability for falling below the threshold.
CVaR is similar to VaR but adds a penalty term for amount short of the threshold.
     Under CVAR, we specify a probability, Rho, e.g., 0.1, and
  then we want the model to choose a) a threshold return,
  and b) a portfolio composition, so as to 
   Maximize  Rho*threshold - (expected shortfall below threshold).
or  equivalently:
    Maxmize  threshold  - (expected shortfall below threshold)/Rho.
So it is similar to VaR except that it adds a penalty term for
the amount by which an outcome falls below the threshold,
  It is easy to see that if all scenarios are equally likely,
  then it is worthwhile increasing the threshold as long as
  less than Rho of the scenarios fall short of the threshold.
  So at an optimum, the probability of falling below the threshold
  is as close as possible to Rho.
    CVaR is a "coherent" risk measure, so it exhibits none of
the anomalous behaviors associated with VaR.


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