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.

Keywords:

Portfolio | CVAR | Conditional Value at Risk | Risk Management |