The PortScenOmegaRatioA.xlsx Model

Portfolio Optimization with the Omega Ratio Risk Measure

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      One definition of the Omega ratio is:
 (Expected Return above threshold)/(Expected return below threshold), or
  E[ MAX(0, R-tau)]/E[ MAX(0, tau-R)] 
    R = return( a random variable) of the portfolio,
    tau = a specified target or threshold return 
  MAX(0, R-tau) = R-tau+MAX(0,tau-R)
 so in terms of expectations
  = (E[R] -tau + E[MAX(0,tau-R)])/ E[MAX(0,tau-R)] 
   = (E[R] -tau )/ E[MAX(0,tau-R)] + 1
   Notice the similarity to the Sharpe ratio:
      (E[R] -tau )/SD( R),   where SD is Standard Deviation. 
So the Omega ratio and the Sharpe ratio effectively differ only in how risk is measured in the denominator.
Effectively, the Sortino ratio uses the semi-vriance as the risk measure.


Portfolio | Markowitz | Risk Management | Omega ratio |