Shortfall risk, the safety-first ratio

Shortfall risk
The risk that the value of portfolio will fall below a minimum threshold, that is:
P(Rp ◁ min. of R)
Where:◁ - smaller than

Safety-first ratio
It is used to monitor shortfall risk, aims to minimize P(E(Rp) ◁ min. of R) and maximize SFRatio=[E(Rp) – min. of R] /σ , which is just similar to sharpe={E(Rp)-Rf }/ σ ,)

Steps to choose an optimal portfolio using the safety-first criterion

1. calculate SFRatio
2. calculate P(E(Rp) smaller than min. of R)=F(-SFRatio)
3. select portfolio with largest SFRatio or lowerest F(-SFRatio)

Roy's safety-first criterion

• Choose portfolio with the highest SFR.