# Safety-first Ratio

Roy’s Safety first criterion states that the optimal portfolio minimizes the probability that portfolio return, RP, falls below RL.

According to this criteria, we select the portfolio with the highest safety first ratio (SFRatio).

**Example**

An investor has a minimum threshold of 2%. He has to make a choice between two portfolios A and B.

| Portfolio A | Portfolio B |

E(R) | 10% | 15% |

s | 20% | 25% |

According to Roy’s Safety-first criteria, which portfolio should he choose?

SFRatio of Portfolio A = (10-2)/20 = 0.40

SFRatio of Portfolio B = (15-2)/25 = 0.52

According to safety-first criteria, we should select portfolio B. Minimum threshold is 0.40 standard deviations away for portfolio A while it is 0.52 standard deviations away for portfolio B.

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