Roys safety first criterion

Roy’s safety-first criterion is a risk management technique that allows an investor to select one portfolio rather than another based on the criterion that the probability of the portfolio’s return falling below a minimum desired threshold is minimized.[1]

For example, suppose there are two available investment strategies—portfolio A and portfolio B, and suppose the investor’s threshold return level (the minimum return that the investor is willing to tolerate) is −1%. then the investor would choose the portfolio that would provide the maximum probability of the portfolio return being at least as high as −1%.

The SFRatio has a striking similarity to the Sharpe ratio. Thus for normally distributed returns, Roy’s Safety-first criterion—with the minimum acceptable return equal to the risk-free rate—provides the same conclusions about which portfolio to invest in as if we were picking the one with the maximum Sharpe ratio.


  1. ^Roy, Arthur D. (1952). “Safety First and the Holding of Assets”. Econometrica. 20 (July): 431–450. doi:10.2307/1907413.

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