Roy's safety-first criterion

Roy's safety-first criterion is a risk management technique, devised by A. D. Roy, 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.

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%.

Thus, the problem of an investor using Roy's safety criterion can be summarized symbolically as:

{\underset {i}{\min }}\Pr(R_{i}<{\underline {R}})

where $Pr(R i < R)$ is the probability of $R i$ (the actual return of asset i) being less than $R$ (the minimum acceptable return).

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