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.
[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%.
Thus, the problem of an investor using Roy's safety criterion can be summarized symbolically as:
If the portfolios under consideration have normally distributed returns, Roy's safety-first criterion can be reduced to the maximization of the safety-first ratio, defined by:
Under normality, The Sharpe ratio is defined as excess return per unit of risk, or in other words: 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.
Roy’s work is the foundation of asset pricing under loss aversion.
His work was followed by Lester G. Telser’s proposal of maximizing expected return subject to the constraint that the Pr(Ri < R) be less than a certain safety level.