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.
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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:
where
Normally distributed return and SFRatio
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:
where
Example
If Portfolio A has an expected return of 10% and standard deviation of 15%, while portfolio B has a mean return of 8% and a standard deviation of 5%, and the investor is willing to invest in a portfolio that maximizes the probability of a return no lower than 0%:
SFRatio(A) = [10 − 0]/15 = 0.67,SFRatio(B) = [8 − 0]/5 = 1.6By Roy's safety-first criterion, the investor would choose portfolio B as the correct investment opportunity.
Similarity to Sharpe ratio
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.