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.
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 is the probability of (the actual return of asset i) being less than (the minimum acceptable return).
Video Roy's safety-first criterion
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 is the expected return (the mean return) of the portfolio, is the standard deviation of the portfolio's return and is the minimum acceptable return.
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 = 1.6
By Roy's safety-first criterion, the investor would choose portfolio B as the correct investment opportunity.
Maps Roy's safety-first criterion
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.
See also
- Omega ratio
- Value at risk
References
Source of article : Wikipedia