Roy’s safety-first criterion, also known as the SFRatio, is an investment decision-making approach that sets a minimum required return for a given level of risk. This criterion allows investors to compare potential portfolio investments based on the probability that the portfolio returns will fall below their minimum desired return threshold.
The Formula for the SFRatio
$$ \text{SFRatio} = \frac{r_e - r_m}{\sigma_p} \ \text{where:}\ r_e = \text{Expected return on portfolio} \ r_m = \text{Investor’s minimum required return} \ \sigma_p = \text{Standard deviation of the portfolio} $$
How to Calculate Roy’s Safety-First Criterion (SFRatio)
The SFRatio is calculated by subtracting the minimum desired return from the expected return of a portfolio and dividing the result by the standard deviation of portfolio returns. The optimal portfolio will be the one that minimizes the probability that the portfolio’s return will fall below a threshold level.
What Does Roy’s Safety-First Criterion Tell You?
The SFRatio provides a probability of achieving a minimum-required return on a portfolio. An investor’s best decision is to choose the portfolio with the highest SFRatio. Investors can use this formula to evaluate various scenarios involving different asset-class weights, investments, and other factors impacting the probability of reaching their minimum return threshold.
Some investors view Roy’s safety-first criterion not just as an evaluation method but also as a risk-management philosophy. By selecting investments that adhere to a minimum acceptable portfolio return, an investor ensures that their investments meet the threshold, with any additional gains considered a bonus.
The SFRatio is closely related to the Sharpe Ratio. For normally distributed returns, the minimum return often matches the risk-free rate.
Key Takeaways
- Roy’s safety-first rule measures the minimum return threshold an investor has for a portfolio.
- Also known as the SFRatio, the formula helps investors compare different investing scenarios to choose the one most likely to meet their required minimum return.
Example of Roy’s Safety-First Criterion
Consider three portfolios with various expected returns and standard deviations. Portfolio A has an expected return of 12% and a standard deviation of 20%. Portfolio B has an expected return of 10% and a standard deviation of 10%. Portfolio C has an expected return of 8% and a standard deviation of 5%. The threshold return for the investor is 5%.
Which portfolio should the investor choose?
- SFRatio for Portfolio A: $\frac{12 - 5}{20} = 0.35$
- SFRatio for Portfolio B: $\frac{10 - 5}{10} = 0.50$
- SFRatio for Portfolio C: $\frac{8 - 5}{5} = 0.60$
Portfolio C has the highest SFRatio and should be selected.
Related Terms: Sharpe Ratio, Investment Risk, Expected Return, Standard Deviation, Portfolio Management, Risk Management.
