Roy's Safety-First Criterion (SFRatio) Definition

Roy's safety-first criterion, also known as the SFRatio, is an approach to investment decisions that sets a minimum required return for a given level of risk. Roy's safety-first criterion allows investors to compare potential portfolio investments based on the probability that the portfolio returns will fall below their minimum desired return threshold.

$SFRatio = \frac{r_e-r_m}{\sigma_p}$SFRatio=σp​re​−rm​​

Where:

• r_e = expected return on portfolio
• r_m = investor's minimum required return
• σ_p = standard deviation of the portfolio

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.

The SFRatio provides a probability of getting a minimum-required return on a portfolio. An investor's optimal decision is to choose the portfolio with the highest SFRatio. Investors can use the formula to calculate and evaluate various scenarios involving different asset-class weights, different investments and other factors that affect the probability of meeting their minimum return threshold.

Some investors feel that Roy's safety-first criterion is a risk-management philosophy in addition to being an evaluation method. By choosing investments that adhere to a minimum acceptable portfolio return, an investor can sleep at night knowing that her investment will achieve a minimum return, and anything above that is "gravy."

The SFRatio is very similar to the Sharpe ratio; for normally distributed returns, the minimum return is equal to the risk-free rate.

• Roy's safety-first rule measures the minimum return threshold an investor has for a portfolio.
• Also known as the SFRatio, investors can use the formula to compare different investing scenarios to choose the one most likely to hit their required minimum return.

Assume three portfolios with various expected returns and standard deviations. Portfolio A has an expected return of 12% with a standard deviation of 20%. Portfolio B has an expected return of 10% with a standard deviation of 10%. Portfolio C has an expected return of 8% with a standard deviation of 5%. The threshold return for the investor is 5%.

Which portfolio should the investor choose? SFRatio for A: (12 - 5) / 20 = 0.35; B: (10 - 5) / 10 = 0.50; C: (8 - 5) / 5 = 0.60. Portfolio C has the highest SFRatio and thus should be selected.