# Roy's Safety-First Criterion (SFRatio) Definition and Calculation

## What Is Roy's Safety-First Criterion – SFRatio?

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.

## The Formula for the SFRatio Is

﻿ \begin{aligned} &SFRatio = \frac{r_e-r_m}{\sigma_p}\\ &\textbf{where:}\\ &r_e = \text{Expected return on portfolio}\\ &r_m = \text{Investor's minimum required return}\\ &\sigma_p = \text{Standard deviation of the portfolio}\\ \end{aligned}﻿

## 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 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.

## Example of Roy's Safety-First Criterion

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.