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

![Roy's Safety-First Criterion (SFRatio)](https://www.investopedia.com/thmb/Rzhsx11MlTj_2CjtO-RDZzfpQi8=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Roys-safety-first-criterion_3-2_final-a5617159ba694d3f9346bdeb73b6b8c9.png)

*— Investopedia / Michela Buttignol*

> **Definition**
>
> Roy's Safety First Criterion is a formula to determine the probability that an investment portfolio will provide the expected returns.

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

Roy's safety-first criterion, also known as the SFRatio, is a risk management approach that sets a minimum required return for a given level of [risk](https://www.investopedia.com/terms/r/risk.asp). It is used to determine the probability that a given portfolio will meet or exceed the investor's expected returns.

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.

### Key Takeaways

*   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.

## Formula for the SFRatio

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

## How to Calculate Roy's Safety-First Criterion (SFRatio)

The SFRatio is calculated by subtracting the minimum desired return from the [expected return](https://www.investopedia.com/terms/e/expectedreturn.asp) of a portfolio and dividing the result by the [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) of [portfolio returns](https://www.investopedia.com/terms/p/portfolio-return.asp). 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](https://www.investopedia.com/terms/r/riskreturntradeoff.asp) 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](https://www.investopedia.com/articles/investing/032415/how-investment-risk-quantified.asp) 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](https://www.investopedia.com/terms/s/sharperatio.asp); for normally distributed returns, the minimum return is equal to the risk-free rate.

## 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.