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Roy's Safety-First Ratio
JohnKwon (john.kwon2**@gmail.com) | 조회 : 605 | Nov, 27, 05:26 PM

## 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}​SFRatio=σp​re​−rm​​where:re​=Expected return on portfoliorm​=Investor’s minimum required returnσp​=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 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.

### Related Terms

Downside Risk Definition

Downside risk is an estimation of a security's potential loss in value if market conditions precipitate a decline in that security's price.

The Sharpe ratio is used to help investors understand the return of an investment compared to its risk.

The expected return is the amount of profit or loss an investor can anticipate receiving on an investment over time.

The modern portfolio theory (MPT) looks at how risk-averse investors can build portfolios to maximize expected return based on a given level of risk.

The capital market line (CML) represents portfolios that optimally combine risk and return.

The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation.

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