Roy’s Safety-First Criterion (SFRatio)

Roy’s Safety‑First Criterion (SFRatio)

Roy’s Safety‑First Criterion (SFRatio) is a risk‑management metric that quantifies the probability a portfolio will meet or exceed an investor’s minimum acceptable return. It helps compare portfolios by measuring how many standard deviations the expected return lies above the investor’s threshold.

Formula

SFRatio = (r_e − r_m) / σ_p

where:
* r_e = expected return of the portfolio
* r_m = investor’s minimum required return (threshold)
* σ_p = standard deviation of portfolio returns

How to calculate

1. Estimate the portfolio’s expected return (r_e).
2. Specify the minimum acceptable return (r_m).
3. Estimate the portfolio’s standard deviation (σ_p).
4. Compute (r_e − r_m) and divide by σ_p.

A higher SFRatio indicates a lower probability that returns will fall below the threshold; investors should prefer the portfolio with the highest SFRatio.

Interpretation

• SFRatio measures distance (in standard deviations) between expected return and the minimum acceptable return.
• If returns are approximately normally distributed, the SFRatio can be converted into the probability that portfolio returns will be below r_m using the standard normal distribution.
• The criterion focuses on downside risk relative to a specific target rather than overall return per unit volatility.

Example

Three portfolios with a threshold r_m = 5%:
* Portfolio A: r_e = 12%, σ_p = 20% → SFRatio = (12 − 5) / 20 = 0.35
* Portfolio B: r_e = 10%, σ_p = 10% → SFRatio = (10 − 5) / 10 = 0.50
* Portfolio C: r_e = 8%, σ_p = 5% → SFRatio = (8 − 5) / 5 = 0.60

Portfolio C has the highest SFRatio and thus the lowest estimated probability of falling below 5%, making it the preferred choice under Roy’s criterion.

Relation to Sharpe ratio and limitations

• The SFRatio resembles the Sharpe ratio; if the minimum acceptable return r_m equals the risk‑free rate and returns are normally distributed, the two measures are mathematically similar.
• Limitations:
• Relies on estimates of expected return and standard deviation, which can be uncertain.
• Assumes return distribution is reasonably symmetric; it may understate downside risk for strongly skewed or fat‑tailed distributions.
• Choice of r_m is subjective and can materially change the ranking of portfolios.

Key takeaways

• SFRatio helps choose portfolios that minimize the chance of failing to meet a specified return target.
• Use it to compare portfolios when a minimum return is the investor’s primary concern.
• Consider distributional assumptions and the sensitivity to the chosen threshold when applying the criterion.