# Roy’s Safety-First Criteria

Written By
Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
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Roy’s Safety-First Criterion, formulated by A.D. Roy in 1952, is a risk management approach in portfolio selection.

This criterion focuses on minimizing the probability of portfolio returns falling below a threshold level, known as the disaster level.

It’s particularly relevant for investors who prioritize capital preservation over high returns.

## Theoretical Framework

Roy’s criterion is grounded in probability theory and is a precursor to Markowitz’s Modern Portfolio Theory.

It diverges from the mean-variance optimization by emphasizing downside risk.

The key concept here is the Safety-First Ratio (SFRatio), which is the difference between the expected return of a portfolio and the threshold return, divided by the standard deviation of the portfolio.

## Mathematical Formulation

The SFRatio is given by:

SFRatio = [E(Rp) – R] / σ

Where:

• E(Rp) = Return of the portfolio
• R = Return threshold
• σ = Standard deviation of the portfolio’s return

## Application in Portfolio Selection

In practice, Roy’s criterion suggests choosing the portfolio that maximizes the SFRatio.

This approach is particularly suitable for risk-averse investors.

It effectively shifts focus from maximizing returns to ensuring that the probability of returns falling below a certain level is minimized.

## Comparison with Other Risk Measures

Unlike Markowitz’s approach, which considers both sides of the return distribution, Roy’s criterion is solely concerned with the left tail, i.e., the downside risk.

This makes it useful for conservative investors who are more concerned about potential losses than high returns.

## Practical Considerations

In implementing Roy’s criterion, traders need to define the threshold level, which can be subjective.

This level could be set as a fixed return rate, like a short-term government bond rate, or tied to a trader or investor’s specific financial needs.

## Limitations and Criticisms

One limitation of this criterion is its reliance on the assumption of normally distributed returns.

In reality, financial markets often exhibit skewness and kurtosis, which can lead to underestimation of risk.

Additionally, the exclusive focus on downside risk might lead to overly conservative portfolios.

## Conclusion

Roy’s Safety-First Criterion offers a unique perspective in portfolio management, emphasizing the minimization of downside risk.

It has limitations, particularly in its assumptions about return distributions.

Nonetheless, it’s a tool for risk-averse investors and those prioritizing capital preservation.

Its influence is evident in the development of subsequent risk management theories and practices in finance.