How to Work with Negative Multiples?

Introduction

Price multiples are among the most widely used tools in financial analysis. Ratios like P/E (Price-to-Earnings) and P/FCF (Price-to-Free-Cash-Flow) allow investors to quickly gauge whether a stock is cheap or expensive relative to its fundamentals. The appeal is obvious: take the market price of a share, divide it by some measure of financial performance, and you have a simple number that can be compared across companies and over time.

But what happens when the denominator turns negative? A company that reports a loss has negative earnings. A firm investing heavily in growth might burn through cash, resulting in negative free cash flow. In these situations, traditional price multiples simply break down—most financial platforms and databases report these values as “N/A” (not applicable), effectively discarding any information about these companies. You cannot meaningfully divide a positive stock price by a negative number and expect the result to tell you anything useful about valuation.

This article presents a transformation method that solves this problem. By converting traditional multiples into bounded scores, we can handle negative values gracefully, maintain meaningful comparisons across all companies, and feed these metrics into quantitative models without worrying about data gaps or infinite values.

The Problem with Traditional Multiples

Consider what happens when you try to build a comprehensive database of company valuations. For each company and each quarter, you want to record the P/E ratio, the P/FCF ratio, and perhaps several other multiples. Everything works fine as long as companies are profitable and generating positive cash flow. But the moment a company slips into the red, you face a choice: leave the field blank, or record some kind of error value.

Neither option is satisfactory. Leaving fields blank creates gaps in your data, which complicates any kind of time series analysis or cross-sectional comparison. Recording an error value means losing information about degrees of unprofitability. A company losing one cent per share is fundamentally different from a company hemorrhaging money, but traditional multiples treat them identically: both are simply undefined.

The following example illustrates this problem using real data from Nike. We have plotted the raw P/FCF ratio for Nike going back to 2020, alongside the same data transformed using the method described in this article.

Understanding the Range of P/E Ratios

Before diving into the transformation, it helps to understand why traditional multiples behave as they do. The P/E ratio is simply price per share divided by earnings per share. A company with a share price of $100 and earnings of $5 per share has a P/E of 20. The same company earning $10 per share would have a P/E of 10.

Lower P/E ratios are more attractive because you pay less for each dollar of earnings. A P/E of 10 means paying ten dollars for every dollar earned; a P/E of 20 means paying twenty. All else equal, lower is better.

The ratio’s mathematical structure creates important edge cases. As earnings approach zero from above, the P/E ratio grows without bound. A company earning just one cent per share with a price of $100 would have a P/E of 10,000. As earnings approach zero, P/E approaches infinity.

Conversely, high earnings relative to price push P/E toward zero, though it can never reach zero for a company with a positive stock price. The theoretical range extends from just above zero to positive infinity. This unbounded nature causes problems in quantitative models.

The Challenge of Measuring Change Over Time

The problems compound when tracking how multiples change over time. Suppose a company’s P/E ratio falls from 15 to 12 after an earnings report. We can calculate the percentage change:

This twenty percent decrease tells us how the market’s valuation has shifted. But we can only compute this when both values are defined. If the company had negative earnings in either quarter, we cannot compute the percentage change at all.

Even when both values are defined, percentage changes can behave erratically. A P/E moving from 5 to 10 is a 100% increase. A P/E moving from 100 to 200 is also a 100% increase. But these changes are very different: the first represents a dramatic valuation shift; the second might simply reflect earnings declining from modest to very low.

Our Proposed Solution

Our transformation addresses all these issues. It converts any traditional multiple into a bounded score between −1 and +1. Positive scores correspond to profitable companies; negative scores to loss-making ones. The magnitude reflects valuation attractiveness.

The key insight: we define a continuous function that maps the entire real number line to the interval [−1, +1]. Companies with excellent valuations (low P/E ratios) score near +1. Companies with poor valuations (high P/E or deep losses) score near −1. Companies at breakeven score exactly zero.

The Mathematical Framework

We denote the traditional multiple as μ, and the transformed score as σ. We also introduce α, the neutral point—the multiple value at which a stock is considered fairly valued. For P/E ratios, a typical α would be 20.

The transformation uses different formulas depending on whether the underlying fundamental value (earnings, cash flow, etc.) is positive or negative.

When the fundamental value is positive, meaning the traditional multiple $\mu$ is well-defined and positive, the transformation is:

When the fundamental value is negative, we extend the definition by allowing negative μ to represent losses relative to price:

Visualizing the Transformation

The interactive plot below shows the transformation across the full range of multiple values. The horizontal axis is the P/E ratio (extended to negative values); the vertical axis is the transformed score. Adjust the slider to see how α affects the curve.

Notice three key features. First, the transformation is continuous across zero—no discontinuity when a company moves from slight profit to slight loss. This continuity is essential for tracking companies over time.

Second, the curve flattens at extremes. Very high P/E ratios produce scores approaching 0; very low P/E ratios approach +1. This bounded behavior prevents outliers from distorting analysis.

Third, when P/E equals α, the score is exactly 0.5. Stocks scoring above 0.5 are cheaper than the industry average; those between 0 and 0.5 are more expensive but still profitable.

Properties of the Transformed Scores

The transformed scores have several desirable properties:

• Bounded: All values fall strictly between −1 and +1, making them suitable for machine learning models
• Meaningful sign: Positive scores indicate profitability; negative scores indicate losses
• Meaningful magnitude: Values near +1 indicate better value; values near −1 indicate worse value

Within the profitable range, the transformation preserves ordering. A P/E of 10 always scores higher than a P/E of 20, which scores higher than a P/E of 50. The scores remain interpretable in the traditional sense.

For loss-making companies, the scores distinguish between degrees of unprofitability. A company with a small loss scores slightly below zero; a company hemorrhaging cash scores near −1. This granularity was absent from traditional ratio analysis, which excluded all loss-making companies.

Setting the Neutral Point Parameter

The parameter α calibrates the transformation to specific contexts. A fair P/E in one sector might be high or low in another—growth industries trade at higher multiples; mature industries at lower ones.

The table below suggests starting values for α across different multiples:

Symbol	Multiple	α
P/E	Price to Earnings	20
P/B	Price to Book	5
P/C	Price to Cash	50
P/S	Price to Sales	6
P/FCF	Price to Free Cash Flow	20

When α equals the industry average, a score of 0.5 marks the boundary between “cheap” and “expensive.” Stocks above 0.5 trade below the average multiple (potentially undervalued). Stocks between 0 and 0.5 trade above average but remain profitable. Stocks below zero are loss-making.

You can refine α based on sector-specific data. If tech stocks typically trade at P/E 30, setting α to 30 means a P/E of 30 produces a score of 0.5.

Measuring Changes in Transformed Scores

One issue remains. While scores are bounded between −1 and +1, percentage changes can still be unbounded. A score moving from −0.1 to +0.1 yields a percentage change of −200%—disproportionately large for a modest movement.

Instead, we measure changes relative to the total range. Since scores span from −1 to +1 (a range of 2), the relative change is:

This relative change Δ is also bounded between −1 and +1. Moving from worst to best score yields Δ = +1; best to worst yields Δ = −1. Typical quarterly movements are much smaller, enabling meaningful cross-company comparisons.

Practical Applications

This transformation enables applications that would be impossible with traditional multiples:

• Quantitative screeners can include all companies, not just profitable ones
• Time series analysis can track valuations continuously as companies move in and out of profitability
• Machine learning models receive bounded inputs without extreme values or missing data—ideal for regression, classification, and neural networks
• Risk management can monitor exposure to loss-making companies; a portfolio averaging 0.6 has a very different risk profile than one averaging −0.2

Conclusion

Traditional price multiples are useful but break down with negative fundamentals. By transforming them into bounded scores, we preserve intuitive interpretation while extending applicability to all companies.

The transformation is continuous, bounded, and meaningful. Positive scores indicate profitable companies (higher = better value). Negative scores indicate losses (lower = deeper losses). The parameter α allows calibration to specific industries.

At Akela Fund, this transformation is central to our quantitative methodology. It lets us analyze all companies—including those in difficult periods—while ensuring our models receive clean, bounded inputs that behave predictably.

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Want to see this methodology in action? Explore our stock screener to see how we apply these transformed multiples across thousands of companies.