A.7.3 Value & Profitability

Basic Prerequisites: 02 · Fundamental Factors and Core Financial Ratios · Valuation Multiples.

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1. Intuition & Practical Objective

Value says buy cheap; profitability says buy good. This page is where the two meet - and where the naivest reading of each fails. The objective is one idea from Robert Novy-Marx (2013): profitability is “the other side of value” - profitable firms earn higher returns than unprofitable ones, even though they are systematically more expensive. And the reverse is the value trap: the cheapest stocks by book-to-market are often cheap because they are unprofitable.

The two facts sit awkwardly together, and resolving them is the whole craft:

• Value works - high book-to-market (cheap) and high earnings-yield firms earned higher average returns (Basu 1983; Fama–French 1992).
• But a naive value sort is a value-trap machine. The cheapest firms by B/M are disproportionately distressed, unprofitable businesses whose cheapness is a correct forecast of deterioration. Buying “cheap” blindly buys the junk.
• Profitability is the filter that rescues it. Novy-Marx’s gross profitability - the rawest measure of pricing power, gross profit over assets - predicts returns with roughly the same power as book-to-market, and it is negatively correlated with it (profitable firms are more expensive). So the two correct each other: value filters the froth, profitability filters the traps.

The practical output is the combined screen: rank on value and profitability and hold the intersection - the “good and cheap” basket that Greenblatt’s magic formula (earnings yield + ROIC) and Piotroski’s F-score (value + quality) both operationalize. This page builds the value and profitability axes; 04 · Quality & F-scores builds the quality composite.

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2. Mathematical Ground Truth & Derivations

Value characteristics. With BE book equity, ME market equity, NI net income:

$$\text{B/M}=\frac{\text{BE}}{\text{ME}},\text{E/P}=\frac{\text{NI}}{\text{ME}}=\frac{1}{\text{P/E}}.$$

Both ask “is the price cheap relative to a fundamental?” High B/M anchors value on book capital; high E/P anchors it on earnings. Both are priced: Fama–French 1992 showed the cross-section is captured by size + B/M, and E/P carries value information of its own.

Profitability - Novy-Marx’s gross profitability. Let $GP=S-\text{COGS}$ be gross profit and TA total assets:

$$\frac{GP}{A}=\frac{S-\text{COGS}}{\text{TA}}.$$

Deliberately stripped down to the layer before SG&A, R&D, interest and taxes, gross profitability is the purest accounting signal of the business’s pricing power - how much of every sales dollar survives the direct cost of goods. Novy-Marx (2013) shows high-$GP/A$ firms earn higher returns despite having higher valuation ratios (more expensive) - the empirical wedge that value alone misses.

The trap and the resolution. Because high-$GP/A$ firms tend to be low-B/M (expensive growth), a single sort on B/M and a single sort on $GP/A$ are two near-independent (in fact mildly negatively correlated) orderings. The two-factorial claim is:

$$\text{good}\&\text{cheap}=\text{rank}(B/M)\cap \text{rank}(GP/A),$$

and the composite that Fama–French 2015 embeds in the model - HML (value) + RMW (profitability) - is precisely this pair, with each roughly neutralized against size.

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3. Computational Implementation - the “other side of value” in one script

Stdlib only. Twelve firms with book equity, market cap, gross profit and assets. The script (a) shows the gross profitability premium is monotone, (b) shows that profitable firms are more expensive yet earn more - the naive value sort loses here because cheap = unprofitable - and (c) shows that within the cheap basket, the profitable firms beat the value traps.

Read the two tercile lines together - they are Novy-Marx’s headline. Gross profitability is a clean monotone premium (5.51 → 6.04 → 7.34%). But a naive value sort goes the wrong way in this universe: the cheapest (highest B/M) tercile earns the least (5.74%) because the cheapest firms are exactly the unprofitable value traps. The resolution is the last block: within the cheap basket, the profitable cheap firms (5.79%) beat the unprofitable ones (5.46%). Profitability doesn’t replace value - it is the filter that lets value work.

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4. Failure Modes & First-Principles Breakdowns

1. The value trap (cheap = bad). The deepest first-principle failure of a naive value sort: cheapness is often a correct market forecast of deterioration. Buy “cheap” blindly and you buy the distressed and the dying. This is why every serious value implementation layers a quality/profitability filter on top (Novy-Marx, Piotroski, Greenblatt).
2. Ignoring the value-profitability confound. Sorting on one without controlling for the other misattributes the premium. A univariate B/M sort that ignores profitability over-weights the traps; a univariate $GP/A$ sort that ignores value over-weights expensive growth names. The two must be conditioned on each other (double-sort or multivariate).
3. Convention drift in “profitability.” Gross profitability, ROE, and ROIC are different numbers with different denominators (assets, equity, invested capital) and different tax/loss conventions - see Core Financial Ratios · Profitability. A “profitability factor” is only comparable if the definition is fixed.
4. Non-monotonicity in practice. Real value and profitability premia are concentrated in extreme deciles and can be weak or negative in the middle of the cross-section - the monotone tercile pattern on this page is a constructed idealization, not a market guarantee (see 05 · Failure Modes).

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5. References

• Fama & French: “The Cross-Section of Expected Stock Returns” (JF, 1992)
• Novy-Marx, Robert: “The Other Side of Value: The Gross Profitability Premium” (JFE, 2013) - gross profitability predicts with roughly the same power as book-to-market, and profitable firms earn more despite higher valuation ratios; verified against the corpus paper.
• Fama & French: “A Five-Factor Asset Pricing Model” (JFE, 2015)
• Basu, Sanjoy: “The Relationship Between Earnings Yield, Market Value and Return for NYSE Common Stocks” (JFE, 1983)
• Greenblatt, Joel: The Little Book That Beats the Market
• Hou, Xue & Zhang: “Digesting Anomalies” (RFS, 2015)

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6. Connected Graph Bridges

• Back: 02 · Fundamental Factors · Index Hub
• Forward: 04 · Quality & F-scores (the composite that layers quality onto value)
• Base: Core Financial Ratios · Valuation Multiples · Graham Criteria & Value Investing
• Factor-model layer: Fundamental Multi-Factor Models