Profitability and Investment Factors

Value and size explained a lot of cross-sectional stock returns, but not everything. Two cheap-looking companies with identical book-to-market ratios can have very different future returns if one is a profitable cash machine and the other is a struggling shell propped up by debt. Fama and French's answer, added in 2015, was two more factors: one that rewards profitability, one that rewards investment discipline.

The analogy

Picture two houses listed at the same price per square foot. One rents out reliably every month and needs little upkeep; the other is a money pit constantly swallowing renovation cash with no rent to show for it. "Cheap per square foot" alone (value) does not distinguish them. You need two more questions: how much income does it actually generate (profitability), and how much is being poured back into it versus paid out (investment). Fama and French built factors around exactly these two questions.

Building the two factors

Profitability (RMW, "robust minus weak"). Sort stocks by operating profitability, revenue minus costs and interest, scaled by book equity, and go long the most profitable third, short the least profitable third:

$\text{RMW}_t = R_{\text{robust},t} - R_{\text{weak},t}.$

In words: a portfolio that is long companies whose businesses actually generate income relative to their book value, and short companies that do not, rebalanced periodically using each company's most recently reported profitability.

Investment (CMA, "conservative minus aggressive"). Sort stocks by how fast total assets grew over the past year, and go long the slowest-growing (most conservative) third, short the fastest-growing (most aggressive) third:

$\text{CMA}_t = R_{\text{conservative},t} - R_{\text{aggressive},t}.$

In words: a portfolio long companies that grew their asset base cautiously, short companies expanding aggressively, on the empirical finding that aggressive asset growth tends to precede weaker, not stronger, future stock returns.

Both factors slot into the regression alongside market, size, and value, giving the five-factor model:

$R_i - R_f = \alpha_i + \beta_1(R_m-R_f) + \beta_2\,\text{SMB} + \beta_3\,\text{HML} + \beta_4\,\text{RMW} + \beta_5\,\text{CMA} + \epsilon_i.$

Picture the horizontal axis as a firm's asset growth rate and the vertical axis as its subsequent one-year return: the negative slope is exactly what CMA is built to capture, fast growers tend to underperform slow growers, on average, holding other factors fixed.

Worked example 1: computing RMW for a small universe

Five stocks have operating profitability (as a fraction of book equity) of 18%, 15%, 10%, 6%, and 2%. Sorting into thirds by profitability, the top group (18%, 15%) goes long, the bottom group (6%, 2%) goes short, the middle stock (10%) is excluded. If the long group returns 9% this month and the short group returns 4%, then $\text{RMW} = 9\% - 4\% = 5\%$ for that month, a profitability portfolio return of positive five percentage points, entirely independent of overall market direction since it is long and short in equal size.

Worked example 2: a stock's five-factor decomposition

A stock has loadings $\beta_1 = 1.1$, $\beta_2 = 0.3$, $\beta_3 = 0.2$, $\beta_4 = -0.5$, $\beta_5 = 0.1$ against a month where the factors realized $R_m-R_f=2\%$, $\text{SMB}=1\%$, $\text{HML}=0.5\%$, $\text{RMW}=3\%$, $\text{CMA}=-1\%$. Expected return, ignoring alpha: $1.1(2)+0.3(1)+0.2(0.5)-0.5(3)+0.1(-1) = 2.2+0.3+0.1-1.5-0.1 = 1.0\%$. The negative RMW loading does real work here: this stock is unprofitable-tilted, so a strong month for profitability actually hurt its expected return by 1.5 points.

What this means in practice

Quality-focused strategies, "buy cheap, profitable, disciplined companies", are effectively long RMW and CMA simultaneously. Risk models that omit these two factors will misattribute a quality tilt's returns to alpha, overstating a quality manager's apparent skill.