Profitability, Investment and Average Returns (Digest Summary)

Several researchers, most notably Fama and French, have shown that stocks with higher
book-to-market ratios provide higher returns. Studies also have found that stock returns
are positively related to the company’s profitability and company strength
(expected net cash flows) and negatively related to accruals. What is different in this
paper is that the authors test for the effects of profitability and investment (asset
growth) on expected returns by estimating the valuation equation in three steps: (1)
first-stage regressions to develop proxies for expected profitability and investment,
(2) second-stage cross-section return regressions with simple proxies (lagged
profitability and asset growth variables) and more complicated proxies (fitted values of
profitability and asset growth variables from first-stage regressions), and (3)
portfolio and model specification tests comparing predicted with actual returns. More
specifically, proxies for the expected values of profitability and investment are
developed based on accounting fundamentals, the company’s stock return,
analysts’ earnings forecasts, and a composite measure of company strength as
explanatory variables.

Tests to explain stock returns are based on multiple regression models starting with the
base model and then adding the other relevant explanatory variables in a progressive
manner. This approach enables the authors to discern the marginal effects of the new
variables and the changes in the overall explanatory power of the model.

The base model consists of just two variables—company size and B/M (book-to-market
ratio)—to explain their effects on stock returns, and only the coefficient for B/M
is significant, showing a positive relation to the stock returns. Next, lagged
profitability and lagged asset growth (simple proxies for expected profitability and
investment) are added to the model. The data show that the stock returns are positively
associated with profitability and negatively associated with asset growth. The
coefficient for B/M remains about the same and is statistically significant. Next,
accruals are added and the coefficient for positive accruals is found to be negatively
related to stock returns. Finally, two variables reflecting company strength
(probability of default on debt and a composite index of company strength developed by
Piotroski [Journal of Accounting Research, 2000]) are included in the
model. The coefficient for the probability of default variable is negative and that for
company strength is positive.

In the second set of regressions, the authors repeat the same format—progressive
addition of explanatory variables—but this time they use the fitted values of
profitability and asset growth (more complicated proxies for expected profitability and
investment) to explain their effects on stock returns. The regression coefficients
reveal that the fitted values (as opposed to lagged values in previous regressions)
produce weaker evidence of profitability effects in stock returns and a lack of
relationship with respect to asset growth. The question that came next is, Why do simple
lagged profitability and asset growth variables produce better descriptions of average
returns than the more complicated proxies do? The authors explain that it could be
caused by two sources of measurement error when the regression-fitted values are used as
explanatory variables for returns.

Next, the authors conduct robust checks comparing predicted returns with actual returns
on portfolios. For this analysis, they allocate individual stocks to one of the two
portfolios formed according to high or low expected returns relative to the median
returns for the year and by two weighting schemes—equally weighted and value
weighted. The findings generally reveal that the predicted average spreads of returns
between high and low portfolios are fairly similar for both equally weighted and
value-weighted portfolios. Interestingly, for equally weighted portfolios, the average
actual return spread (between low and high portfolios) is larger than the corresponding
prediction spread. For value-weighted portfolios, the average actual return spread
(between low and high portfolios) is smaller than the corresponding prediction spread.
From this, the authors infer that the average return effects are stronger among smaller
companies. Addition of lagged profitability and asset growth to the base model (with the
company size and book-to-market ratio already in the model) increases the average
predicted spreads and actual spreads, but only modestly. Adding positive and negative
accruals increases those values further. The measures of company strength do not seem to
have any economically meaningful information about expected returns beyond what is
conveyed by profitability, asset growth, and accruals.

The authors then check for pervasiveness of return predictions and specification of the
model. For this analysis, the authors allocate individual stocks to different portfolios
formed according to two size groups—small and big—and three book-to-market
groups—from low to high.

In baseline regressions (with only company size and B/M as explanatory variables), the
variation in average spreads (between predicted high-minus-low returns) is rather large
among the six size–B/M portfolios. The average actual spreads in returns replicate
the predicted spreads reasonably well, with the exception of the small-growth portfolio.
All six size–B/M portfolios show improvement in average predicted and actual
return spreads with the addition of lagged profitability and growth to the base model.
Adding lagged accruals to the model increases the high-minus-low spreads modestly in all
six size–B/M groups for both predicted and actual returns (again with the
exception of the small-growth group).