A long stream of papers documents correlations between firm characteristics and future stock returns.
Empirical asset pricing research interprets some of these observed ‘characteristic’correlations as
evidence of a risk–return relationship and then proceeds to construct asset pricing models with
common risk factors based on the characteristics, as in Fama and French (1993). Many of the
characteristicsinvolve accounting numbers, such as book-to-price,book rate-of-return, and investment.
However, thesecharacteristics have largely been identifiedsimply by observing what predicts returns in
the data, a data mining exercise that has resulted in a proliferation of characteristics.
A number of
explanations for the phenomena have been offered, although many of these are just conjectures.
Presumably to emphasizethe severity of the problem, Novy-Marx (2014) findsthat returns predicted by
many of the observed characteristics can be explained by sunspots, the conjunction of the planets, the
temperature recorded at Central Park Weather Station in Manhattan, and other seeming absurdities.
This paper presents a framework for identifying valid accounting characteristics for asset pricing,
yielding additional conditions for the identification beyond simply predicting returns in the data. The
framework develops from an expression that connects expected returns to expectations of earnings and
earnings growth, with the connection to risk determined by accounting conditions. An identified
characteristic is one that satisfies those conditions. The ability to predict returns empirically then serves
We apply the framework to investigate book-to-price (B/P), identified in a ‘characteristic
regression model,’by Fama and French (1992) (FF) who then proceeded to construct an asset pricing
model in Fama and French (1993) that includes a book-to-price factor. That model stands as perhaps
the premier empirical asset pricing model, though subsequent research has expanded the set of
characteristics to promote additional common factors, resulting in a proliferation of factors (as well as
There is little theory for why B/P might indicate risk, though conjectures abound.
Our framework provides an explanation: under a specified accounting that bears resemblance to
generally accepted accounting principles (GAAP), B/P forecasts expected earnings growth that the
market deems to be at risk. Our empirical analysis supports the predictions from our framework.
However, while the framework validates B/P in the FF model, it also points to earnings-to-price
(E/P) as a valid characteristic. Indeed, with no expected earnings growth, E/P alone predicts the
expected return and B/P is irrelevant. With growth, the weight shifts to B/P. The paper also shows that
the relative weights are related to firm size, another FF factor: for smaller firms that typically have
higher growth expectations, B/P is important for forecasting returns but, for large firms with lower
growth expectations, B/P is not important while E/P takes primacy. Further, the paper shows how the
relative weights on E/P and B/P depend on the accounting, with the expected return under fair value
In a survey of published papers and working papers, Harvey, Liu, and Zhu (2016) find 316 predictors, a number they say
likely under-represents the total. Green, Hand, and Zhang (2013, 2014) find that, of 333 characteristics that have been
reported as predictors of stock returns, many predict returns incrementally to each other.
Additional factors include momentum (Jegadeesh & Titman, 1993), investment (Hou, Xue, & Zhang, 2015; Liu, Whited,
& Zhang, 2009), profitability (Fama & French, 2015; Novy-Marx, 2012), accruals quality (Francis, LeFond, Olsson, &
Schipper, 2005), among others.
Explanations for book-to-price include: (i) distress risk (Fama & French, 1992); (ii) the risk of ‘assets in place’vs. ‘risk of
growth options’(Berk, Green, & Naik, 1999; Zhang, 2005); (iii) low profitability (Fama & French, 1993); (iv) high
profitability (Novy-Marx, 2012); (v) investment (Cooper, Gulen, & Schill, 2008; Gomes, Kogan, & Zhang, 2003; Hou
et al., 2015; Novy-Marx, 2012); (vi) operating leverage (Carlson, Fisher, & Giammarino, 2004); and (vii) q-theory
(Cochrane, 1991, 1996; Lin & Zhang, 2013).
PENMAN ET AL.