A framework for identifying accounting characteristics for asset pricing models, with an evaluation of book‐to‐price

Date01 September 2018
AuthorFrancesco Reggiani,İrem Tuna,Stephen H. Penman,Scott A. Richardson
Published date01 September 2018
DOI: 10.1111/eufm.12171
A framework for identifying accounting
characteristics for asset pricing models, with
an evaluation of book-to-price
Stephen H. Penman
Francesco Reggiani
Scott A. Richardson
İrem Tuna
Department of Accounting, Columbia
Business School, New York
Email: shp38@columbia.edu
Department of Business Administration,
University of Zurich, Zurich, Switzerland
AQR Capital Management, Greenwich,
Department of Accounting, London
Business School, London, UK
Emails: srichardson@london.edu;
Funding information
PwC Switzerland
We provide a framework for identifying accounting
numbers that indicate risk and expected return. Under
specified accounting conditions for measuring earnings and
book value, book-to-price (B/P) indicates expected returns,
providing justification for B/P in asset pricing models.
However, the framework also points to earnings-to-price
(E/P) as a risk characteristic. Indeed, E/P, rather than B/P, is
the relevant characteristic when there is no expected
earnings growth, but the weight shifts to B/P with growth.
Using this framework we resolve a puzzle: in contrast to
previous empirical research, we find that leverage is
positively associated with future returns, as predicted by
accounting principles, book-to-price, earnings-to-price, growth and risk
G11, G12, M41
We are grateful to the Editor, Lu Zhang, and an anonymous referee for their helpful comments on prior drafts. We thank
Andrew Ang, David Ashton, Ray Ball, Stephen Brown, Jason Chen, Peter Christensen, Kent Daniel, Francisco Gomes,
Antti Ilmanen, Ralph Koijen, Matt Lyle, Patricia OBrien, Jim Ohlson, Tapio Pekkala, Ruy Ribeiro, Tjomme Rusticus, Kari
Sigurdsson as well as seminar participants at Bristol University, London Business School, Norges Bank Investment
Management, Stockholm School of Economics, The University of Chicago Booth School of Business, University of
Waterloo, University of Technology Sydney, and University of Zurich for helpful discussions and comments. Earlier
versions of the paper were under the title, An Accounting-Based Characteristic Model for Asset Pricing.Francesco
Reggiani acknowledges support from PwC Switzerland.
© 2018 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2018;24:488520.
A long stream of papers documents correlations between firm characteristics and future stock returns.
Empirical asset pricing research interprets some of these observed characteristiccorrelations as
evidence of a riskreturn 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
as validation.
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 placevs. 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).
accounting (where B/P =1) given by E/P, but with the weight shifting to B/P under historical cost
accounting (where B/P is typically different from 1).
The paper also applies the framework to investigate the pricing of financing leverage risk in the FF
model. FF factors are said to incorporate financing risk, but there is no formal analysis as to why.
Indeed, Penman, Richardson, and Tuna (2007) show that the FF model does not price financing
leverage appropriately. Our framework separates the components of E/P and B/P that pertain to
operating risk from those that pertain to financing risk, with the expected returns associated with each
identified and reconciled to the expected equity return in accordance with the Modigliani and Miller
(1958) leveraging equation.
This separation enables us to revisit an issue long outstanding in empirical asset pricing: While a
basic tenet of modern finance, formalized in Modigliani and Miller (1958), states that, for a given level
of operating risk, expected equity returns are increasing in financial leverage, research has had difficulty
in documenting the positive relation. Indeed, papers largely report negative returns to leverage.
This is
puzzling given how fundamental the idea is that leverage requires a return premium. The failure to
validate such a fundamental tenant of modern finance is presumably due to a failure to identify and
control for operating risk. By unlevering E/P and B/P to capture operating risk, we are able to show that
equity returns are increasing in leverage. This not only yields an empirical documentation of the
leverage effect that has escaped earlier research, but also validates our framework: it identifies operating
risk such that one observes that leverage is appropriately priced. And it points to a deficiencyin the FF
model: both E/P and B/P are relevant and, once that is recognized, leverage prices according to theory.
Our analysis maintains the standard assumption in asset pricing research that the market prices risk
efficiently. There is no imperative, of course, but we wish to address the research on its own grounds.
The framework involves two key ideas. First, expected returns can be expressed in terms of expected
earnings and subsequent earnings growth, with that expected return determined by the risk that these
expected outcomes will not be realized. Second, given price, B/P and E/P are accounting phenomena,
so how they connect to risk and return depends on the accounting. With the focus on B/P, the
framework establishes conditions for the accounting for book value under which B/P can (or cannot)
indicate the risk of expected earnings and earnings growth not being realized. Further, as book value
and earnings articulate under accounting principles, the accounting for book value also determines
earnings, and thus E/P is also identified as a potential risk characteristic.
We stress that the framework is not a formal model that connects accounting characteristics to
priced risk. That would require a generally accepted asset pricing model (that identifies priced risk),
and that we (collectively) do not have. While the general form is laid out in no-arbitrage asset pricing
theory in terms of common risk factors and sensitivities to those factors, it is the identification of factors
that has proved difficult. That, of course, is what the ad hoc empirical approach is trying to do
identifying characteristics from correlations with returns in the data and it is at this level that this
paper operates. However, rather than identifying characteristics simply by observed correlations with
returns, the framework sets up additional conditions to be satisfied. The empirical analysis then tests
whether these conditions are indeed satisfied.
See Bhandari (1988), Johnson (2004), Nielsen (2006), George and Hwang (2010), Ippolito, Steri, and Tebaldi (2011), and
Caskey, Hughes and Liu (2012), for example. Penman et al. (2007) report the negative relation with the FF model.

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