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

• Date: 01 September 2018
• Author: Francesco Reggiani,İrem Tuna,Stephen H. Penman,Scott A. Richardson
• Published date: 01 September 2018
• DOI: http://doi.org/10.1111/eufm.12171

DOI: 10.1111/eufm.12171

ORIGINAL ARTICLE

A framework for identifying accounting

characteristics for asset pricing models, with

an evaluation of book-to-price

Stephen H. Penman

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Francesco Reggiani

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Scott A. Richardson

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İrem Tuna

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1

Department of Accounting, Columbia

Business School, New York

Email: shp38@columbia.edu

2

Department of Business Administration,

University of Zurich, Zurich, Switzerland

Email:

francesco.reggiani@business.uzh.ch

3

AQR Capital Management, Greenwich,

Connecticut

4

Department of Accounting, London

Business School, London, UK

Emails: srichardson@london.edu;

ituna@london.edu

Funding information

PwC Switzerland

Abstract

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

theory.

KEYWORDS

accounting principles, book-to-price, earnings-to-price, growth and risk

JEL CLASSIFICATION

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 O’Brien, 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.

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© 2018 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2018;24:488–520.

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INTRODUCTION

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.

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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

characteristics).

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There is little theory for why B/P might indicate risk, though conjectures abound.

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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

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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.

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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.

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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).

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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.

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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.

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THE FRAMEWORK: CONNECTING E/P AND B/P TO

EXPECTED RETURNS

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.

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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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