Accounting Ratios and the Cross‐section of Expected Stock Returns

• Date: 01 November 2014
• DOI: http://doi.org/10.1111/jbfa.12092
• Author: Adriana S. Cordis
• Published date: 01 November 2014

Journal of Business Finance & Accounting

Journal of Business Finance & Accounting, 41(9) & (10), 1157–1192, November/December 2014, 0306-686X

doi: 10.1111/jbfa.12092

Accounting Ratios and the Cross-section

of Expected Stock Returns

ADRIANA S. CORDIS*

Abstract: Under clean-surplus accounting, the log return on a stock can be decomposed

into a linear function of the contemporaneous log return on equity, the contemporaneous

log dividend–price ratio (if the stock pays a dividend), and both the contemporaneous and

lagged values of the log book-to-market equity ratio. This paper studies the implications of

this decomposition for the cross-section of conditional expected stock returns. The empirical

analysis reveals that the log accounting ratios capture cross-sectional variation in both the

conditional mean and conditional variance of log stock returns, which is consistent with the

decomposition. It also brings fresh insights to the relation between firm size (market equity)

and conditional expected stock returns. The evidence indicates that the conditional median

return increases with firm size, while the conditional return skewness decreases with firm size.

Empirically, the skewness effect outweighs the median effect, leading to the well-documented

inverse relation between size and average returns. The results of out-of-sample tests suggest that

investors could use the information provided by the observed values of the log accounting ratios

to formulate more effective portfolio strategies.

Keywords: log returns, clean surplus, return on equity, book-to-market ratio, dividend yield, size

effect, portfolio skewness

1. INTRODUCTION

Stocks with high book-to-market equity (B/M) ratios tend to have higher average

returns than stocks with low B/M ratios (Rosenberg et al., 1985; Fama and French,

1992, 1993; Lakonishok et al., 1994; Barber and Lyon, 1997). This is also true for

stocks with high dividend–price (D/P) ratios (Naranjo et al., 1998; Lemmon and

Nguyen, 2008; Park and Kim, 2010). These empirical regularities are sometimes

cited as evidence of market inefficiency. The claim is that stocks with high B/M

and D/P ratios are more likely to be undervalued than stocks with the oppo-

site characteristics. Researchers who subscribe to this line of reasoning, such as

*The author is an Assistant Professor of Accounting at the College of Business Administration, Winthrop

University. The author thanks Chris Kirby for providing very detailed comments and advice, and Michael

Ryngaert for a number of helpful suggestions that improved the paper.The author is also grateful to seminar

participants at Winthrop University for comments on an earlier draft. (Paper received 24 July, accepted

15 September.)

Address for correspondence: Adriana S. Cordis, Department of Accounting, Finance and Economics,

College of Business Administration, Winthrop University, 701 Oakland Avenue, Rock Hill, SC 29733, USA.

e-mail: cordisa@winthrop.edu

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Lakonishok et al. (1994), Haughen (1995) and LaPorta (1996), contend that the

observed relation between accounting ratios and average stock returns is indicative

of irrational pricing. Proponents of market efficiency, on the other hand, argue that

the accounting ratios simply proxy for unobserved risk factors.

Regardless of which viewpoint one favors, the ongoing nature of the debate

highlights the need to develop a better understanding of why certain accounting

variables convey information about the cross-sectional properties of stock returns. I

propose a simple strategy for developing new insights in this regard. It is similar in

spirit to the well-known approach of Campbell and Shiller (1988). These authors

show that the logarithm of the gross return on a dividend-paying stock can be closely

approximated by a linear function of the log D/P ratio and log dividend growth rate.

This linear approximation has proven to be very useful in empirical research because

it can be combined with linear time-series models, such as vector autoregressive

(VAR) specifications, to generate a range of testable predictions about the behavior

of conditional expected stock returns.

I begin the analysis by considering the implications of clean-surplus accounting for

non-dividend-paying stocks. Using simple algebra, I show that the gross return on

such a stock can be expressed as a multiplicative function of the contemporaneous

return on equity (ROE), the contemporaneous B/M ratio, and the lagged B/M ratio.

Consequently, the conditional expected log return for the stock can be decomposed

into a sum of three components: the conditional expected value of the log ROE, the

conditional expected value of the log B/M ratio, and the lagged (i.e., observed) value

of the log B/M ratio. This decomposition has several noteworthy features.

First, it is derived without reference to any stock valuation model, and should

therefore hold under all valuation models. The question of whether stocks are

priced rationally or irrationally does not come into play. Second, it implies that the

lagged value of the log B/M ratio, which is observable to investors, is one determinant

of the conditional expected log stock return. This is interesting given that some

researchers view the evidence of a B/M effect in average stock returns as indicative of

market inefficiency. Third, it implies that any variable that has some ability to forecast

log ROE or the log B/M ratio should have some power to forecast log stock returns.

In view of this last feature, it is natural to posit that lagged values of the log

accounting ratios should capture cross-sectional variation in conditional expected log

stock returns. Suppose, for example, that the dynamics of the log ROE and log B/M

ratio are described by a VAR(1) process. Under these circumstances, the conditional

expected value of the log stock return is linear in the lagged values of the log ROE

and log B/M ratio. If this is true for a majority of non-dividend-paying stocks, then a

cross-sectional regression of log stock returns on lagged values of the log ROE and log

B/M ratio should be reasonably well specified. I investigate the performance of such

regressions using data for NYSE, AMEX and NASDAQ firms.

To extend the regression analysis to dividend-paying stocks, I employ the ap-

proximate linearization technique of Campbell and Shiller (1988). Under clean-

surplus accounting, the log ROE can be approximated by a linear function of the

contemporaneous log B/M ratio, the contemporaneous log D/P ratio, and the

contemporaneous log dividend growth rate. By combining this approximation with

that of Campbell and Shiller (1988), I obtain an additive decomposition of the

conditional expected log stock return for dividend-paying stocks. It takes the same

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general form as the decomposition for non-dividend-paying stocks, but it includes

the conditional expected value of the log D/P ratio as an additional term.

I fit the cross-sectional regressions suggested by the theoretical analysis using

monthly observations of firm-level stock returns and annual observations of the

accounting ratios. The returns are obtained from the Center for Research in Security

Prices (CRSP) monthly stock file and the accounting variables are obtained from the

Compustat annual industrials file. The sample period for the returns begins in July

1972 and ends in June 2013. All of the regressions use the same timing convention as

Fama and French (1992), i.e., the monthly stock returns from July of year tto June of

year t+1 are matched with Compustat information for fiscal years that end in calendar

year t−1. This ensures that the accounting ratios employed in the regressions are

lagged by a minimum of 6 months, and are therefore known to investors prior to the

start of the holding period over which the stock returns are measured.

The approach used to fit the regressions and conduct statistical inference is

straightforward. For each month in the sample period, I regress the log stock returns

for the available firms on the lagged values of the log accounting ratios. This produces

a time series of estimated slope coefficients. Two different sets of regressions are

estimated each month: one for non-dividend-paying stocks and another for dividend-

paying stocks. After fitting all of the monthly regressions, I assess whether the log

accounting ratios help to explain the cross-sectional variation in conditional expected

log stock returns. This is accomplished by looking at the t-statistics of the average

slopes for each category of stocks. The t-statistics are computed using the Fama and

MacBeth (1973) methodology.

As predicted by the theoretical analysis, the regressions produce clear evidence of a

relation between expected log returns and the lagged values of the log accounting

ratios. The average slopes for the log B/M ratio and log ROE are positive and

statistically significant for both categories of stocks, as is the average slope for the log

D/P ratio in the case of dividend-paying stocks. On the whole, the relation appears to

be somewhat stronger for non-dividend-paying stocks than for dividend-paying stocks.

This shows up primarily in the estimates for the log B/M ratio. The regression using

non-dividend-paying stocks produces an average slope for this variable that is almost

twice as large as that produced by the regression using dividend-paying stocks.

But further investigation reveals that the relation between the accounting ratios and

the cross-section of expected stock returns is more complicated than it initially seems.

If I use returns instead of log returns as the dependent variable in the regressions,

I obtain strikingly different results. Although the average slope for the log B/M

ratio remains positive and statistically significant for both non-dividend-paying and

dividend-paying stocks, the sign of the average slope for log ROE switches from positive

to negative. In addition, the average slope for the log D/P ratio becomes statistically

indistinguishable from zero. This marked sensitivity of the regression estimates to

the choice of returns or log returns as the dependent variable extends to other

specifications as well.

For instance, regressing returns on the log B/M ratio and logarithm of market

equity (ME) produces estimates similar to those reported by Fama and French (1992).

The average slope for the log B/M ratio is positive, the average slope for log ME is

negative, and each is statistically significant at the 1% significance level for both non-

dividend-paying and dividend-paying stocks. However, if I specify log returns instead

of returns as the dependent variable, I find that the average estimated slope for the log

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