Expected versus Ex Post Profitability in the Cross‐Section of Industry Returns

• Date: 01 June 2019
• Author: Andrew Detzel,Jack Strauss,Philipp Schaberl
• Published date: 01 June 2019
• DOI: http://doi.org/10.1111/fima.12231

Expected versus Ex Post Profitability in

the Cross-Section of Industry Returns

Andrew Detzel, Philipp Schaberl, and Jack Strauss∗

Asset pricing theory predicts a positive cross-sectionalrelation between expected profitability and

expected returns. However, empirical studies typically use lagged ex post profitability as a proxy

for expected profitability. In this article, we use out-of-sample combination forecasts to estimate

expected industry-level operatingprofit, gross profit, operating cash flow,and net income. We then

construct real-time industry-rotation strategies based on high and low expected profitability. For

each measure except gross profit, these predicted-profitability strategies earn significant alpha

net of transaction costs and outperform strategiesbased on ex post profitability.

Numerous recent studies document that firm prof itability positively predicts the cross-section

of stock returns in North America, Asia, and Europe (e.g., Fama and French, 2006, 2015, 2017;

Novy-Marx, 2013; Ball et al., 2015; Hou, Xue, and Zhang, 2015). Motivated by this evidence,

investment companies and information providers such as Dimensional Fund Advisors, AQR, and

MCSI offer profitability-based products (e.g., Trammel, 2014; Kalra and Celis, 2016). Although

these studies all use historical (ex post) measures of profitability, the underlying theory predicts

a positive relation between expected returns and expected profitability in the cross-section. In

this article, we propose a novel method of forecasting profitability out of sample and investigate

whether expected profitability contains important asset pricing information not captured by ex

post profitability.

We estimate expected profitability with forecast combination methods to extract information

from a panel of candidate predictors. Combination forecasts are weighted averages of individ-

ual forecasts and benefit from a diversification-like effect. If the prediction errors of individual

forecasts are imperfectly correlated, combination forecasts can be more accurate out of sample

than even the best individual forecast (for a recent survey, see Timmermann, 2006). Consistent

with the diversification benefit, prior studies show that combination forecasts significantly im-

prove the predictability of economic time series such as output or stock returns out of sample

(e.g., Stock and Watson, 2004; Rapach, Strauss, and Zhou, 2010; Detzel and Strauss, 2018). By

choosing weights based on historical forecast performance, combination forecasts can also, over

time, effectively extract relevant information from a set of candidate predictors.

To use combination forecasts, aggregating individual stocks into portfolios is necessary

to obtain regular-frequency time series with low idiosyncratic noise. For our asset-pricing

tests, these portfolios must plausibly have variation in returns attributable to variation in

predicted profitability that is orthogonal to ex post profitability. Based on this criterion, we

follow Detzel and Strauss (2018) and forecast profitability of industry portfolios as opposed to

For helpful comments and suggestions, we thank Bing Han (Editor) and an anonymous referee as well as conference

participants at the 2015 FrontRange Finance Seminar.

∗Andrew Detzel is an Assistant Professor of Finance in the Daniels College of Business at the University of Denver in

Denver,CO. Philipp Schaberlis an Assistant Professor of Accounting in the Monfort College of Business at the University

of Northern Colorado in Greeley, CO. Jack Strauss is a Professor and the Miller Chair of Applied Economics in the

Daniels College of Business at the University of Denver in Denver, CO.

Financial Management •Summer 2019 •pages 505 – 536

506 Financial Management rSummer 2019

characteristic-sorted portfolios. The latter have little cross-sectional variation in returns that is

uncorrelated with the sorting characteristic (e.g., Lewellen, Nagel, and Shanken, 2010). Industry

selection is further central to many real-world equity strategies and is therefore interesting to

asset managers and investors. Value-weighted industries also have relatively low transaction

costs as they put little weight on small-cap stocks. This benefit increases the likelihood that

investors can actually capture cross-sectional patterns in industry returns.

Several of the studies cited here compare the performance of different measures of profitability

in predicting returns. Contributing to this body of research, we evaluate the performance of

expected versions of different profitability measures. Using our combination forecast methods,

we construct out-of-sample predicted-profitability measures for operating profit (OP), g ross

profit (GP), operating cash flow (CF), and net income (NI).1

Toconstruct our set of candidate predictors, we f irst include all four profitability measures given

that they are all driven bythe same underlying state variables. Our remaining candidate predictors,

which are motivated by theory and prior evidence, include: industry-level real investment, stock

returns, and book-to-market (BM) ratios, as well as the cross-sectional average (aggregate) of the

industry-level predictors and their recursively estimated principal components.

We apply our out-of-sample forecasts of profitability to construct portfolio-rotation strategies

that buy portfolios with the highest predicted profitability and short por tfolios with the lowest

predicted profitability. Testing whether these portfolios outperform asset pricing factors based on

ex post profitability assesses whether expected profitability contains signif icant incremental asset

pricing information. To ensure investorscan capture the alphas we f ind, we correct our strategies

for transaction costs and evaluate their performance using a generalized alpha that accounts for

these costs following Novy-Marx and Velikov (2016). This method involves estimating effective

transaction costs for individual stocks and applying them to our trading strategies. These strategy

transaction costs precisely capture variation in transaction costs over time and across portfolios.

FollowingHou et al. (2015), we use quarterly accounting data, which are the timeliest available,

but limit the sample period due to data availability. Data over the five-year period 1975:1–1979:4

serve as an initial training sample for our combination forecasts, and we recursively expand this

training sample each quarter to generate the subsequent quarter’s forecasts. We assess forecast

and trading-strategy performance for the out-of-sample period from 1980:1 to 2015:4.

We summarize our findings as follows. Over 1980:1–2015:4, the industry-specific, aggregate,

and principal-components-based predictors significantly predict each measure of profitability

at the quarterly frequency for each industry. On average, each industry’s prior-quarter (ex post)

profitability predicts current-quarter prof itability with in-sample R2s of 3% to 33% depending on

choice of OP,GP,CF,orNI. Adding the other industry- and aggregate-level predictor variables

increases adjusted R2s to 18% to 52%. This increase is significant at the 1% level for all four

profitability measures and nearly all industries. Similarly,adding the principal components of each

profitability measure, which captures cross-industry predictive information, further signif icantly

increases predictability for most industries’ profitability with adjusted R2s increasing to 20% to

61% on average. Overall, the in-sample evidence shows that industry-level, aggregate-level, and

cross-industry accounting and market variables forecast industry profitability.

Our choice of out-of-sample combination forecast method, discounted mean-squared forecast

error (DMSFE), assigns weights to individual forecasts that are inverselyrelated to their historical

mean-squared forecast errors (MSFEs). The DMSFE method therefore effectively extracts rele-

vant forecasting information from our set of candidate predictors over time. On average,DMSFE

1Our order in the text and tables of the profitability measures reflects the order of their introduction in the literature, with

OP, the most recently introduced, first.

Detzel, et al. rExpected versus E x Post Profitability 507

forecasts have 6% to 25% lower out-of-sample mean-squared forecast errors than a simple au-

toregression benchmark for each industry’sprof itability, depending on the choice of OP,GP,CF,

or NI. Clark and West(2007) statistics indicate that these forecast er ror reductions are significant

for 66% to 93% of industries. Thus, our combination forecasts are relatively precise estimates of

expected profitability compared to the ex post values of OP,GP,CF, and NI.

The long legs of the industry-rotation strategies based on predicted profitability earn large

average excess returns, ranging from 9.7% to 11.2% per year. Conversely, the short legs earn

2.3% to 3.5% less per year on average. With the exception of the GP-based strategies, the long

legs earn significant alphas of about 3% per year with respect to the Hou et al. (2015) model,

which includes a factor based on ex post profitability. Controlling for transaction costs reduces

this figure to 2.3% to 2.6% per year, but the statistical significance remains.2In contrast to

the long legs, the alphas for the short legs of our predicted-profitability strategies are generally

insignificant. These results are interesting given that alphas are generally stronger on the short

legs of anomaly strategies where arbitrage costs are higher (e.g., Stambaugh, Yu, and Yuan,

2012). Moreover, impediments to short selling would not prevent a real investor from capturing

the net-of-costs alphas on our strategies.

We also form long-short strategies based on ex post OP,GP,CF, and NI. In contrast to the

predicted-profitability strategies, the ex post strategies do not earn significant alphas with respect

to the Hou et al. (2015) model. Moreover, with the exception of strategies based on predicted

GP, the long legs of the predicted-profitability strategies (and the long-short strategies based

on predicted OP and CF) each earn significant alphas with respect to a four-factor model that

consists of the Hou et al. (2015) market, size, and investment factors along with our long-short

strategy based on ex post profitability. Thus, predicted profitability contains significant asset

pricing information that is not captured by ex post profitability.

Although prior studies such as Novy-Marx (2013) and Ball et al. (2015) find differences

in how well the ex post version of each metric predicts the cross-section of returns, we find

that performance is qualitatively similar for strategies based on predicted OP,CF, and NI.In

contrast, strategies based on predicted GP perform similarly to those based on ex post GP.

This is not surprising given that GP—revenues minus cost of goods sold (COGS)—omits time-

varying expenses such as sales, general, and administrative, and is the most persistent measure

of profitability. Hence, industries with the highest GP typically have the highest expected GP as

well. This finding is also related to Kisser (2014), who finds that the gross prof itability premium

is largely driven by persistent differences in operating leverage. Firms with low variable costs

such as low COGS will have persistently high operating leverage and GP, all else equal.

The main contribution of this study is to evaluate the role of expected profitability in the

cross-section of returns. Our study is related to Detzel and Strauss (2018) who use combination

forecasts to predict industry returns out of sample with the cross-section of industry BM ratios

and form trading strategies based on these predicted returns. In contrast to their study, we use

a different set of predictor variables with a different economic motivation and sort industries

based on predicted profitability, not predicted returns. This study is further related to the broader

literature that tries to forecast stock returns out of sample (e.g., Goyal and Welch, 2008; Rapach

et al., 2010; Kelly and Pruitt, 2013). Rather than predict returns, we predict profitability out of

sample, which results in cross-sectional variation in expected returns.

This article proceeds as follows. Section I explains the theoretical importance of expected

profitability. Section II describes our data and combination forecast methods. Section III presents

2The reductions in alpha from correcting our strategies for transaction costs are not large because of the relatively low

cost of trading value-weighted industries compared to trading the Hou et al. (2015) factors.