The q‐Factors and Macroeconomic Conditions: Asymmetric Effects of the Business Cycles on Long and Short Sides*

Date01 December 2020
AuthorTai‐Yong Roh,Changjun Lee,Jangkoo Kang,Byoung‐Kyu Min
Published date01 December 2020
The q-Factors and Macroeconomic
Conditions: Asymmetric Effects
of the Business Cycles on Long
and Short Sides*
Discipline of Finance, Business School, The University of Sydney, Sydney, Australia
Graduate School of Finance, Korea Advanced Institute of Science and Technology
(KAIST), Seoul, Republic of Korea
College of Business, Hankuk University of Foreign Studies, Seoul, South Korea and
Advanced Institute of Finance and Economics, Liaoning University,
Shenyang, China
We examine whether the q-factorsthe investment factor (INV) and the
return-on-equity factor (ROE)are related to the macroeconomy. We nd
reliable evidence that returns on INV are positively related to future eco-
nomic growth. When conditioning on good and bad states of the business
cycle, we show that returns on INV are signicantly higher during good
states than bad states. We also nd that the conditioning effect of economic
conditions on INV is asymmetric between long and short sides of INV. On
the other hand, we nd that returns on ROE are negatively associated with
future aggregate earnings change. The relations remain robust even in the
presence of business cycle variables and after controlling for the book-to-
market effect.
JEL Codes: G12
Accepted: 14 November 2018
Understanding the cross-section of expected stock returns has long been a
central research question for nancial economists. Among empirical asset-
pricing models, the Fama and French (1993) three-factor model has served
as a benchmark for risk adjustment, since it explains most CAPM-related
anomalies (Fama and French 1996). However, the empirical performance of
* The authors thank Huining Cao (the Editor) and the an anonymous referee for valuable comments
to improve the article greatly. This study was supported by Hankuk University of Foreign Studies
Research Fund.
© 2018 International Review of Finance Ltd. 2018
International Review of Finance, 20:4, 2020: pp. 897921
DOI: 10.1111/ir.12250
the FamaFrench three-factor model has weakened over the last two
decades. For example, it does not capture the associations of average returns
with short-term prior returns, nancial distress, net stock issues, and asset
Motivated by q-theory, Hou et al. (2015) (hereafter, HXZ) develop a new
four-factor model as an alternative. The four factors are (i) the market factor
(MKT), dened as the realized market excess return, (ii) the size factor (SMB),
dened as the difference between the returns on small-market equity and big-
market equity portfolios, (iii) an investment factor (INV), dened as the differ-
ence between the returns on low investment-to-assets portfolios and high
investment-to-assets portfolios, and (iv) a return-on-equity factor (ROE), dened
as the difference between the returns on high return-on-equity portfolios and
low return-on-equity portfolios. The empirical performance of the HXZ four-
factor model is striking. It explains many cross-sectional patterns of average
stock returns that the famous FamaFrench three-factor model fails to account
for, including (i) the momentum effect, (ii) the nancial distress anomaly, and
(iii) other anomalous patterns associated with net stock issues and asset growth.
Despite the HXZ four-factor models outstanding empirical performance, it is
not obvious whether its estimates of expected returns represent a reward for
bearing risk or a result associated with nonrisk characteristics. This uncertainty
arises because the q-factors are composed of portfolio returns constructed from
rm characteristics, and are not macro variables themselves (although the fac-
tors are motivated by q-theory). One necessary condition for any factor serving
as an accurate measure of risk adjustment is that it should, at some level, relate
to intuitive macroeconomic risk. The present paper aims to better understand
the ability of INV and ROE to explain anomalous returns by thoroughly exam-
ining the relation between the q-factors and actual macroeconomic
To take one step in that direction, we rst ask whether the performance of
zero-cost portfolios, INV and ROE, is related to future economic growth. For
INV, we nd that the average returns of INV are higher in good economic states
1 The momentum effect refers to the fact that stocks with high (low) returns over the preceding
several months tend to have high (low) future returns (Jegadeesh and Titman 1993). The
nancial distress anomaly refers to the negative association between average returns and
nancial distress using the common measures of bankruptcy risk as proxies of nancial dis-
tress (Campbell et al. 2008). The negative association between average returns and net stock
issues is referred to as the net stock issues anomaly (Daniel and Titman 2006; Pontiff and
Woodgate 2008). The asset growth anomaly refers to the scenario in which rms that invest
more earn lower subsequent average returns (Titman et al. 2004; Cooper et al. 2008).
2 HXZ (2015) include the size factor in their q-factor model because (i) it helps explain the aver-
age returns across the size deciles and (ii) the addition of size factor enables them to compare
the empirical performance of their model with the Carhart (1997) model since the two
models have the same number of factors. In this paper, however, we do not study the size fac-
tor since the goal of our paper is to investigate the relation between q-factors and macroeco-
nomic conditions.
© 2018 International Review of Finance Ltd. 2018898
International Review of Finance

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