The size premium and macrovolatility risks: Evidence from U.S. and U.K. equity markets

• Published date: 01 July 2019
• Author: Sungjun Cho
• DOI: http://doi.org/10.1002/ijfe.1717
• Date: 01 July 2019

Received: 14 June 2016 Revised: 11 December 2018 Accepted: 4 January 2019

DOI: 10.1002/ijfe.1717

RESEARCH ARTICLE

The size premium and macrovolatility risks: Evidence from

U.S. and U.K. equity markets

Sungjun Cho

Alliance Manchester Business School,

Crawford House, University of

Manchester, Oxford Road,Manchester

M13 9PL, UK

Correspondence

Sungjun Cho, Alliance Manchester

Business School, Crawford House,

University of Manchester, Oxford Road,

Manchester M13 9PL, UK.

Email: sungjun.cho@mbs.ac.uk

JEL Classification: E32; E52; G12

Abstract

The size effect is alive well but visible only when the economy is in high volatil-

ity regimes. This paper develops variant conditional asset pricing tests for the

size effect with independent business cycle and volatility regimes and shows that

the size effect is present conditionally during the high-volatility regimes. This

result is robust across two countries (United States and United Kingdom) with

various specifications and the January effect. An economic rationale for the rela-

tion between the size premium and macrovolatility risk is provided through the

capital-market-imperfection hypothesis.

KEYWORDS

capital-market imperfections, great moderation, the size premium, volatility-regime switching

1INTRODUCTION

Banz (1981) first reports that small-capitalization firms

on the New York Stock Exchange (NYSE) earned higher

average returns than is predicted by the CAPM from 1936

to 1975. Fama and French (1993) adopt this empirical

fact and develop their three-factor asset pricing model

with the market excess return (RMRF) and two mim-

icking portfolios based on market capitalization (SMB)

and book-to-market (HML). The Fama–French model has

become an industry standard because it can explain the

averagereturn variations across portfolios formed on many

different characteristics. Fama and French interpret their

two mimicking portfolios as risk factors capturing a risk

premium for the relative distress of firms in the context

of ICAPM while the underlying economic source of the

risk premium has not yet fully understood. Further, the

same empirical findings are documented with interna-

tional data, and as a result, international Fama–French

three-factor models are developed (see for instance,

Griffin, 2002; Bekaert, Hodrick, & Zhang, 2009).

van Dijk (2011) surveys the literature on the size effect

and identifies two seemingly contradictory developments

in research since the late 1990s; many theoretical models

are developed to explain the size effect (e.g., Berk, Green,

& Naik, 1999), but most of the empirical studies find that

the size effect has disappeared since the early 1980s. For

example, Horowitz, Loughran, and Savin (2000) report

that U.S. small firms did not earn higher average realized

returns than big firms after its discovery in 1980, and Dim-

son and Marsh (1999) find the similar phenomenon for the

U.K. data. Schwert (2003) asserts that “it seems that the

small-firm anomaly has disappeared since the initial pub-

lication of the papers that discovered it." It is well known

that if the anomalies are a result of data-snooping bias,

these are expected to disappear in the data soon after they

have been reported. If this is indeed the case, the SMB

factor may not be interpreted as a systematic risk factor

to generate a risk premium in the rational-asset-pricing

model.

Interestingly, Hou and van Dijk (2010) argue that the

size effect exists in ex ante expected returns but might

not be visible in realized returns. They show that small

firms experience large negative profitability shocks after

the early 1980s, while big firms experience large positive

shocks. After filtering out this noise, they find a robust

Int J Fin Econ. 2019;24:1271–1286. wileyonlinelibrary.com/journal/ijfe ©2019 John Wiley & Sons, Ltd. 1271

1272 CHO

size effect in expected returns and ask for a revival of aca-

demic research on the size effect. Based on the careful

summary of the literature, van Dijk (2011) (p. 3263) also

argues “it is premature to conclude that the size effect has

gone away...whether and how existing models can be rec-

onciled with known patterns in the returns on small and

large stocks is not clear." Finally Fama and French (2015)

show the evidence for the size effect in U.S. market using

their five-factor model.

This paper documents a new stylized fact on the size

effect to resolve this seemingly puzzling issue. Specifically,

motivated by Lettau, Ludvigson, and Wachter (2008),

this paper develops conditional asset pricing tests using

regime-switching models for the growth rate of U.S.indus-

trial production and the U.S. or U.K. size premium. As

a result, mean and volatility regimes are separately iden-

tified. The estimated mean regimes are closely tracking

business-cycle patterns, and the volatility regimes pick

up the so-called great moderation from 1984 to 2007.

While it is often said that recessions coincides with the

high-volatility regimes, the correlation of two regimes in

United States are moderate (e.g., 0.26 since July 1963).

The empirical findings from these conditional tests

unequivocally indicate that the U.S. or U.K. SMB factor

earns a significant risk premium only in uncertain macroe-

conomic states (measured as high-volatility regimes of

industrial production growth), even though it has almost

zero risk premium unconditionally. This new stylized fact

on the relation between the size premium and macro-

volatility risks is quite robust across various specifica-

tions and with the January effect. Arguably, the so-called

“Great Moderation"coined by Ben Bernanke (or low macro

volatility regimes) has effectively masked the size effect

until recently. Kim and Nelson (1999) and McConnell

and Perez-Quiros (2000) show that U.S. output volatility

had declined substantially in the early 1980s. This period

coincides with the initial publication of the size effect.

However, the size effect has been resurrected since the

recent financial crisis coupled with uncertain economic

environment. For example, the average monthly size pre-

mium for US was 1.615% during 2008.

Interestingly, recent empirical asset-pricing studies also

emphasize the role of macroeconomic volatility move-

ments in determining risk premia. For example, Boguth

and Kuehn (2013) show that time variation in consump-

tion volatility is a negatively priced source of risk for vari-

ous test portfolios. Bansal, Kiku, Shaliastovich, and Yaron

(2014) also find that macroeconomic volatility risks (mea-

sured as realized variance of industrial production growth)

carry a sizeable positive risk premium and help explain

the cross-section of expected equity returns. Further, the

empirical findings of this paper suggest that the changing

macroeconomic volatility has an important implication

on the changing size premium. While it is not yet fully

understood why macrovolatility risks are important for

understanding risk premia, we have one good theoretical

explanation on the size premium. Perez-Quiros and Tim-

mermann (2000), based on the imperfect capital-market

theories, claim that small firms with little collateral do

not have the same access to credit markets that are

enjoyed by large firms and argue that the high returns to

small firms (SMB) might be compensation for taking this

credit-related risk because small firms are more affected

by tight-credit market conditions interpreted as recession

periods.

Perhaps, in well-developed U.S. and U.K.financial mar-

kets, recession itself would not hamper raising capitals

for the small-sized firms unless it coincides with the

high uncertainty. While the lack of data makes it diffi-

cult to test this hypothesis directly, there are some indi-

rect evidence to support this line of arguments. First,

using OECD data, Mendicino (2007) documents a nega-

tive and significant relation between credit market size

(financial depth) and the volatility of output, consump-

tion, investment, investment in residential properties, and

housing prices. Tang and Yan (2010) find that average

credit-default swap (CDS) spreads are increasing in gross

domestic product (GDP) growth volatility. Further, Baum,

Caglayan, and Ozkan (2009) report the potentially adverse

effects of macroeconomic volatility on the allocation of

banks' lending behavior. This adverse effects would affect

small firms significantly because small firms are more

dependent on bank loans while large firms have bet-

ter access to direct sources of credit such as commer-

cial paper (e.g., Gertler & Gilchrist, 1994). Finally the

credit crunch induced by higher macroeconomic volatil-

ity could hit small firms with less collateral the hardest

while larger firms were less affected by renegotiating their

loans or using commercial paper or corporate bonds (e.g.,

Holmstrom & Tirole, 1997).

The rest of the paper is organized as follows: Section

2 discusses the empirical models; Section 3 describes the

data; Section 4 presents the estimation results; and Section

5 concludes.

2EMPIRICAL MODELS

This section develops empirical methods used to test the

existence of the size premium; the first subsection briefly

describes a regime-switching model with mean and volatil-

ity regimes for the U.S. industrial-production growth, and

the second subsection explains how to test whether a factor

is redundant unconditionally. The third subsection com-

bines these two models and presents the main econometric

specifications for conditional asset pricing tests.