Fama–French in China: Size and Value Factors in Chinese Stock Returns

• Author: Yuan Shao,Jiang Wang,Can Chen,Grace Xing Hu
• Published date: 01 March 2019
• DOI: http://doi.org/10.1111/irfi.12177
• Date: 01 March 2019

Fama–French in China: Size and

Value Factors in Chinese Stock

Returns*

GRACE XING HU

†,‡

,CAN CHEN

§

,YUAN SHAO

§

AND JIANG WANG

‡,¶,k

†

School of Economics and Finance, University of Hong Kong, Hong Kong

‡

CAFR, Shanghai, P.R. China

§

Shanghai Advanced Institute of Finance, Shanghai Jiao Tong University,

Shanghai, P.R. China

¶

MIT, Sloan School of Management, Cambridge, MA, USA and

k

NBER, Cambridge, MA, USA

ABSTRACT

We investigate the size and value factors in the cross-section of returns for

the Chinese stock market. We find a significant size effect but no robust

value effect. A zero-cost small-minus-big (SMB) portfolio earns an average

premium of 0.61% per month, which is statistically significant with a t-value

of 2.89 and economically important. In contrast, neither the market portfo-

lio nor the zero-cost high-minus-low (HML) portfolio has average premiums

that are statistically different from zero. In both time-series regressions and

Fama–MacBeth cross-sectional tests, SMB represents the strongest factor in

explaining the cross-section of Chinese stock returns. Our results contradict

several existing studies which document a value effect. We show that this

difference comes from the extreme values in a few months in the early years

of the market with a small number of stocks and high volatility. Their impact

becomes insignificant with a longer sample and proper volatility adjustment.

JEL Codes: G10; G12; G15

Accepted: 18 December 2017

I. INTRODUCTION

A large body of asset pricing literature has been devoted to document and

explain cross-sectional stock returns beyond the classic Capital Asset Pricing

Model (CAPM). Earlier papers include Stattman (1980), Banz (1981, 1983), and

Chan et al. (1991), which found empirical cross-sectional return patterns

* The authors acknowledge the support from China Academy of Financial Research (CAFR) and are

grateful to Meiling Chen, Chenjun Fang, Yue Hu, and Lun Li for valuable research assistance. The

authors benefit greatly from comments from Jun Pan, Fangzhou Lu and the seminar participants at

the Chinese International Conference of Finance 2016. We are also deeply grateful to the support

from our industry partner, WIND Info at Shanghai, China.

© 2018 International Review of Finance Ltd. 2018

International Review of Finance, 19:1, 2019: pp. 3–44

DOI: 10.1111/irfi.12177

inconsistent with the CAPM. In two influential papers, Fama and French (1992,

1993), the authors showed that size, as measured by market capitalization, and

value, as measured by the book-to-market ratio, are the two most significant

factors in explaining the cross-sectional returns in the US stock market. Since

then, size and value premiums have become two of the most widely used

“asset-pricing”factors in the United States and global equity markets.

1

There has been limited study on the cross-sectional returns in the Chinese

stock market, even though it has quickly grown to be the second largest in the

world by market capitalization.

2

Research has been hindered by the lack of high

quality data and by the short history of the market. Existing work relies on data

of varied quality and sample periods and obtains results often inconsistent with

each other.

3

Such a situation is particularly unsatisfying as most empirical work

on the Chinese stock market needs an empirical pricing model to benchmark

risk and returns. Taking advantage of a complete database recently put together,

we hope to provide a more definitive empirical calibration of the return factors

in the Chinese stock market.

Inparticular,weexaminetheroleofsizeandvaluefactorsinexplainingthe

cross-sectional returns in the Chinese A-share market from its beginning in

1990–2016. Our benchmark sample period is from July 1995 to December 2016,

which contains enough number of stocks in the cross-section. We find that size is

strongly associated with cross-sectional returns. The average returns on the 10 port-

folios formed on the basis of market capitalization show a robust negative relation-

ship with the underlying stocks’size. The average return on the smallest size decile

is 1.84% per month during the period, versus 0.10% on the largest size decile. A

long-short portfolio which longs the smallest size portfolio and shorts the largest

size portfolio earns an average return of 1.23% per month, not only economically

large but also strongly significant at the 1% level. Moreover, the observed relation-

ship between stock returns and firm size cannot be explained by the market factor,

as the market beta is flat across the 10 size-sorted portfolios. By comparison, we

observe no pattern in the average returns of the 10 book-to-market (B/M)-sorted

portfolios. A long-short portfolio which longs the highest B/M ratios portfolio and

shorts the lowest B/M ratios portfolio earns an average return of 0.38% per month

with a t-value of only 1.51, which is not statistically significant from zero.

We then follow the methodology in Fama and French (1993) to construct

two zero-cost portfolios, small-minus-big (SMB), and high-minus-low (HML), to

1 Studies of non-US markets Fama and French (2012), Brückner et al. (2014), Michou

et al. (2013), Veltri and Silvestri (2011), Moerman (2005), Nartea et al. (2008), Chou

et al. (2012), Docherty et al. (2013), Cordeiro and Machado (2013), Agarwalla et al. (2013),

Drew and Veeraraghavan (2002), among others.

2 See, for example, monthly report for 2014 by the World Federation of Exchanges.

3 These papers include Cakici, Chan, and Topyan (2015a), Chen et al. (2010), Carpenter

et al. (2014), Wang and Xu (2004), Cakici, Chatterjee, and Topyan (2015b), Hilliard and

Zhang (2015), Cheung et al. (2015), Wang and Di Iorio (2007), Wong et al. (2006), Wu

(2011), Eun and Huang (2007), Huang and Yang (2011), Chen et al. (2007), Morelli (2012),

and so forth. We will discuss these papers in more detail later.

© 2018 International Review of Finance Ltd. 20184

International Review of Finance

mimic risk factors related to size and value in the Chinese stock market. Over

our sample period, SMB earns an average return of 0.61% per month, or 7.32%

per year. The average return of SMB is not only economically large but also

strongly significant with a t-value of 2.89. In contrast, neither the market port-

folio R

M

−R

f

nor the factor mimicking portfolio HML has significant average

returns during the same sample period. The average excess return of the market

portfolio is 0.52% per month with a t-value of 1.22; the average return of HML

is 0.23% per month with a t-value of 1.40. The dominant performance of SMB

over the market portfolio and HML implies that size is likely to be important in

explaining cross-sectional returns, while the market portfolio and HML are not.

For formal asset pricing tests, we employ both the time-series and the Fama–

MacBeth regressions. In the time-series regression, we first form 25 portfolios

on the basis of size and book-to-market ratio. There is a large dispersion in the

average excess returns across the 25 portfolios, ranging from −0.58% per month

to 1.94% per month. Among them, nine portfolios have significant positive

average excess returns. We then regress the excess returns of the 25 stock port-

folios on the market portfolio R

M

−R

f

and the two factor mimicking portfolios

SMB and HML.

The time-series regression results show that the three factors capture strong

common variations in the stock returns of the 25 portfolios, as reflected in the

significant slopes on the three risk factors and the high R

2

values of the regres-

sions. More important, judging on the basis of the intercepts of the time-series

regressions, the three factors together successfully capture the cross-sectional

variations in average returns on the 25 portfolios. The remaining intercepts,

that is, the αs, of the regressions of the excess returns on the 25 portfolios on

the three factors, R

M

−R

f

, SMB, and HML, are small in magnitude, ranging from

−0.36% to 0.46% per month. Using the Gibbons–Ross–Shanken test, we obtain

aF-statistic of 1.42 with p-value 0.79 and therefore cannot reject the hypothesis

that the intercepts across the 25 portfolios are jointly zero.

Moreover, the three factors contribute differently to the reduction of

αs. Using the market factor R

M

−R

f

alone, the intercepts remain strongly signifi-

cant and widely dispersed. Twelve out of the 25 portfolios still have positive

intercepts that are significant from zeros and two portfolios have negative

significant intercept. Similarly, HML also plays a weak role in explaining cross-

sectional returns. Whether used alone or in combination with the market fac-

tor, the intercepts of majority portfolios in the bottom three size quintiles

remain large and statistically significant. In contrast, SMB, when used as the

sole risk factor, can make the intercepts of all portfolios statistically insignifi-

cant from zeros. Putting all evidence together, it is clear that SMB is the most

important factor in explaining the cross-sectional variations in average stock

returns.

We then perform the Fama–MacBeth regression to estimate the risk pre-

miums associated with the market, SMB, and HML factors. The results are con-

sistent with the time-series regression findings. SMB is estimated to have a risk

premium of 0.96% per month, strongly positively significant with a t-value of

© 2018 International Review of Finance Ltd. 2018 5

Fama–French in China