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price from underlying value, imparts bias to estimates in mean returns and return premia. To mitigate the effects of noisy prices
on empirical regressions, we follow their suggestion for bias correction by constructing the VW portfolios, using the prior month
market cap as the weighting variable. The six portfolios that are double sorted based on Size and B/M are denoted as SH, SN, SL,
BH, BN, and BL, and the value factor HML is calculated as [(SH − SL) / 2 + (BH − BL) / 2]. The profitability and investment factors
of the 2 × 3 sorts, RMW and CMA, are defined similarly using OP and Inv instead of B/M as the second sorting criterion. The Size
factor, SMB, is the average of the three stock portfolio returns (SMB
B/M
,SMB
OP
,andSMB
Inv
), which are constructed by averaging
the difference between three small and large B/M, OP, and Inv stock portfolio returns for each month, respectively. As a proxy for
the excess market portfolio return, Mkt, we use VW monthly return including all A-share stocks listed on SHSE and SZSE in excess
of the monthly deposit interest rate calculated using the one-year deposit interest rate.
The second approach in our tests is for portfolios constructed from the 2 × 2 sorts on Size and B/M, OP, or Inv, where the
breakpoint for MBM and GEM A-share stocks is the median MBM market cap and the other three firm characteristics. Similar
to those factors from the 2 × 3 sorts
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, factors from the 2 × 2 sorts are also roughly neutral with respect to Size. However, the
HML, RMW and CMA factors are only neutral with respect to their own firm characteristics, as they are constructed without con-
trolling for the other two firm variables. For example, the average HML return is a mix of premiums related to B/M, OP, and Inv
since it is constructed without isolating the effects of the latter two variables. To further jointly neutralize the effects of four firm
characteristics, the return on factors is constructed from the 2 × 2 × 2 × 2 sorts on Size, B/M, OP, and Inv. We construct 16 VW
portfolios from the intersections of two Size groups, two B/M groups, two OP groups, and two Inv groups using MBM medians as
breakpoints. Then, factors from the 2 × 2 × 2 × 2 sorts are calculated as the differences between average returns on eight port-
folios (small minus big, high minus low B/M, robust minus weak OP or conservative minus aggressive Inv). Unlike factors from
the 2 × 3 or 2 × 2 sorts, factors from the 2 × 2 × 2 × 2 sorts are roughly neutral with respect to the other three variables.
The SMB factor, for example, is roughly neutral with respect to value, profitability, and investment. In other words, it better iso-
lates the premiums in average returns related to B/M, OP, and Inv. One should note, however, that the five-factor exposures for
HML, RMW, and CMA from the 2 × 3 and 2 × 2 sorts may isolate the premia in average returns related to value, profitability, and
investment as effectively as the factors from the 2 × 2 × 2 × 2 sorts, as multivariate regression coefficients estimate marginal ef-
fects. Moreover, there is no reason to expect that neutrality with respect to firm characteristics may lead to low correlation be-
tween factor returns. Details on the construction of factors is provided in Table A.1.
2.2.2. LHS portfolios
We construct 25 Size-B/M, Size-OP, and Size-Inv portfolios to use as LHS assets in asset pricing regressions. The Size, B/M, OP,
and Inv quintile breakpoints use only MBM stocks, while the sample includes all MBM and GEM stocks. The 25 VW double-sorted
portfolios are then calculated using prior month VW monthly excess returns from July of year t to June of year t +1,rebalancing
the portfolios at the end of June each year. Similar to the problem of factor construction shown above, the Size-B/M, Size-OP, and
Size-Inv portfolios do not isolate value, profitability, and investment effects in average returns because their firm characteristics
(B/M, OP, and Inv) are correlated. Following FF (2015a), we construct portfolios with 2 × 4 × 4 sorts on Size and pairs of the
other three variables (B/M, OP, and Inv). To spread stocks more evenly, the portfolios are allocated to two Size groups (Small
and Big) using the MBM median market cap breakpoint. Stocks in each Size group are then allocated independently to four B/
M, OP, or Inv groups using MBM quartile breakpoints specific to the Size group.
2.3. Summary statistics for factor returns
Panel A of Table 1 shows descriptive statistics for the means, standard deviations and t-statistics of monthly factor returns. In U.S.
data for 1963–2013, FF (2015a) find that the factors for three versions appear with significantly positive risk premiums. In our sample,
however, we find that only the mean monthly time series premium for the SMB factor is significantly different from zero. Size pre-
miums (average SMB returns) for China for 1997–2015 are large, 1.014% per month (from the 2 × 3 sorts) to 1.041% per month
(from the 2 × 2 sorts) for the three versions of the factors. Recall that each factor except Mkt from the 2 × 2 and 2 × 3 sorts controls
for Size and one other firm characteristic. The factors from the 2 × 2 × 2 × 2 sorts control for all four firm characteristics. Joint controls
have little effect on SMB. The standard deviations of SMB are similar, but with more than 3.6 standard errors from zero, larger than
those in FF (2015a) (more than 2.3 standard errors from zero). The correlations of the different versions of SMB are also very high,
from 0.986 to 1.000, largely because the Size breakpoint for the three versions of SMB is the MBM median market cap, and they
use all stocks for factor construction.
The three versions of the Mkt factor have large positive equity premiums (average Mkt returns) (insignificant), 0.833% per month
(t = 1.440). The results in Table 1 show that the descriptive statistics for the HML, RMW, and CMA factors rely on the version of factor
portfolio constructions. The average HML, RMW, and CMA returns are larger in the 2 × 3 sorts than the 2 × 2 and the 2 × 2 × 2 × 2 sorts
mainly because in former versions, stocks in the middle 40% of B/M, OP, and Inv are excluded for factor construction. For example,
the average HML return is 0.132% per month in the 2 × 3 sorts versus 0.060% per month in the 2 × 2 sorts and 0.041% per month in
the2×2×2×2sorts.Profitability premiums (average RMW returns) for China are low, 0.021% per month in the 2 × 3 sorts, 0.011%
per month in the 2 × 2 sorts, and even become slightly negative in the 2 × 2 × 2 × 2 sorts (− 0.009% per month). Investment premiums
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Gray and Johnson (2011) construct the AGfactor (a factor-mimicking portfolio based on asset growth) that is neutral with respect to B/M rather than Size. In an
untabulated analysis, we replicate their approach by constructing the profitability and investment fact ors neutral to B/M, along the lines of Gray and Johnson
(2011). The results remain robust and are available upon request.
145Q. Lin / Emerging Markets Review 31 (2017) 141–163