Anomalies and Multi-Factor Models in the Chinese Market

Abstract

A stock market anomaly refers to the occurrence of excess returns in stocks that cannot be fully explained by traditional asset pricing models or the efficient market hypothesis. Studying these anomalies allows scholars to gain deeper insights into the stock market and provides investors with opportunities to capitalize on these irregularities for higher returns. In this paper, the size and value factors in the Chinese stock market are empirically tested for the period from January 2002 to December 2021, leading to several conclusions. First, the CH-3 model is found to be more suitable for the Chinese market compared to the FF-3 model. Additionally, the interpretation of anomalies using CH-3 differs from prior research, particularly regarding the CH-4 model, which incorporates a share turnover factor. These differences may stem from potential data mining effects.

Full text

Highlights in Business, Economics and Management
ECRM 2024
Volume 44 (2024)
159
Anomalies and Multi-Factor Models in the Chinese Market
Yiheng Feng
School of Economics and Management, Nanjing University of Science and Technology, Nanjing,
China
976470151@qq.com
Abstract. A stock market anomaly refers to the occurrence of excess returns in stocks that cannot
be fully explained by traditional asset pricing models or the efficient market hypothesis. Studying
these anomalies allows scholars to gain deeper insights into the stock market and provides investors
with opportunities to capitalize on these irregularities for higher returns. In this paper, the size and
value factors in the Chinese stock market are empirically tested for the period from January 2002 to
December 2021, leading to several conclusions. First, the CH-3 model is found to be more suitable
for the Chinese market compared to the FF-3 model. Additionally, the interpretation of anomalies
using CH-3 differs from prior research, particularly regarding the CH-4 model, which incorporates a
share turnover factor. These differences may stem from potential data mining effects.
Keywords: Anomalies, Multi-factor model, Investment strategy portfolio.
1. Introduction
Both domestic and international stock markets exhibit phenomena of excess returns that cannot be
fully explained by asset pricing models or the efficient market hypothesis, which scholars refer to as
stock market anomalies. In the United States, scholars have studied and published research on
hundreds of stock market anomalies, while in China, the number of published studies on such
anomalies remains relatively small, leaving many anomalies yet to be explored. From the perspective
of the efficient market hypothesis, there should not be so many anomalies in the market, and two
main reasons could explain their occurrence.
The first is data mining. In the United States, numerous scholars have demonstrated that many
published stock market anomalies are actually spurious, resulting from data mining. For example,
Linnainmaa and Roberts (2018) constructed new out-of-sample data to examine the performance
differences of 36 accounting-based anomalies in the U.S. stock market, both in-sample and out-of-
sample. Their analysis revealed that most of these anomalies failed out-of-sample, suggesting that
they are more likely a product of data mining rather than unknown risks or mispricing. Similar
research has been conducted in China as well. For instance, Hou, Xue, and Zhang (2017) replicated
447 anomalies proposed by the academic community, covering six categories: momentum,
value/growth, investment, profitability, intangible assets, and trading frictions. After excluding the
impact of small-cap stocks, 64% of these anomalies were no longer significant; if the t-statistic
threshold was raised to 3.0, 85% of the anomalies lost significance. Furthermore, using the four-factor
model proposed by Hou, Xue, and Zhang (2015) as the pricing model, 98% of the anomalies lost
significance, with only 11 anomalies remaining valid.
The second possible reason for anomalies is related to the choice of regression models used to
explain them. If only the CAPM model is used as the explanatory model, many anomalies will show
significant alpha values that CAPM cannot explain. However, as pricing models become more refined
and the number of factors increases, many anomalies become insignificant. Thus, there is still ample
room for further exploration of anomaly factors in the Chinese market.
By conducting in-depth research on stock market anomalies, we can not only enhance our
understanding of market mechanisms but also provide investors with strategic insights, enabling them
to capitalize on these irregularities to achieve excess returns.

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2. Literature review
Stock market anomalies (or market anomalies) refer to the phenomenon of excess returns in stocks
that cannot be fully explained by asset pricing models or the efficient market hypothesis. Anomaly
factors (or abnormal variables) are indicators that describe these phenomena, which may not have a
specific meaning but can reliably explain average cross-sectional stock returns. Not long after the
CAPM model was introduced, foreign scholars discovered the existence of stock market anomalies,
and in the following decades, hundreds of anomalies were identified. Since the establishment of the
Shanghai Stock Exchange at the end of 1990, although China's securities market has only had a
history of over 20 years, the modern investment theories of Western securities markets have gradually
drawn the attention of domestic scholars. Over the past two decades, Chinese scholars have conducted
extensive research on China's stock market and have discovered numerous anomalies. According to
the methodology of Hou, Xue, and Zhang (2018), these anomalies can be broadly categorized into
five types: inertia, value and growth, investment, profitability, and trading frictions.
First, in terms of inertia anomalies, the unexpected earnings effect is a typical example. Many
scholars have conducted in-depth studies on the unexpected earnings phenomenon in China and have
confirmed its existence. Furthermore, research has revealed different factors driving this phenomenon,
with some scholars approaching it from the perspective of the efficient market hypothesis, while
others explain it from a behavioral finance viewpoint. The research on inertia and reversal phenomena
is also varied; some scholars have found that the Chinese stock market exhibits short-term and long-
term inertia along with medium-term reversals, while other studies suggest that the reversal
phenomenon is significant but inertia is not.
Second, regarding value and growth anomalies, the book-to-market ratio effect and the price-to-
earnings ratio (P/E) have been widely studied. Liu et al. (2018), using data from the Chinese A-share
market between 2000 and 2016, compared metrics such as earnings-to-price ratio (E/P), book-to-
market ratio, asset-to-market ratio, and cash flow-to-market ratio, concluding that the E/P ratio is
more suitable as a value factor in the Chinese market. Similarly, multiple studies have shown a
significant negative correlation between the P/E ratio and stock returns, meaning that the higher the
P/E ratio, the lower the future stock returns.
Regarding investment anomalies, domestic research generally suggests that there is a significant
negative correlation between investment rates and stock returns in the Chinese stock market. For
profitability anomalies, the applicability of the Fama-French five-factor model in the Chinese market
has been repeatedly tested. While some studies have found that the profitability factor does not yield
significant excess returns, others, such as Liu, Stambaugh, and Yuan (2018), have shown a significant
positive correlation between the profitability factor and expected stock returns.
Lastly, trading friction anomalies include size effects and idiosyncratic volatility. Meng Yong et
al. (2019) found that size effects are significantly present in the A-share market, with smaller firms
earning higher average returns than larger firms. However, some studies show that size effects are
not significant in other markets. Additionally, Zhang Bing (2021) used data from 1996 to 2016 to
demonstrate that stable idiosyncratic volatility anomalies exist in the Chinese stock market, with
higher idiosyncratic volatility stocks tending to have higher expected returns.
In terms of anomaly explanation models, Fama and MacBeth (1973) were the first to test the
CAPM model, finding a significant positive relationship between market beta and returns. However,
subsequent research uncovered numerous anomaly factors that CAPM could not explain. To better
account for these market anomalies, Fama and French (1993) introduced the three-factor model,
which added size and book-to-market factors to explain the excess returns that CAPM could not
account for. However, the three-factor model also faced challenges, such as the presence of
momentum effects, which raised questions about its explanatory power. Carhart (1997) added a
momentum factor to the Fama-French three-factor model, resulting in the four-factor model.
Over time, more anomalies were discovered, prompting researchers to propose new pricing models.
Hou, Xue, and Zhang (2015) introduced the q-factor model based on the q-theory, incorporating
market, size, investment, and profitability factors. They demonstrated that the q-factor model

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outperformed the Fama-French three-factor and Carhart four-factor models in explaining anomalies.
Similarly, Fama and French (2015) recognized the need to add new factors to their pricing model,
proposing a five-factor model that includes investment and profitability factors. Additionally,
Stambaugh and Yuan (2017) constructed a mispricing four-factor model by aggregating multiple
anomaly factors, showing that this model performed better than the q-factor model and the Fama-
French five-factor model in explaining anomalies.
Liu, Stambaugh, and Yuan (2018) proposed the CH three-factor model for the Chinese market.
After excluding the smallest 30% of stocks by market capitalization, they selected the earnings-to-
price ratio (EP) as the value factor and demonstrated that the CH three-factor model is more suitable
for the Chinese market than the Fama-French three-factor model. Lastly, Daniel, Hirshleifer, and Sun
(2020) introduced the Daniel-Hirshleifer-Sun three-factor model, applying behavioral finance to asset
pricing and explaining mispricing phenomena, further expanding the understanding of stock market
anomalies.
3. Data and variable definitions
3.1. Data
The research subject of this paper includes all A-share stocks listed on the Shanghai and Shenzhen
stock exchanges, excluding financial companies and stocks with missing data. The data types used
include monthly stock trading data and financial statement data, with all raw data sourced from the
GTA CSMAR financial database.
Although China's securities market has developed for over twenty years, the available historical
data for research is not abundant, particularly in the early stages of market development, where the
number of stocks was relatively small, making it difficult to meet the requirements for large-scale
and repeated grouping. Additionally, cash flow statement data has only been disclosed since 1998,
and quarterly financial statement data became gradually available from 2002. The factors constructed
in this paper rely on data from the three major financial statements, with most factors being built
based on quarterly data. To ensure consistency, the sample data period used for constructing the
quarterly factors spans from January 2002 to December 2021.
We also impose several filters. First, we exclude stocks that have become public within the past
six months. Second, we exclude stocks having (i) less than 120 days of trading records during the
past 12 months or (ii) less than 15 days of trading records during the most recent month. The above
filters are intended to prevent our results from being influenced by returns that follow long trading
suspensions. Third, we eliminate the bottom 30% of stocks ranked by market capitalization at the end
of the previous month. Market capitalization is calculated as the closing price times total shares
outstanding, including nontradable shares.
3.2. Variable definitions
We survey the literature documenting anomalies in China and compile, to the best of our
knowledge, an exhaustive list of stock characteristics identified as cross-sectional predictors of future
returns. This list comprises nine categories: size, value, profitability, volatility, investment, accruals,
illiquidity, reversal, and turnover. Within each category, one or more firm-level characteristics are
identified as predictors of returns. The anomalies categorized are as follows:
Size: The stock’s market capitalization is used in this category. It is computed as the previous
month’s closing price times total A shares outstanding, including nontradable shares.
Value: Three variables are used. Earnings-price ratio (EP). Earnings equals the most recently
reported net profit excluding nonrecurring gains/losses. A stock’s EP is the ratio of earnings to the
product of last month-end’s close price and total shares. Book-to-market ratio (BM). Book equity
equals total shareholder equity minus the book value of preferred stocks. A stock’s BM is the ratio of
book equity to the product of last month-end’s close price and total shares. Cash-flow-to-price (CP).
Cash flow equals the net change in cash or cash equivalents between the two most recent cash flow

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statements. A stock’s CP is the ratio of cash flow to the product of last month-end’s close price and
total shares.
Profitability: Profitability is assessed using firm-level Return on Equity (ROE) calculated at a
quarterly frequency. ROE is a key financial metric that measures a company's ability to generate
profit from its shareholders' equity. Specifically, the value of ROE is determined by the ratio of a
firm's earnings to its book equity.
Volatility: Stocks with lower historical volatility tend to provide better future performance.
Volatility refers to the degree of variation in a stock's price over time, often measured by the standard
deviation of returns. Stocks with lower historical volatility tend to provide better future performance.
This observation can be attributed to the fact that lower volatility stocks are perceived as less risky
by investors. Consequently, these stocks often attract a more stable investor base and can experience
less dramatic price swings during market fluctuations.
Investment: Companies that invest less (or have lower asset growth) often generate higher returns.
Illiquidity: Stocks that are less liquid typically yield higher returns due to the liquidity premium.
Reversal: The sorting measure used is the stock’s one-month return, computed as the cumulative
return over the past 20 trading day
Turnover: Higher turnover rates may indicate momentum effects, where stocks with higher trading
volumes can lead to greater future returns.
4. Methodology
4.1. Fama-French Three-Factor Model
Fama and French (1993) expanded on the Capital Asset Pricing Model (CAPM) by introducing
two additional factors: value (FFHML) and size (FFSMB), proposing the Fama-French three-factor
model, which is regarded as the pioneer of multifactor models:

  
 

 
  
󰇛󰇜 
󰇛󰇜 (1)
Where 
represents the risk-free rate for stock ; 
denotes the market return at time ;

signifies the expected return of asset  at time ; 
  
 is the market risk premium;
󰇛󰇜 is the expected return of the size factor; 󰇛󰇜is the expected return of the book-
to-market ratio factor; and 
, 
, 
represent the stock's exposure to the respective
factors.
To construct the value and size factors, Fama and French (1993) utilized the book-to-market ratio
(BM) and market capitalization, applying a 2×3 independent double sorting method. In the sorting
process, they used the median market capitalization of firms listed on the New York Stock Exchange
(NYSE) to categorize companies on the NYSE, NASDAQ, and American Stock Exchange (AMEX)
into two groups: small-cap (Small) and large-cap (Big). Similarly, they divided the firms listed on the
NYSE into three groups based on the 30th and 70th percentiles of the BM ratio: firms with BM above
the 70th percentile were classified as High, those below the 30th percentile as Low, and those in
between as Middle.
After these classifications, six groups were formed, labeled as S/H, S/M, S/L, B/H, B/M, and B/L.
The returns of the stocks within each group were then value-weighted to create six investment
portfolios. Using these portfolios, Fama and French (1993) constructed the HML and SMB factors
using the following methodology:
  
󰇛    󰇜
󰇛    󰇜 (2)
  
󰇛  󰇜
󰇛  󰇜 (3)

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4.2. CH Three-Factor and Four-Factor Models
The CH three-factor model differs from the Fama-French three-factor model in that its value factor
is based on the earnings-price (EP) ratio. Additionally, to eliminate the influence of the "shell" effect,
the model excludes the smallest 30% of companies by market capitalization when constructing its
three factors. The model’s specific form is as follows:

  
 

 
  
󰇛󰇜 
󰇛󰇜 (4)
Where 
represents the risk-free rate for stock ; 
denotes the market return at time ;

signifies the expected return of asset  at time ; 
  
 is the market risk premium; The
terms 
 
, 󰇛󰇜, 󰇛󰇜denote the expected returns of the market factor, size factor,
and the earnings-price ratio factor, respectively. The coefficients 
, 
, 
 represent the
stock’s exposure to these respective factors.
The construction of the factors is similar to that of the Fama-French three-factor model, so it will
not be discussed in detail here.
The high turnover rate of a stock may be driven by investor optimism. Regulations on short-selling
not only limit the correction of overpriced stocks but also establish a link between sentiment and
turnover. As Baker and Stein (2004) suggested, when investors are pessimistic about a stock, non-
investors may avoid participating in the market because short-selling regulations prevent them from
acting on their negative sentiment. Conversely, when investors are optimistic, they tend to buy stocks
in large quantities. Therefore, short-selling regulations often associate high turnover (high liquidity)
with optimism rather than pessimism.
Based on this sentiment-driven rationale, we construct a four-factor model using abnormal
turnover (the ratio of last month's turnover to the previous year's average turnover). The construction
of the turnover factor follows the same approach as that of the value factor. We replace the EP ratio
with abnormal turnover, with the only difference being that we go long on stocks with low factor
values (reflecting investor pessimism) and short on stocks with high factor values (reflecting investor
optimism). We name this factor PMO, and by adding PMO to the three-factor model, we derive the
CH four-factor model.
5. Empirical Results
5.1. Comparison of FF-3 and CH-3 Models
Table 1 lists the alpha coefficients and corresponding t-values of the size and value factors for each
model compared to the other model. The CH-3 model effectively explains the size and value factors
of the FF-3 model. Specifically, the alpha for FFSMB in CH-3 is only -0.0001 per month, with a t-
value of -0.1249, while the alpha for FFHML is -0.0020, with a t-value of -0.7073. In contrast, FF-3
fails to adequately explain the size or value factors of CH-3. However, FF-3 has an SMB of 0.0024
and a t-value of 3.3202, while the alpha for VMG is 0.0070 with a t-value of 4.1446, indicating that
the CH-3 model clearly outperforms the FF-3 model.
Table 1. Comparison of FF and CH: Alpha
Factors
CH-3
FF-3
FFSMB
-0.0001
(-0.1249)
FFHML
-0.0020
(-0.7073)
SMB
0.0024***
(3.3202)
VMG
0.0070***
(4.1446)

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The GRS test (Gibbons, Ross, and Shanken, 1989) is used to assess pricing errors of n assets under
a given factor model, specifically testing whether the alpha values are jointly equal to zero. When
comparing the two multifactor models, the factors from both models are tested as both assets and
pricing models.The results in Table 2 indicate that when using SMB and VMG as factor models, the
pricing errors for FFSMB and FFHML can be considered zero (p-value = 0.77); conversely, when
using FFSMB and FFHML as pricing models, significant non-zero pricing errors for SMB and VMG
remain (p-value = 0.00011914). This implies that SMB and VMG perform better than FFSMB and
FFHML.
Table 2. Comparison of FF and CH: GRS
Factors
CH-3
FF-3
FFSMB, FFHML
0.5050
(0.7769)
SMB, VMG
18.0705
(0.0001)
5.2. Explanation of Anomalies by FF-3 and CH-3 Models
Due to the relatively high size premium in the Chinese stock market, the anomaly variables and
size may obscure the effect of anomalies on unconditional sorting. Therefore, we opted for a value-
neutral alpha to screen for anomalies. The screening methods for the 14 anomalies are as follows:
For unconditional sorting, we construct deciles by sorting based on the anomaly variables (for CP
and EP, only positive values are screened). Then, we create a long-short strategy using deciles one
through ten, and within each decile, we form an equally weighted portfolio.
For value-neutral sorting, we first construct size deciles by sorting based on the market
capitalization from the previous month. Within each size decile, we then sort based on the anomaly
variables to create ten deciles. Finally, we build the anomaly decile portfolios used in our analysis.
We extract the stocks within the anomaly deciles from each size decile, apply equal weights to their
returns, and construct the return portfolios based on the market capitalization of the individual stocks.
Similar to unconditional sorting, the long-short strategy is based on deciles one through ten.
Table 3. CH-3's Explanation of Anomaly Factors
Panel A:Unconditional sorts
Anomaly




󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
ME
-0.0008
0.0031
1.3966
-0.5287
-0.8498
0.1901
39.6614
-13.6113
EP
-0.0046
0.0380
0.6396
-1.0427
-2.1883
1.0731
8.7832
-14.4779
BM
0.0069
-0.1339
-0.3972
-1.2612
1.4883
-1.5282
-2.3841
-7.1119
CP
-0.0010
0.0211
0.1259
0.4629
1.2992
-1.0074
-0.0010
0.0211
ROE
-0.0114
0.0116
0.7818
-0.6683
-4.1157
0.2494
6.6736
-5.9871
1-month vol
-0.0010
-0.1875
0.2094
1.2512
-0.2612
-2.8863
1.3441
9.2106
MAX
0.0012
-0.2497
0.0984
0.7799
0.3365
-3.7156
0.6523
6.0541
1m return
0.0037
-0.0820
0.6681
0.2648
0.7900
-0.8945
4.0740
1.4084
12m return
-0.0106
0.0527
0.8935
0.6524
-2.0882
0.6567
5.6633
3.2336
1m turn
0.0095
-0.2393
0.2866
-0.0150
2.4234
-2.5405
1.5677
-0.0803
Panel B: Size-neutral sorts
Anomaly




󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
EP
0.0006
0.0374
0.1132
0.8664
0.4956
2.1286
2.5470
17.8364
BM
-0.0045
0.1663
0.2482
0.9197
-1.3463
3.0075
2.1384
6.9899
CP
-0.0008
-0.0157
-0.0091
0.1531
-0.6383
-0.7792
-0.2198
4.1902
ROE
0.0049
-0.0580
-0.0479
0.4533
2.1394
-1.5225
-0.6345
5.0956
1-month vol
-0.0069
0.1777
-0.2200
-0.8466
-2.4863
4.3130
-2.5943
-8.4624
MAX
-0.0081
0.0846
-0.2210
-0.5842
-3.3396
2.3781
-3.3072
-6.8519
1m return
-0.0081
0.0846
-0.2210
-0.5842
-3.3396
2.3781
-3.3072
-6.8519
12m return
-0.0094
0.1774
-0.1875
-0.6540
-4.2305
5.4532
-2.7893
-7.6726
1m turn
-0.0182
0.1358
-0.1713
-0.1870
-6.3385
2.4809
-1.5834
-1.4673

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Table 3 lists the corresponding results of CH-3: in the empirical study of the U.S. stock market,
the results confirmed that CH-3 can fully explain the profitability anomaly related to Return on Equity
(ROE). In the U.S. market, the positive correlation between profitability and average returns led to
the inclusion of this factor in the models of Hou et al. (2015) and Fama and French (2015). However,
in the Chinese stock market, the explanatory power of CH-3 differs. Specifically, the monthly average
alpha of ROE is -0.0114 under unconditional screening and 0.0049 under market capitalization
screening, with corresponding t-values of -4.1157 and 2.1394, respectively. In terms of the volatility
anomaly, under unconditional screening, the alpha generated by the previous month's average daily
volatility and the single-day maximum return is not significant. However, under market capitalization
screening, both show significant alpha.
For the size and value anomalies, CH-3 performs well under both unconditional and market
capitalization screening, explaining the size (ME), earnings yield (EP), book-to-market ratio (BM),
and cash flow yield (CP), with insignificant alpha. However, for the turnover and reversal anomalies,
CH-3 shows different results. Under unconditional screening, CH-3 can explain the 1-month return
reversal factor but fails to explain the 12-month and 1-month turnover rates. Under market
capitalization screening, both the turnover factor and the reversal factor exhibit significant alpha.
Table 4. FF-3's Explanation of Anomaly Factors
Panel A:Unconditional sorts
Anomaly




󰇛󰇜
󰇛󰇜
󰇛󰇜󰇜
󰇛󰇜
ME
-0.0010
0.0298
1.4759
-0.1663
-0.9733
1.4753
38.2928
-3.7932
EP
-0.0117
0.1228
1.1201
-0.2121
-4.6307
3.3462
15.0814
-3.7383
BM
0.0012
0.0505
-0.0702
-1.5105
0.6389
1.4702
-1.3829
-32.9840
CP
-0.0021
0.0211
0.1821
0.1330
-0.8647
0.4671
1.9777
2.5069
ROE
-0.0167
0.0423
1.1520
0.2361
-6.2648
0.9782
14.9978
3.5071
1-month vol
0.0080
-0.3288
-0.3528
0.7375
2.1496
-4.7863
-2.8119
6.4446
MAX
0.0069
-0.3325
-0.2872
0.4234
1.9143
-5.1328
-2.1122
3.5932
1m return
0.0075
-0.1194
0.4324
0.1442
1.7289
-1.3137
2.9488
0.7969
12m return
-0.0061
-0.0568
0.6376
0.8663
-1.4102
-0.8216
4.3373
6.5545
1m turn
0.0116
-0.2264
0.1320
-0.2589
2.8114
-2.8133
0.8423
-1.5152
Panel B: Size-neutral sorts
Anomaly




󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
EP
0.0080
-0.0492
-0.3376
0.2353
4.1282
-1.5137
-6.5566
5.0632
BM
-0.0008
0.0304
0.0297
1.1518
-0.6054
1.2928
0.6679
31.6786
CP
0.0010
-0.0261
-0.1113
-0.0735
0.7280
-1.2637
-3.1430
-2.3729
ROE
0.0106
-0.0822
-0.3963
-0.2921
4.8448
-2.2401
-6.2004
-5.6765
1-month vol
-0.0129
0.2790
0.1359
-0.5335
-4.6579
6.5866
1.8620
-7.3115
MAX
-0.0128
0.1509
0.0690
-0.2880
-5.0831
4.2491
1.0326
-3.7706
1m return
-0.0128
0.1509
0.0690
-0.2880
-5.0831
4.2491
1.0326
-3.7706
12m return
-0.0144
0.2555
0.0887
-0.3685
-6.0394
7.4538
1.4466
-5.6259
1m turn
-0.0213
0.1456
0.0293
0.1426
-7.0082
3.0202
0.3041
1.3158
Table 4 lists the corresponding results of FF-3. FF-3 can only explain the size (SIZE) and value
(Value) anomalies among the six anomaly factors. Under unconditional screening, only size (ME),
book-to-market ratio (BM), cash flow yield (CP), and 12-month return show non-significance and
can be explained by FF-3. In the case of market capitalization screening, only the book-to-market
ratio (BM) and cash flow yield (CP) can be explained by FF-3. Compared to CH-3, FF-3 explains
significantly fewer anomalies.
5.3. Explanation of Anomalies by the CH-4 Model
In the article by Liu, Stambaugh, and Yuan (2018), the Chinese version of the three-factor model
proves ineffective against reversal and turnover anomalies. The reversal phenomenon is well
established; it is so pronounced that one can construct portfolios based on returns sorted over nearly
any time window, resulting in observable return reversals in the future. Conversely, turnover is
closely related to the structure of retail-dominated traders and the constraints associated with short

Highlights in Business, Economics and Management
ECRM 2024
Volume 44 (2024)
166
selling. High turnover often indicates a greater presence of irrationality and excessive attention from
sentiment-driven traders toward certain stocks. Frequent trading tends to inflate the recent prices of
these stocks, leading to a decline in future returns. The restrictions on short selling mean that short
sellers cannot capitalize on this irrationality, thus failing to suppress the price increases of high-
turnover stocks.
To address these issues, Liu et al. (2018) introduced a fourth factor—the turnover factor PMO
(Pessimistic Minus Optimistic)—in addition to the original three-factor model. The core logic behind
this addition is that factors with low turnover tend to achieve higher returns compared to those with
high turnover. This adjustment resulted in the development of a four-factor model specifically for the
Chinese market.
Table 5. CH-4's Explanation of Anomaly Factors
Panel A:Unconditional sorts
Anomaly





󰇛󰇜
󰇛󰇜
󰇛󰇜󰇜
󰇛󰇜
󰇛󰇜
ME
-0.0012
0.0092
1.3876
-0.5356
0.0500
-1.1692
0.6133
42.2023
-13.6416
1.1091
EP
-0.0041
0.0311
0.6498
-1.0349
-0.0561
-1.9576
0.8107
8.1230
-14.7232
-0.6677
BM
0.0040
-0.0876
-0.4659
-1.3140
0.3786
0.8278
-1.1109
-2.8857
-7.6657
1.8497
CP
-0.0014
0.0277
0.1160
-0.0879
0.0543
-0.6047
0.5480
1.0946
-1.0922
0.5089
ROE
-0.0100
-0.0111
0.8154
-0.6424
-0.1854
-3.4501
-0.2439
6.6309
-5.8177
-1.8256
1-m vol
-0.0061
-0.1043
0.0860
1.1563
0.6804
-1.8190
-1.9299
0.5612
9.2746
4.3107
MAX
-0.0054
-0.1430
-0.0600
0.6583
0.8727
-1.8405
-2.5255
-0.4937
7.5231
7.5899
1m return
-0.0022
0.0140
0.5256
0.1554
0.7849
-0.4557
0.2150
3.8258
0.9307
4.3722
12m return
-0.0133
0.0956
0.8299
0.6036
0.3506
-2.6041
1.1405
5.1704
2.8570
1.5920
1m turn
-0.0026
-0.0415
-0.0070
-0.2405
1.6182
-1.3318
-1.1842
-0.1118
-3.8612
27.1777
Panel B: Size-neutral sorts
Anomaly





󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
EP
0.0006
0.0378
0.1127
0.8660
0.0029
0.4609
2.2203
2.4404
17.6086
0.0704
BM
-0.0029
0.1394
0.2882
0.9504
-0.2204
-0.8334
2.6203
2.4444
7.4163
-1.4497
CP
-0.0006
-0.0196
-0.0033
0.1575
-0.0318
-0.4503
-0.9309
-0.0764
4.1585
-0.7221
ROE
0.0035
-0.0352
-0.0817
0.4273
0.1864
1.4859
-1.0169
-1.0859
-4.7865
2.0737
1-m vol
-0.0039
0.1288
-0.1474
-0.7908
-0.3999
-1.5672
2.9788
-1.8036
-7.9214
-3.4802
MAX
-0.0041
0.0203
-0.1257
-0.5110
-0.5256
-1.9766
0.5977
-2.3925
-7.8564
-8.2673
1m return
-0.0041
0.0203
-0.1257
-0.5110
1.9766
-2.3925
0.8564
-8.2673
-0.0041
0.0203
12m return
-0.0079
0.1532
-0.1516
-0.6264
-0.1978
-3.5154
4.5610
-2.2947
-7.1719
-2.3561
1m turn
-0.0104
0.0077
0.0189
-0.0409
-1.0482
-6.7834
0.2628
0.2984
-0.7063
-17.5742
After incorporating the PMO factor, let's examine the explanatory power of the new four-factor
model on the ten anomalies discussed in the previous section. Under unconditional screening, the
model shows improved explanatory power for the reversal and turnover anomalies. However, the
alpha of the 12-month return anomaly remains significant, with a t-value of -2.6041, indicating that
it still cannot fully explain the turnover anomaly.
In the case of market capitalization screening, CH-4 still fails to explain the reversal and turnover
anomalies, with the 1-month return, 12-month return, and 1-month abnormal turnover remaining
significant. This contrasts with the original claim that the newly added PMO effectively addresses
the shortcomings of the three-factor model, allowing all ten anomalies to be well explained by the
four-factor model. This discrepancy suggests that the inclusion of the PMO factor in the formation of
the CH-4 model may involve a degree of data mining.
6. Summary
First, the comparison between CH-3 and FF-3 shows that, whether in terms of alpha or GRS tests,
CH-3 can effectively explain the size and value factors of FF-3, while FF-3 lacks corresponding
explanatory power in return. Furthermore, CH-3 demonstrates a significantly stronger explanatory
ability for anomaly factors compared to FF-3, indicating that CH-3 is more suitable for application in
the Chinese market. This finding not only highlights CH-3's advantage in capturing market
characteristics but also reveals FF-3's limitations in the Chinese context, suggesting that investors
may achieve more accurate predictions by considering CH-3 in asset pricing and investment decision-
making.

Highlights in Business, Economics and Management
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Volume 44 (2024)
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Second, the explanatory results of CH-3 for anomaly factors in this paper do not entirely align with
related studies, particularly in the case of the CH-4 factor constructed after incorporating the turnover
factor. This discrepancy may be associated with factors related to data mining. The introduction of
the turnover factor during the construction of CH-4 may have triggered complex interactions with
other anomaly factors, leading to inconsistencies with existing literature. Therefore, although CH-4
provides a new perspective, its results should be interpreted with caution to avoid biases stemming
from excessive reliance on data mining. Further research could examine the robustness of these
factors by using different samples or employing alternative validation methods to enhance the
reliability of the conclusions.
Acknowledgements
The authors would like to appropriate support from the National Natural Science Foundation of
China (Nos. 72001109 and 72301242).
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