2. Literature Review
2.1. Research on Herding Behavior of Mutual Funds
Institutional investors, represented by mutual funds, have a clear advantage in terms of professional skills compared to individual investors. However, ample research has shown that the trading behavior of mutual funds is not entirely rational, and herding behavior is one important manifestation of this
[6] | Yao L S, Wu N N. Research on herding behavior of institutions and individuals based on LSV model. Chinese Journal of Management Science, 2018, 26(07): 55-62. |
[7] | Cheng T X, Liu L Y, Guan Y Z. Empirical study on herding behavior of QFII and domestic institutional investors. Journal of Management Science, 2014, 27(04): 110-122. |
[8] | Hudson Y, Yan M, Zhang D. Herd behaviour & investor sentiment: Evidence from UK mutual funds. International Review of Financial Analysis, 2020, 71: 101494. https://doi.org/10.1016/j.irfa.2020.101494 |
[9] | Wang H, Li S, Ma Y. Herding in open-end funds: evidence from China. The North American Journal of Economics and Finance, 2021, 57: 101417. https://doi.org/10.1016/j.najef.2021.101417 |
[6-9]
. Existing literature has delved into the reasons behind herding behavior among mutual funds. Bikhchandani and Sharma (2000) argue that due to the relatively opaque information in emerging market, managers of mutual funds engage in direct imitation of their peers' investment strategies to reduce costs in information acquisition, leading to herding behavior
. Maug and Naik (2011) point out that fund managers, to avoid being penalized for underperforming, tend to follow the major investment strategies of their peers in order to achieve the average performance level
[11] | Maug E, Naik N. Herding and delegated portfolio management: The impact of relative performance evaluation on asset allocation. The Quarterly Journal of Finance, 2011, 1(02): 265-292. https://doi.org/10.1142/S2010139211000092 |
[11]
. Research by Cai et al. (2011) find evidence of herding behavior of securities analysts, with fund managers engaging in information reprocessing based on the information produced by analysts' research reports, thereby triggering herding behavior among mutual funds
[12] | Cai Q F, Yang K, Lin J B. The superimposition of herding behavior and market impact: empirical study based on the behavior of securities analysts and institutional investors. China Industrial Economics, 2011, (12): 111-121. |
[12]
.
The examination of herding behavior among mutual funds is initially conducted by Lakonishok et al. (1992), who find no significant herding behavior among US mutual funds
. However, subsequent studies by Hudson et al. (2020) reveal varying degrees of herding behavior among the majority of US mutual funds
. In the study of Chinese market, Cheng et al. (2014) employ various measures and empirically examined the relationship between herding behavior of Qualified Foreign Institutional Investors (QFII) and domestic institutional investors
[6] | Yao L S, Wu N N. Research on herding behavior of institutions and individuals based on LSV model. Chinese Journal of Management Science, 2018, 26(07): 55-62. |
[6]
. Additionally, Yao and Wu (2018) show that institutional investors exhibited stronger herding behavior than individual investors, and among institutional investors, mutual funds exhibited an increasing trend of herding over the years
[7] | Cheng T X, Liu L Y, Guan Y Z. Empirical study on herding behavior of QFII and domestic institutional investors. Journal of Management Science, 2014, 27(04): 110-122. |
[7]
. Wang et al. (2021) indicate that, except for income funds, all other types of funds have confirmed the existence of herding, which is mainly driven by non fundamental factors
.
The research on the price effects of herding has not yet reached a consensus. Some studies suggest that herding behavior among mutual funds exacerbates mispricing, while others indicate that herding behavior may accelerate price adjustments to reasonable levels. Wermers (1999) argues that herding behavior among mutual funds is selective, with investors more willing to herding buy when stock price is undervalued and herding sell when it is overvalued
. Through trading, they facilitate the adjustment of price towards to the fundamental value, and reduce mispricing. Caglayan et al. (2021) provide evidence for rational herding behavior in mutual funds through empirical analysis, and the results show that herding behavior in mutual funds significantly reduces the return synergy between Chinese stocks
. On the other hand, studies by Brown et al. (2014) and Zhu et al. (2019) suggest that during the process of imitating and following the herd, investors neglect their private information, causing the information held by those being imitated to be further reinforced in trading, leading to overreaction and mispricing
[4] | Brown N C, Wei K D, Wermers R. Analyst recommendations, mutual fund herding, and overreaction in stock prices. Management Science, 2014, 60(1): 1-20. https://doi.org/10.1287/mnsc.2013.1751 |
[5] | Zhu F F, Li H X, Xu J G, et al. The influencing factors and price effects of short-term herding behavior: an empirical test based on high-frequency data. Journal of Financial Research, 2019, (07): 191-206. |
[4, 5]
. Therefore, the impact of herding behavior among mutual funds on mispricing remains debatable.
2.2. Research on Measurement of Mispricing
Mispricing is a significant manifestation of market inefficiency in capital markets. Existing literature has discussed the reasons for mispricing from three aspects: information providing, information intermediaries, and information reception. Traditional financial research suggests that managers with information advantages have incentives to engage in earnings management to influence investors' judgments about the company's future development and value, leading to deviations in stock price and intrinsic value
[14] | Song Y L, Li Z W. Accrual anomalies in A-share companies. Journal of Management World, 2009, (08): 17-24+187. |
[14]
. Media studies argue that news media and securities analysts, as important intermediaries connecting information providers and receivers, play a crucial role in improving investors' information interpretation abilities. Several studies have found that as news media coverage deepens and securities analysts become involved, firm-specific information is more thoroughly explored, thus alleviating the problem of stock mispricing
[15] | Huang J, Guo Z R. News media reporting and capital market pricing efficiency: analysis based on stock price synchronization. Journal of Management World, 2014, (05): 121-130. |
[15]
. Behavioral finance research focuses more on the decision-making process of information receivers, suggesting that investor irrational behavior and limited arbitrage are important factors leading to mispricing and the persistence of mispricing
[16] | Li K, Xu L B, Zhu W Y. Short selling restrictions and stock mispricing: Evidence from the margin trading system. Economic Research Journal, 2014, 49(10): 165-178. |
[17] | Li Z S, Chen C, Lin B X. Has the short selling mechanism improved the pricing efficiency of the Chinese stock market—— evidence based on natural experiments. Economic Research Journal, 2015, 50(04): 165-177. |
[16, 17]
.
From a methodological perspective, measurement methods for mispricing can be classified into three categories. The first category compares the deviation between stock price and a certain benchmark to reflect mispricing. The key challenge in this method lies in determining the benchmark value. Commonly used approaches include Relative Valuation
[18] | Li W, Yang X, Yin X. Non-state shareholders entering of state-owned enterprises and equity mispricing: Evidence from China. International Review of Financial Analysis, 2022, 84: 102362. https://doi.org/10.1016/j.irfa.2022.102362 |
[18]
, Absolute Valuation
, and Regression Valuation
. The second category employs Discretionary Accruals (DACCR) as a proxy variable for mispricing. Xie (2001) empirically confirms that companies with higher discretionary accruals tend to be overvalued by the market
. While discretionary accruals can to some extent reflect the degree of mispricing, their limitations, such as time delay, restrict their accuracy and reliability as a measurement of mispricing. The third category employs cumulative abnormal returns as a proxy variable for mispricing. This empirical research method implicitly assumes that pricing of stocks is efficient and the stock price reflect intrinsic value
.
As significant participants in the stock market, mutual funds play a dual role as both information intermediaries and information recipients, exerting a significant influence on pricing. Traditional literature suggests that mutual funds typically have access to more information channels and professional information processing teams, enabling them to accurately assess value information and make correct trading decisions, thereby driving stock prices towards to their fundamental values
. Additionally, holding by mutual funds attracts more securities analysts to track and analyze stocks, leading to increased corporate information disclosure, and reduces mispricing
. Numerous empirical studies have confirmed the positive role of mutual funds in asset pricing
. However, some literature argues that managers of mutual funds, as information recipients, may not exhibit entirely rational information processing and trading decisions
[7] | Cheng T X, Liu L Y, Guan Y Z. Empirical study on herding behavior of QFII and domestic institutional investors. Journal of Management Science, 2014, 27(04): 110-122. |
[8] | Hudson Y, Yan M, Zhang D. Herd behaviour & investor sentiment: Evidence from UK mutual funds. International Review of Financial Analysis, 2020, 71: 101494. https://doi.org/10.1016/j.irfa.2020.101494 |
[7, 8]
. Therefore, the impact of mutual funds on asset pricing remains debatable.
3. Research Design
3.1. Data and Sample
The data on holdings by mutual funds is sourced from the CSMAR database, while data on market trading of listed companies are obtained from the WIND database. The period of study spans from 2010 to 2023. Since mutual funds only disclose the top ten holdings in their quarterly reports, but provide detailed information on all stock holdings in their semi-annual and annual reports, this article only selects data from the semi-annual and annual reports. During the study period, data on holdings by 7,453 mutual funds was collected for analysis.
The following filters were applied to data on listed companies which are held by mutual funds: firstly, companies that have been listed for less than one year were excluded; secondly, financial companies were excluded; thirdly, companies with abnormal operations (identified as ST and *ST), suspended trading, or delisted were excluded. After applying these filters, the collected data in this article includes 1,369 listed companies. To ensure consistency in frequency of data, the article selects semi-annual and annual financial data, resulting in a sample of 25,671 observations.
Moreover, to eliminate the influence of outliers, all continuous variables were subject to trimming at the 1% upper and lower tails. In the subsequent empirical analysis, the sample sizes used in different sections may slightly vary due to the specific research focus.
3.2. Measurement
3.2.1. Stock Price Deviation
We focus on the impact of herding behavior on mispricing. We mainly use deviation between stock price and intrinsic value as the measure of mispricing:
where represents the market price of the stock at time , and represents the intrinsic value calculated through fundamental analysis. If is bigger than 0, the stock is considered overvalued. Conversely, if is less than 0, it suggests that the stock is considered undervalued.
For this study, the approach proposed by Zhao (2003) is employed to estimate the intrinsic value of stocks
[26] | Zhao Z J. Analysis of deviationd of stock price from intrinsic value. Economic Research Journal, 2003, (10): 66-74+93. |
[26]
. According to the prevailing theory of value determination, the intrinsic value of a stock is determined by the present value of its future cash flows:
(2)
where represents accounting earnings. represents the discount rate or cost of capital. represents taking the expectation.
The accounting earning can be expressed as the sum of normal earnings and abnormal earnings , that is, .
Assuming that investors' expectations regarding the return on net assets remain unchanged. And the company has an infinite lifespan, it is recognized that as external competition intensifies, the excess returns generated by innovation and monopoly tend to diminish over time. Eventually, after a certain period denoted as , the company can only generate normal earnings. In light of this, the intrinsic value of a stock can be expressed as the summation of the present value of expected normal earnings and excess earnings.
(3)
Let
represent the growth rate of net asset, and
represent the return on net assets. Under the given condition of dividend payout ratio, Equation (
4) can be rewritten as:
(4)
Assuming that , , . The intrinsic value can be expressed as:
(5)
It should be noted that, when calculating the intrinsic value of a company using Equation (
5),
represents the dividend discount rate, which consists of two components: risk-free rate and risk premium. In this study, we use the one-year benchmark interest rate for fixed deposits converted to a semi-annual rate is used as the risk-free rate, and the risk premium is calculated using the Carhart four-factor model. Additionally,
represents the limited period during which the company obtains excess returns. The simulation results by Zhao (2003) show that when the dividend payout ratio is 0.3 (the average dividend payout ratio in the sample studied in this paper)
[26] | Zhao Z J. Analysis of deviationd of stock price from intrinsic value. Economic Research Journal, 2003, (10): 66-74+93. |
[26]
, the duration of excess returns obtained by the company is almost linearly related to the intrinsic value. In other words, the choice of
hardly affects the relationship between herd behavior and deviation of stock price. In fact, this study tests different values of
in the empirical section, and the regression results are consistent. In the subsequent report, we only present the empirical results for
.
3.2.2. Herding Behavior
Lakonishok et al. (1992) introduced the classical Lakonishok-Shleifer-Vishny (LSV) model, which aims to assess the herding behavior exhibited by investors during the trading of individual stocks
. This approach quantifies the level of of herding by examining the percentage of investors engaged in one-sided trading in the stock market. Specifically, the herding behavior of investors when trading stock
at time
can be represented as follows:
(6)
where represents ratio of net buying, represents the number of investors who are net buyers, and represents the number of investors who are net sellers. The expected value of can be approximated by the arithmetic average of this ratio across all stocks at time , denoted by :
(7)
in Equation (
7) represents the adjustment factor, which indicates the expected value of the absolute difference
when there is no herding effect present in the market. In the absence of herding behavior, investors' decisions are considered independent of one another. However, certain factors, such as a general market rise (fall), can cause investors to make similar buying or selling decisions, resulting in a nonzero value for
. Under the assumption of independent investor decisions, the variable
follows a binomial distribution
, where
is defined as the sum of net buyers and net sellers, given by
. We have:
(8)
(9)
Wylie (2005) raises concerns about the assumption that
follows a binomial distribution
[27] | Wylie S. Fund manager herding: A test of the accuracy of empirical results using UK data. The Journal of Business, 2005, 78(1): 381-403. https://doi.org/10.1086/426529 |
[27]
. The author argues that the investment probability of a mutual fund manager for a specific stock may not solely rely on
but also on factors like the initial size and net cash flow of the mutual fund. However, Wylie (2005) discovers that the herding effect, as measured by the LSV method, remains effective when a sufficient number of participating funds are involved
[27] | Wylie S. Fund manager herding: A test of the accuracy of empirical results using UK data. The Journal of Business, 2005, 78(1): 381-403. https://doi.org/10.1086/426529 |
[27]
. To address the issue of stocks with a small number of participating funds, the study follows the approach outlined by Qi et al. (2006). Specifically, if the number of participating buying or selling funds is less than 5, these stocks are excluded from the sample
[28] | Qi B, Yuan K, Hu Q, et al. An empirical study on herding behavior of securities investment funds in China. Securities Market Herald, 2006, (12): 49-57. |
[28]
.
The value of
calculated from Equation (
6) represents the percentage of investors for stock
in period
, that exhibit unidirectional (can be either buying or selling) herding behavior in the market surpassing the expected number. The higher absolute value of
indicates a stronger presence of herding behavior among investors. Wermers (1999) distinguishes investor trading into buying and selling. If the net buying ratio of investors exceeds the expected level, it is categorized as herding buying
. Conversely, if the net buying ratio of investors falls below the expected value, it is classified as herding selling. Based on this framework, two indicators are proposed to measure the extent of buying and selling herding behavior:
(10)
(11)
According to the definition, it is important to note that, for stock and period , we can observe either BHM (Buying Herding Measure) or SHM (Selling Herding Measure). A large value of BHM indicates a strong buying herd, while a large value of SHM indicates a strong selling herd.
Several alternative measurements of investor herding based on the LSV method have been proposed by Shi (2001) and Xu et al. (2013)
[3] | Xu N X, Yu S Y, Yi Z H. Herding behavior of institutional investors and the risk of stock price collapse. Journal of Management World, 2013, (07): 31-43. |
[29] | Shi D H. Trading behavior and market impact of securities investment funds. The Journal of World Economy, 2001, (10): 26-31. |
[3, 29]
. If the difference
is close to its expected value
, the herding behavior is not considered statistically significant. According to Xu et al. (2013), herding behavior is deemed to exist when the imbalance of net buying ratio
, exceeds a specific threshold. This threshold is defined as the mean plus the standard deviation. In this study, we employ a similar approach by including only the sample data where
exceeds is greater than the threshold.
Shi (2001) proposed an alternative simplified method
[29] | Shi D H. Trading behavior and market impact of securities investment funds. The Journal of World Economy, 2001, (10): 26-31. |
[29]
(12)
According to the definition in Equation (
12), the herding behavior measure obtained falls within the ranges of 0.5 to 1, indicating the proportion of funds that participate in the same buying or selling behavior for stock
in period
, relative to all stocks. A higher value signifies a more significant herding behavior.
In the subsequent empirical analysis, this paper utilizes the herding behavior measure proposed by Xu et al. (2013). Additionally, for robustness testing, we employ the methodology proposed by Shi (2001).
3.2.3. Control Variables
This study also incorporates several control variables that capture various aspects of the firm's characteristics. These variables, as referenced from Xu et al. (2013), are commonly used in empirical research and provide additional insights into the factors that influence stock mispricing
[3] | Xu N X, Yu S Y, Yi Z H. Herding behavior of institutional investors and the risk of stock price collapse. Journal of Management World, 2013, (07): 31-43. |
[3]
. The control variables included in this study are as follows: (1) Stock turnover rate (turn): This variable reflects investors' sentiment and is calculated as the ratio of the trading volume of a stock within a six-month period to its outstanding shares; (2) Stock volatility (sigma): This variable measures the level of individual stock risk and is represented by the standard deviation of weekly returns of the stock over a six-month period; (3) Size of the listed company (size),: This variable indicates the scale of the listed company and is measured by the natural logarithm of the total assets of the firm; (4) Book-to-market ratio (mb): This variable captures company growth using the ratio of equity to market value; (5) Return on total assets (roa): This variable evaluates the company's operational performance using the ratio of after-tax net profit to total assets. Descriptive statistics of the variables are presented in
Table 1.
Table 1. Descriptive statistics of variables.
Variables | | Mean | Sd | Min | Max |
| 30139 | 0.106 | 0.993 | -1.560 | 12.106 |
| 25671 | 0.110 | 0.109 | -0.057 | 0.730 |
| 11819 | 0.105 | 0.113 | -0.057 | 0.730 |
| 13852 | 0.115 | 0.106 | -0.057 | 0.503 |
| 38324 | 231.2 | 199.678 | 0.000 | 2353.1 |
| 38023 | 0.059 | 0.049 | 0.000 | 5.066 |
| 36398 | 2.629e+10 | 1.113e+11 | 0.000 | 2.753e+12 |
| 36403 | 0.659 | 0.279 | 0.000 | 1.729 |
| 37379 | 0.024 | 0.678 | -31.296 | 108.366 |
The average deviation of stock prices in the selected sample is 0.106, indicating an overall positive deviation of stock prices from intrinsic value. This finding is consistent with the results reported by Zhao (2003)
[26] | Zhao Z J. Analysis of deviationd of stock price from intrinsic value. Economic Research Journal, 2003, (10): 66-74+93. |
[26]
. The average herding calculated using the classic LSV method in this study is 0.110, slightly higher than the findings of Qi et al. (2006) potentially due to the variation in the time window used
[28] | Qi B, Yuan K, Hu Q, et al. An empirical study on herding behavior of securities investment funds in China. Securities Market Herald, 2006, (12): 49-57. |
[28]
. Two HM indices used in this study indicate a higher measure for buying behavior compared to selling behavior, which is consistent with the findings of Yao and Wu (2018)
[7] | Cheng T X, Liu L Y, Guan Y Z. Empirical study on herding behavior of QFII and domestic institutional investors. Journal of Management Science, 2014, 27(04): 110-122. |
[7]
.
3.3. Regression Models
This study employs the following model to examine the influence of the overall herding behavior of mutual funds, without distinguishing the trading direction, on the extent of stock price deviation from underlying fundamentals.
(13)
whereas, represents the absolute degree of stock price deviation. denotes the overall herding behavior. represents the control variables.
In order to account for the trading direction of herding behavior, his study aims to differentiate between buying and selling and examine their respective impacts on stock price overvaluation or undervaluation. Consequently, the dependent variable is defined as the stock price deviation, which can take on positive or negative values. A positive indicates that the stock price is overvalued, while a negative value suggests that the stock price is undervalued. The following regression model is constructed to test this relationship.
(14)
(15)
whereas, represents the stock price deviation. The variable denotes herding buying, while represents herding selling. Additionally, represents the control variables included in the analysis.
4. Empirical Results
4.1. Herding Behavior and Stock Price Deviation
Table 2 presents the regression results examining the relationship between mutual fund herding behavior and stock price deviation. Columns (1), (3), and (5) utilize the classical LSV model proposed by Lakonishok et al. (1992)
. Columns (2), (4), and (6) use the simplified herding behavior index introduced by Shi (2001)
[29] | Shi D H. Trading behavior and market impact of securities investment funds. The Journal of World Economy, 2001, (10): 26-31. |
[29]
.
It is important to note that when calculating the intrinsic value of a company using formula (
5), the parameter 'n' represents the limited period during which the company obtains excess returns. According to Zhao 's (2003) simulation, which considers a dividend payout ratio is 0.3 (the average dividend payout ratio in this study’s ample), the duration of excess returns obtained by the company exhibits a minimal impact on the relationship between herding behavior and stock price deviations
[26] | Zhao Z J. Analysis of deviationd of stock price from intrinsic value. Economic Research Journal, 2003, (10): 66-74+93. |
[26]
. In fact, we conducted empirical analysis testing different values of ‘n’, and the regression results remained consistent. In the subsequent report, we present the regression results solely for 'n=10'.
Table 2. Herding behavior and stock price deviation (full sample).
Variables | (1) | (2) |
| 0.008 (1.500) | 0.008 (1.120) |
| 0.007 (0.940) | 0.001 (0.120) |
| 0.089*** (6.370) | 0.101*** (7.110) |
| 0.027*** (6.770) | 0.032*** (7.190) |
| -0.655*** (-50.520) | -0.691*** (-51.820) |
| -0.256*** (-45.190) | -0.272*** (-45.420) |
| 1.757*** (53.750) | 1.792*** (53.210) |
| | |
| | |
| 19616 | 19535 |
| 0.306 | 0.301 |
| 176.030*** | 170.950*** |
Table 3. Herding behavior and stock price deviation (subsample).
| subsample of buying | subsample of selling |
Variables | (3) | (4) | (5) | (6) |
| 0.018*** (2.920) | 0.023*** (2.620) | | |
| | | 0.001 (0.170) | 0.010 (1.100) |
| 0.35*** (3.650) | 0.030*** (3.050) | 0.010 (1.060) | 0.011 (1.090) |
| 0.068*** (3.900) | 0.082*** (4.650) | 0.068*** (4.140) | 0.071*** (4.200) |
| 0.022*** (4.210) | 0.026*** (4.530) | 0.015*** (3.280) | 0.018*** (3.530) |
| -1.255*** (-76.280) | -1.281*** (-76.180) | -1.247*** (-83.070) | -1.267*** (-80.790) |
| -0.431*** (-61.040) | -0.447*** (-60.380) | -0.461*** (-69.170) | -0.479*** (-66.640) |
| 0.334*** (8.520) | 0.357*** (8.860) | 0.603*** (14.880) | 0.621*** (14.690) |
| | | | |
| | | | |
| 9057 | 9060 | 10559 | 10475 |
| 0.775 | 0.769 | 0.771 | 0.758 |
| 631.470*** | 612.410*** | 722.540*** | 667.630*** |
Columns (1) and (2) of
Table 2 present the empirical results based on the full sample. These results demonstrate that both the classical LSV method proposed by Lakonishok et al. (1992) and the simplified herding behavior index introduced by Shi (2001) show a positive correlation between the herding behavior and the degree of stock price deviation from fundamentals. The result indicates that herding behavior of mutual funds may result in mispricing in stock market.
In addition, we differentiate between herding behavior in the buying and selling directions. Columns (3) and (4) of
Table 2 present the test results based on the subsample of herding buying. The coefficient is significantly positive, suggesting that herding buying of mutual funds leads to the overvaluation of stock prices. On the other hand, Columns (5) and (6) of
Table 2 present the test results based on the subsample of herding selling. These results indicate no significant relationship between mutual fund herding selling and the deviation of stock prices from fundamental. This finding suggests, to a certain extent, that there is an asymmetrical impact of herding buying and selling by mutual funds on mispricing.
Based on the above results, it can be concluded that while herding selling has little impact on mispricing, the observed effect on mispricing in the full sample analysis is primarily driven by the impact of herding behavior in the buying direction.
4.2. Portfolio Analysis
The above analysis reveals that stocks subjected to herding buying by mutual funds tend to be relatively higher valued compared to other stocks based on current information. However, it is crucial to explore whether this finding could be attributed to mutual funds having access to undisclosed information. It is plausible that herding behavior by mutual funds actually contributes to price discovery in the stock market. To investigate this, it is necessary to observe the subsequent price performance of the stocks following the herding buying. If the herding buying creates a price bubble rather than facilitating price discovery, one would expect the prices to decline and revert back to their intrinsic values in the subsequent period.
To gain insights into whether herding buying leads to mispricing or serves as a mechanism for price discovery, the study utilizes the methodologies proposed by Wermers (1999) and Zhu et al. (2019) to construct different portfolios based on the herding measure
[2] | Wermers R. Mutual fund herding and the impact on stock prices. The Journal of Finance, 1999, 54(2): 581-622. https://doi.org/10.1111/0022-1082.00118 |
[5] | Zhu F F, Li H X, Xu J G, et al. The influencing factors and price effects of short-term herding behavior: an empirical test based on high-frequency data. Journal of Financial Research, 2019, (07): 191-206. |
[2, 5]
. The cumulative excess returns of these portfolios are examined to determine if herding behavior is associated with price reversals. The study employs a formation period of 6 months and holding periods of 1 and 6 months, respectively. The construction method for the portfolios is as follows: Stocks are sorted based on their herding effect during the formation period. The top 20% of stocks with the highest herding buying form the Strong Buying portfolio (BS), while the bottom 20% of stocks with the lowest herding buying form the Weak Buying portfolio (BW). Similarly, the top 20% of stocks with the highest herding selling form the Strong Selling portfolio (SS), and the bottom 20% of stocks with the lowest herding selling form the Weak Selling portfolio (SW). Additionally, the study includes a zero-cost hedge portfolio: Long the portfolio with the strongest herding buying and short the portfolio with the strongest herding selling (BS-SS). By analyzing the performance of these portfolios, the study aims to shed light on the relationship between herding behavior, mispricing, and price discovery in the stock market.
The excess return of a specific stock during a given period is calculated as the difference between its ordinary return and the weighted average return of all stocks in that period, . The excess return of each investment portfolio is then determined by taking the arithmetic average of the individual excess returns of all stocks within the portfolio, given by , where represents the number of stocks in the portfolio. Furthermore, the cumulative excess return of stock over a specific time period (from to ) can be defined as the sum of its excess returns during that period, expressed as . Similarly, the cumulative excess return of a portfolio is calculated as the arithmetic average of the cumulative excess returns of all stocks within the portfolio, .
In this study, the portfolios constructed using the LSV method and the simplified herding measures exhibit similar results. The subsequent presentation will focus solely on presenting the outcomes derived from the empirical analysis conducted using the LSV method.
Table 4. Portfolio analysis.
portfolio | (1) | (2) | (3) | (4) |
| 0.286*** (176.580) | 0.225*** (24.089) | -0.008* (-1.749) | -0.017** (-2.121) |
| -0.009*** -22.099) | 0.013** (2.562) | -0.013*** (-3.243) | -0.021*** (-3.354) |
| 0.267*** (188.207) | -0.119*** (-24.459) | -0.024*** (-6.975) | -0.040*** (-7.398) |
| -0.009*** (-22.264) | -0.041*** (-9.909) | -0.014** (-3.815) | -0.020*** (-3.678) |
| - | 0.344*** (4.362) | 0.015** (1.983) | 0.023** (2.043) |
Table 4 presents the cumulative excess returns of different investment portfolios. The empirical results reveal the following observations: (1) Portfolios in which mutual funds exhibit herding behavior through buying (BS, BW) demonstrate positive excess returns in the current period. However, these returns become significantly negative after holding the portfolios for three month and six months. This suggests the presence of price reversal, indicating an overreaction. Notably, portfolio with strong buying activity by mutual funds (BS) exhibit a more pronounced degree of price reversal, aligning with the findings of Zhu et al. (2019). (2) Portfolios in which mutual funds exhibit herding behavior through selling (SS, SW) exhibit negative excess returns in the current period. These negative returns do not experience a subsequent reversal; instead, they persist and remain statistically significantly negative even after being held for three month and six months.
4.3. Mutual Fund Herding and the Role of Other Market Participants
The empirical findings demonstrate an intriguing asymmetry in the impact of mutual fund herding on price deviation, where buying herding behavior leads to positive price deviations, while selling herding behavior does not result in significant negative price deviation. This imbalance cannot be explained by the difference in the magnitude of buying and selling herding by mutual funds, as the descriptive statistics in
Table 1 indicate similar mean and maximum values. Other market participants likely play a role in this disparity. When mutual funds engage in buying herding, their actions influence and encourage similar trading behavior among others, resulting in an overvaluation of stocks and positive price deviations. Conversely, in the case of selling herding, the absence of substantial negative price deviations suggests that other market participants absorb the selling pressure without initiating significant selling themselves. This leads to a more balanced market response, preventing significant undervaluation and negative price deviations.
In order to gain a deeper understanding of this issue, we will explore the involvement of other market participants alongside mutual funds in this analysis. It is important to note that, apart from exchange-traded open-end index funds, most mutual funds seldom engage in margin trading and securities lending. In this context, margin trading refers to the practice where investors borrow money to invest in stock market. On the other hand, securities lending refers to the process where investors borrow stocks from others to engage in short selling activities. As a result, the levels of margin trading and security lending can serve as a suitable proxy for capturing the sentiment of investors who are not mutual funds. To investigate how the buying and selling herding behavior of mutual funds influences the sentiments and trading directions of these other market participants, and subsequently creates asymmetric impacts on mispricing, this study constructs the following empirical mode:
(16)
(17)
(18)
(19)
Among them, is the balance of margin trading, while is the balance of securities lending. denotes the variable for herding buying, while represents the variable for herding selling.
Table 5. Mutual fund herding, margin trading and security lending.
| margin trading | security lending |
variables | (1) | (2) | (3) | (4) |
| 0.056*** (5.230) | | -0.031* (-1.880) | |
| | 0.115*** (9.990) | | -0.049*** (-2.930) |
| 0.583*** (4.640) | 0.184** (2.090) | -0.091 (-0.490) | -0.055 (-0.420) |
| | | | |
| | | | |
| 5696 | 7505 | 5735 | 7564 |
| 0.186 | 0.180 | 0.066 | 0.065 |
| 29.340*** | 37.110*** | 9.130*** | 11.920*** |
Table 5 presents the regression results. In columns (1) and (3), we observe the results for models (16) and (18), respectively, with the regressor being BHM. The results reveals that the coefficient associated with the herding effect of mutual fund buying is significantly positive for margin trading. This indicates that other investors tend to follow the buying behavior of mutual funds and make similar purchase decisions.
However, the effect of mutual fund buying on securities lending is not statistically significant, suggesting that mutual fund buying does not have a significant impact on short selling activities. As a result, the upward stock price deviations are primarily driven by the co-directional leveraged trading, where investors amplify market trends by using margin trading to take advantage of the buying pressure. Short selling, on the other hand, does not play a significant role in balancing the buying pressure created by mutual fund buying.
In Columns (2) and (4) of the regression results (models
17 and
19), we observe the findings related to the herding effect of mutual fund selling. The results indicate that the coefficient associated with the herding effect of mutual fund selling is significantly positive for margin trading. However, for securities lending balance, the coefficient is non-significantly negative, which means that mutual fund selling does not have a significant impact on short selling activities. This suggests that when mutual funds engage in substantial selling activities, other investors do not follow suit by making corresponding selling decisions. Instead, they adopt buying decisions. This counter-directional leveraged trading works to prevent negative stock price deviations.
4.4. Robustness Test
As mentioned earlier, this study utilizes the well-established LSV method introduced by Lakonishok et al. (1992) and the simplified herd behavior measure indicator developed by Shi (2001) to conduct the regression analysis. The obtained regression results, which are presented in
Table 2 and
Table 3, consistently hold across the entire sample as well as the subsamples of herding buying and herding selling. This consistency across different samples indicates the robustness of the conclusions derived from the analysis.
In order to test the robustness of the results, this study considers using a different method to estimate the intrinsic value and measure the price deviation. It is acknowledged that the bankruptcy of a company carries significant economic and social costs, and authorities often strive to prevent such occurrences for listed companies. Therefore, as an alternative approach, this study employs the scenario where the company's survival period is limited, in contrast to assuming an infinite survival period as in the previous research. To recalculate the intrinsic value of the company and the degree of price deviation, we adopt the method proposed by Gu et al. (2011) to recalculate the intrinsic value and conduct regression analysis and report the results in
Table 6 and
Table 7 [30] | Gu Z H, Hao X C, Zhang Y J. Short selling constraint, investor behavior and pricing foam in A-share market. Journal of Financial Research, 2011, (02): 129-148. |
[30]
. The empirical results are generally consistent with
Table 2 and
Table 3.
Table 6. Robustness test (full sample).
Variables | (1) | (2) |
| 0.008* (1.940) | 0.014** (2.460) |
| 0.005 (0.072) | 0.008 (1.270) |
| 0.083*** (7.280) | 0.079*** (7.070) |
| 0.109*** (31.570) | 0.115*** (30.800) |
| -0.061*** (-5.870) | -0.051*** (-4.950) |
| -0.076*** (-19.760) | -0.078*** (-20.300) |
| 0.774*** (28.860) | 0.768*** (28.880) |
| | |
| | |
| 21200 | 21299 |
| 0.165 | 0.170 |
| 85.100*** | 88.530*** |
Table 7. Robustness test (subsample).
Variables | subsample of buying | subsample of selling |
(3) | (4) | (5) | (6) |
| 0.013** (2.050) | 0.015* (1.800) | | |
| | | -0.001 (-0.160) | 0.005 (0.550) |
| 0.008 (0.830) | 0.011 (1.230) | 0.001 (0.060) | 0.006 (0.580) |
| 0.098*** (5.870) | 0.097*** (5.960) | 0.086*** (4.990) | 0.073*** (4.350) |
| 0.105*** (20.040) | 0.121*** (21.230) | 0.107*** (21.390) | 0.103*** (19.310) |
| -0.086*** (-5.560) | -0.082*** (-5.420) | -0.073*** (-4.750) | -0.058*** (-3.800) |
| -0.070*** (-12.100) | -0.072*** (-12.380) | -0.081*** (-14.530) | -0.083*** (-14.920) |
| 0.694*** (18.470) | 0.689*** (18.470) | 0.763*** (17.830) | 0.749*** (17.680) |
| | | | |
| | | | |
| 9666 | 9751 | 11534 | 11548 |
| 0.175 | 0.187 | 0.159 | 0.159 |
| 41.58*** | 45.440*** | 44.200*** | 44.330*** |