Herding Insider Traders: The Case of Opportunistic Insiders

Abstract

In this study, I used regression analysis to examine the relation between stock return dispersion from the market returns and market portfolio returns as a measure of herding behaviour in opportunistic insider traders from 2014 to 2024 in the USA. Opportunistic insiders place a trade in the same calendar month for at least three consecutive years. I found no evidence of statistically significant and negative relationship between return dispersions and market returns, either absolute or squared. This result implies that there is no herding behaviour. The results are robust to large stock price movements and changes in market volatility. My results are important for regulators and investors. Future research may involve the herding behaviour of insiders who follow trading plans.

1. Introduction

Company insiders, such as managers and boards of directors, are typically in possession of material non-public information (MNPI) about their companies. Insiders can be classified as opportunistic and routine traders. Routine insiders follow a specific detectable trading pattern. According to Cohen et al. (2012), routine insiders trade in the same calendar month for at least a certain number of years. Routine trading is predictable and identifiable because it is driven by diversification, hedging, or liquidity needs. For example, a routine trade may take place in specific calendar months after an insider receives a bonus, which is typically accompanied with discount plans on their company stock. On the contrary, opportunistic insider trading does not follow a specific detectable trading pattern. Opportunistic trading activities convey rich information on future price movements. As a result, opportunistic insiders earn higher returns on their future trades, and portfolios based on opportunistic trading exhibit higher abnormal returns relative to routine ones (Cohen et al., 2012; Ali & Hirshleifer, 2017).

There is recent evidence in the literature that associates opportunistic insider trading with herding behaviour. More specifically, Mansi et al. (2025) reported that insiders buy (sell) more when retail investors herd to sell (buy) the stock. Moreover, the association between insider and retail investors is more pronounced when firms have weak corporate governance and low CSR scores. Neupane et al. (2021) found that foreign institutional investors mimic opportunistic buy trades, especially when firms operate under opaque information environment and have low levels of corporate governance.

Ali and Hirshleifer (2017) reported that firms’ insiders are inclined to exhibit opportunistic behaviour for several reasons. One of them is that there may be a corporate culture that tolerates or even encourages such behaviour. Another reason may be that there is the incentive of preventing losses or gaining profits when they use MNPI to trade their companies’ stocks. This is consistent with the findings of Ma and Jiang (2024) who argued that insiders, both routine and opportunistic, sell when their company’s stock price is close to its term peak and buy when the stock price is close to its term bottom. This is because insiders influence corporate information disclosure before and around insider transactions.

This study contributes to the literature that tries to reveal the mechanisms behind opportunistic insider trading. More specifically, I calculated the cross-sectional absolute deviation (CSAD) and cross-sectional standard deviation (CSSD) of stock returns from market returns. By employing regression analysis, I examined the hypothesis of the presence of a statistically significant and negative relation between cross-sectional deviation measures (CSAD and CSSD) and dummy variables that indicate large price movements. Moreover, I used regression analysis to test the hypothesis of a statistically significant and negative relation between cross-sectional deviation measures (CSAD and CSSD) and market returns as an indicator of herding behaviour in stock prices around the date that opportunistic insiders’ trades took place. I based my analysis on return dispersion techniques since they have been used to examine herding behaviour in stock markets, e.g., in the work of Christie and Huang (1995), Chang et al. (2000), Gleason et al. (2004), and Tan et al. (2008). Since insiders trade stocks that are traded on the stock market, return dispersion methods will be useful in examining the existence of insiders’ herding behaviour. I focused on the USA market of insider trading from 2014 to 2024. I separated the universe of insider trading into insider purchases and sales. For each dataset, I followed Cohen et al. (2012) to identify transactions of opportunistic insider traders. I found no statistically significant and negative relations. This result is evidence of a lack of herding behaviour. Moreover, models with $CSAD$ as a dependent variable exhibited higher predictive power, as indicated by the lower values of the mean squared error and mean absolute error. My results are important for regulators who try to uncover the trading strategies of insiders and reduce the manipulation of stock prices. Moreover, my results have implications for external traders who try to decode the signals of stock price movements.

The rest of this paper is organised as follows: Section 2 outlines the dataset and methodology. Section 3 presents the results of the regression analysis on the herding behaviour as well as the robustness checks. Section 4 concludes the paper.

2. Data and Methodology

In this study, I investigated the herding behaviour of purchases and sales by insiders that took place from 1 January 2014 to 31 December 2024 in the USA. I downloaded the transaction data for the ten-year period studied in the FACTSET database provided by Wharton Research Data Services. I separated the dataset into two parts: one for the open market and private purchases of companies’ shares and another one for the open market and private sales of companies’ shares by insiders. All shares were held directly and not through derivatives, such as options. Moreover, all shares were held directly by the insider person and not through another entity. In addition, trades placed on the same date for the same stock were only considered once in the dataset. In other words, I do not consider that a stock was traded by several insiders on the same date. I followed Cohen et al. (2012) to identify routine and opportunistic insider traders in both datasets. According to them, insiders that placed an order for at least three consecutive years are characterised as routine insider traders. Any other insider is characterised as an opportunistic insider trader. Even though Cohen et al. (2012) report that this method is a “noisy proxy” for identifying opportunistic insiders, this way is sufficient to illustrate their main point; it is less likely for insiders that trade on information about their firm to be regular in their timing, whereas it is more likely for insiders that make trades for diversification or liquidity reasons be regular in their timing. For instance, an insider driven by diversification or liquidity reasons often places trades after receiving a bonus. Typically, bonuses are paid out in the same month each year, and it is quite usual for insiders to receive discount plans on their company stock. Moreover, Cohen et al. (2012) applied alternative ways to separate opportunistic from routine insiders with similar results.

Routine traders and their trades were dropped from the dataset. I ended up with two datasets of opportunistic purchases and sales covering the period from 2014 to 2024. Specifically, I analysed 207,401 cases of opportunistic purchases that included 6976 companies and 225,796 cases of opportunistic sells that included 6524 companies. All cases took place on day $t$, where $t$ is the effective date of the transaction that corresponds to the transaction date of the trade on SEC Form 4.

I matched the FACTSET companies’ ID with PERMNO codes, and I downloaded the daily closing prices from CRISP/COMPUSTAT Merged for the stocks of the companies in my dataset. Then, I calculated the daily returns ($R_t$) of each firm as $R_t=100\times \left(P_t-P_{t-1}\right)/P_{t-1}$, where $P_t$ is the standardised closing stock price on day $t$, and $P_{t-1}$ is the standardised closing stock price on day $t-1$. Standardised closing prices were calculated by subtracting the mean and dividing by the standard deviation of our sample.

Market returns were downloaded from CRISP as the returns of an equally weighted portfolio of shares on NYSE and AMEX. In my analysis, I used the standardised values of returns by subtracting the mean and dividing by the standard deviation of our sample.

To study the herding behaviour of opportunistic insider traders, I followed the methodologies of Christie and Huang (1995), Chang et al. (2000), Gleason et al. (2004), and Tan et al. (2008). All methodologies assume that herding behaviour has a substantial impact on stock prices. In other words, by examining the dispersion of stock returns from the returns of the market portfolio, conclusions on herding behaviour can be drawn. Christie and Huang (1995) proposed the cross-sectional standard deviation ($CSSD$) method to measure the presence of herding behaviour in equity returns. $CSSD$ is defined as ${CSSD}_t=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N{\left(R_{i,t}-R_{m,t}\right)}^2}{\left(N-1\right)}}}$, where ${CSSD}_t$ is the value of the cross-sectional standard deviation on day $t$, $R_{i,t}$ is the return of stock $i$ on day $t$, $R_{m,t}$ is the market return on day $t$, and $N$ is the number of assets on day $t$. Christie and Huang (1995) argued that individual asset returns’ dispersions from the market returns should be relatively low in the presence of herding behaviour. Moreover, herding behaviour is more prevalent during periods of large price movements or market stress, which is defined by the extreme lower and higher tails of asset return distribution. Christie and Huang (1995) suggested the following model:

$${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$$

where ${CSSD}_t=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N{\left(R_{i,t}-R_{m,t}\right)}^2}{\left(N-1\right)}}}$, $D_t^L$ and $D_t^U$ are dummy variables taking values of one when the market return at time $t$ lies in the extreme lower and higher tails of the return distribution, respectively, ${\beta }^L$ and ${\beta }^U$ are the estimated coefficients of dummy variables $D_t^L$ and $D_t^U$, respectively, $\alpha$ is a constant, and ${\epsilon }_t$ is the error term. Following Christie and Huang (1995), I applied the 5th and the 95th percentile as the extreme lower and higher tail of the market return distribution, respectively. For a robustness check, I applied the 1st and the 99th percentile as cutoff values for the extremes of the market return distribution. Negative and statistically significant ${\beta }^L$ and ${\beta }^U$ can be used as evidence of herding behaviour.

Alternatively, Chang et al. (2000) proposed the cross-sectional absolute deviation ($CSAD$) as a measure of individual asset return dispersion from the market return. $CSAD$ is defined as ${CSAD}_t={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|R_{i,t}-R_{m,t}\right|$, where ${CSAD}_t$ is the value of the cross-sectional absolute deviation on day $t$, $R_{i,t}$ is the return of stock $i$ on day $t$, $R_{m,t}$ is the market return on day $t$, and $N$ is the number of assets on day $t$. Chang et al. (2000) argued that during normal conditions the relationship between $CSAD$ and market returns will be linear and during periods of abrupt price changes will be quadratic. Specifically, they considered the following model:

$${CSAD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$$

where ${CSAD}_t={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|R_{i,t}-R_{m,t}\right|$, $R_{m,t}$ is the market return on day $t$, ${\gamma }_1$ and ${\gamma }_2$ are the estimated coefficients of the absolute and squared values of market returns, respectively, $\alpha$ is a constant, and ${\epsilon }_t$ is the error term. During normal market conditions, in the absence of herding behaviour, the dispersion of asset returns from the market return will increase linearly with the absolute values of market returns. Hence, a positive and statistically significant ${\gamma }_1$ can be used as evidence of absence of herding behaviour. However, during periods of large price movements, investors are prone to herding behaviour and the cross-sectional absolute deviation of stock returns will increase with the market return at a decreasing rate. Therefore, a statistically significant and negative ${\gamma }_2$ may be used as supporting evidence of herding behaviour.

Following Gleason et al. (2004), to obtain a more comprehensive analysis and to test the robustness of our results, I tested two additional models:

$${CSAD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t\mathrm{and}{CSSD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$$

Return volatility can be used to characterise periods of market stress. Periods of large price movements and volatility in stock returns may create asymmetries in herding behaviour. To capture the asymmetric effects that the volatility of stock markets may cause to herding behaviour, I followed Tan et al. (2008) and further estimated the following models:

$${CSAD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t,ifVOLishigh$$

$${CSAD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t,ifVOLislow$$

where variables with the superscript VOL–HIGH refer to the scenario in which the market volatility is high, and variables with the superscript VOL–LOW refer to the scenario in which the market volatility is low. I separated our dataset into two parts: one in which market volatility is high and another in which market volatility is low. Market volatility was calculated as the standard deviation of the daily market return times the square root of 252 trading days. The standard deviation of the daily market return was calculated as the standard deviation of the raw market return of the previous 30 days. The days when market volatility exceeded the moving average of volatility over the previous 30 days comprised the dataset of high market volatility. The days when market volatility did not exceed the moving average of volatility over the previous 30 days comprised the dataset of low market volatility. A statistically significant and negative coefficient, ${\gamma }_2^{VOL-HIGH}$ or ${\gamma }_2^{VOL-LOW}$, can be used as an indication of the presence of herding behaviour during periods of high and low market volatility, respectively. For deeper analysis as well as robustness checks, I further considered the following models:

$${CSSD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t,ifVOLishigh,$$

$${CSSD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t,ifVOLislow$$

To deal with the autocorrelation and homoscedasticity of the residuals, I calculated the generalised least squares (GLS) to estimate the parameters of all models (Brooks, 2014, pp. 136, 150). The errors follow a first-order autoregressive process.

The models assume that in the presence of herding stock, returns tend to concentrate around the returns of the market portfolio. Hence, dispersion measures CSAD or CSSD can be used to test herding behaviour. Variables CSAD and CSSD are calculated for each time point t, where t is the effective date of the transaction that corresponds to the transaction date of the trade on SEC Form 4. Hence, the dispersion measures focus on the dispersion of stock returns on days on which insiders trade. Overall, the estimated coefficients of the models can be used to extract implications on herding behaviour on days that stocks are traded by insiders.

3. Results and Robustness Checks

GLS regression analysis further illuminated the herding behaviour of insider traders. Table 1 and Table 2 present the regression results using the dataset of opportunistic purchases and sales over the period 2014 to 2024. After regressing $CSAD$ and $CSSD$ on dummy variables that indicate when market return lies in the extreme lower and higher tails of the return distribution, the estimated coefficients for both dummies and both datasets of opportunistic purchases and sales are not negative and statistically significant. On the contrary, they are positive and statistically significant, which indicates that there is a large dispersion of asset returns from the market return during periods of large price movements. This is not an indication of herding behaviour.

Table 1. Herding behaviour of opportunistic purchases from 2014 to 2024.

${CSAD}_t=\mathit{\alpha }+{\mathit{\beta }}^L{D}_t^L+{\mathit{\beta }}^U{D}_t^U+{\mathit{\epsilon }}_t$ (5th/95th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.5384 *** (0.0165)	1.7776 *** (0.0623)	1.4948 *** (0.0623)	36.45%	2765
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (5th/95th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.7082 *** (0.0500)	1.8037 *** (0.2139)	1.5820 *** (0.2139)	4.22%	2765
${CSAD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.6371 *** (0.0159)	3.4302 *** (0.1381)	2.8376 *** (0.1391)	30.37%	2767
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.8092 *** (0.0475)	3.6215 *** (0.4585)	2.9761 *** (0.4588)	3.59%	2767
${CSAD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$
$\alpha$	${\gamma }_1$	${\gamma }_2$	$Adj.R^2$	$T$
0.0322 *** (0.0139)	1.0009 *** (0.0197)	0.0004 (0.0031)	72.96%	2765
${CSSD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$
$\alpha$	${\gamma }_1$	${\gamma }_2$	$Adj.R^2$	$T$
0.1802 ** (0.0717)	1.0434 *** (0.1015)	−0.0006 (0.0119)	9.78%	2765
${CSAD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-HIGH}$	${\gamma }_1^{VOL-HIGH}$	${\gamma }_2^{VOL-HIGH}$	$Adj.R^2$	$T$
0.0080 (0.0117)	1.0046 *** (0.0151)	0.0013 (0.0017)	97.62%	456
${CSAD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-LOW}$	${\gamma }_1^{VOL-LOW}$	${\gamma }_2^{VOL-LOW}$	$Adj.R^2$	$T$
0.0345 ** (0.0166)	1.0060 *** (0.0251)	−0.0016 (0.0049)	66.33%	2308
${CSSD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-HIGH}$	${\gamma }_1^{VOL-HIGH}$	${\gamma }_2^{VOL-HIGH}$	$Adj.R^2$	$T$
0.0833 * (0.0482)	0.9956 *** (0.0622)	0.0134 * (0.0072)	73.42%	456
${CSSD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-LOW}$	${\gamma }_1^{VOL-LOW}$	${\gamma }_2^{VOL-LOW}$	$Adj.R^2$	$T$
0.1827 ** (0.0861)	1.0973 *** (0.1301)	−0.0172 (0.0252)	7.13%	2308

This table presents estimated coefficients of the models employed to study the herding behaviour of opportunistic purchases from 2014 to 2024 in the USA. Standard errors are reported in parentheses. ${CSAD}_t$ is the cross-sectional absolute deviation on day $t$; ${CSSD}_t$ is the cross-sectional standard deviation on day $t$; $D_t^L$ and $D_t^U$ are dummy variables, taking values of one when the market return at time $t$ lies in the extreme lower and higher tails of the return distribution, respectively; ${\beta }^L$ and ${\beta }^U$ are the estimated coefficients of dummy variables $D_t^L$ and $D_t^U$, respectively; $R_{m,t}$ is the market return on day $t$; ${\gamma }_1$ and ${\gamma }_2$ are the estimated coefficients of the absolute and squared values of market returns, respectively; $\alpha$ is a constant; and ${\epsilon }_t$ is the error term. Superscripts $VOL-HIGH$ and $VOL-LOW$ correspond to high and low market volatility, respectively. The 5th/95th and 1st/99th cutoffs are the percentiles of the market return distribution. The values of the adjusted $R^2$ of each model as well as the number of time series observations ($T$) are also shown. *, **, and *** correspond to p-values of 10, 5, and 1% levels, respectively.

Table 2. Herding behaviour of opportunistic sales from 2014 to 2024.

${CSAD}_t=\mathit{\alpha }+{\mathit{\beta }}^L{D}_t^L+{\mathit{\beta }}^U{D}_t^U+{\mathit{\epsilon }}_t$ (5th/95th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.5348 *** (0.0179)	1.8597 *** (0.0686)	1.4693 *** (0.0686)	32.86%	2766
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (5th/95th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.7848 *** (0.0515)	2.2431 *** (0.2204)	1.4926 *** (0.2204)	4.9%	2766
${CSAD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.6312 *** (0.0173)	3.9336 *** (0.1467)	2.8207 *** (0.1481)	31.39%	2767
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)
$\alpha$	${\beta }^L$	${\beta }^U$	$Adj.R^2$	$T$
0.8783 *** (0.0488)	5.8397 *** (0.4666)	3.1499 *** (0.4672)	6.82%	2767
${CSAD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$
$\alpha$	${\gamma }_1$	${\gamma }_2$	$Adj.R^2$	$T$
0.0881 *** (0.0140)	0.8452 *** (0.0199)	0.0469 *** (0.0032)	76.02%	2766
${CSSD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$
$\alpha$	${\gamma }_1$	${\gamma }_2$	$Adj.R^2$	$T$
0.5367 *** (0.0690)	0.3318 *** (0.0978)	0.2100 *** (0.0155)	21.72%	2766
${CSAD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-HIGH}$	${\gamma }_1^{VOL-HIGH}$	${\gamma }_2^{VOL-HIGH}$	$Adj.R^2$	$T$
0.0268 (0.0218)	0.9590 *** (0.0228)	0.0087 ** (0.0038)	96.09%	456
${CSAD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-LOW}$	${\gamma }_1^{VOL-LOW}$	${\gamma }_2^{VOL-LOW}$	$Adj.R^2$	$T$
0.0830 *** (0.0153)	0.8499 *** (0.0247)	0.0514 *** (0.0037)	71.58%	2309
${CSSD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+{\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-HIGH}$	${\gamma }_1^{VOL-HIGH}$	${\gamma }_2^{VOL-HIGH}$	$Adj.R^2$	$T$
0.1496 (0.1127)	1.0344 *** (0.1175)	−0.0032 (0.0196)	49.40%	456
${CSSD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+{\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$
${\alpha }^{VOL-LOW}$	${\gamma }_1^{VOL-LOW}$	${\gamma }_2^{VOL-LOW}$	$Adj.R^2$	$T$
0.5196 (0.0751)	0.3229 (0.1213)	0.2365 (0.0180)	21.57%	2309

This table presents estimated coefficients of the models employed to study the herding behaviour of opportunistic sales from 2014 to 2024 in the USA. Standard errors are reported in parentheses. ${CSAD}_t$ is the cross-sectional absolute deviation on day $t$; ${CSSD}_t$ is the cross-sectional standard deviation on day $t$; $D_t^L$ and $D_t^U$ are dummy variables, taking values of one when the market return at time $t$ lies in the extreme lower and higher tails of the return distribution, respectively; ${\beta }^L$ and ${\beta }^U$ are the estimated coefficients of dummy variables $D_t^L$ and $D_t^U$, respectively; $R_{m,t}$ is the market return on day $t$; ${\gamma }_1$ and ${\gamma }_2$ are the estimated coefficients of the absolute and squared values of market returns, respectively; $\alpha$ is a constant; and ${\epsilon }_t$ is the error term. Superscripts $VOL-HIGH$ and $VOL-LOW$ correspond to high and low market volatility, respectively. The 5th/95th and 1st/99th cutoffs are the percentiles of the market return distribution. The values of the adjusted $R^2$ of each model as well as the number of time series observations ($T$) are also shown, **, and *** correspond to p-values of 10, 5, and 1% levels, respectively.

Indications of herding behaviour are not found after regressing the $CSAD$ and $CSSD$ of stock returns on the absolute values of the returns of the market portfolio and on the squared values of the returns of the market portfolio. Specifically, when the dependent variable is $CSAD$, the estimated coefficient for the absolute market returns in both datasets are positive and statistically significant. When the dependent variable is $CSSD$, the estimated coefficient for the absolute market returns is positive and statistically significant in the dataset of opportunistic purchases, whereas it is positive and not statistically significant in the dataset of opportunistic sales. The linear and positive relationships between individual asset return dispersion and market return imply that individual stocks do not follow the aggregate market behaviour. Focusing on the estimated coefficient of the squared market returns, the results are not in favour of herding behaviour. In the dataset of opportunistic purchases, the estimated coefficient of the squared market returns is positive and negative when the dependent variable is $CSAD$ and $CSSD$, respectively. In both models, the estimated coefficient remains not statistically significant. In the case of opportunistic sales, the estimated coefficients of the squared market returns are positive and statistically significant. These results indicate that the cross-sectional absolute deviation of stock returns will increase with the market return at an increasing rate, which is not supporting evidence of herding behaviour.

The absence of herding behaviour is further implied after grouping the samples of opportunistic purchases and sales based on the days of high and low volatility in the market. When market volatility is high, the estimated coefficients of the absolute values of the returns of the market portfolio are positive and statistically significant for both opportunistic purchases and sales. Moreover, the estimated coefficients of the squared values of the returns of the market portfolio are positive and statistically significant in most cases. When market volatility is low, the estimated coefficients of the absolute market returns are positive and statistically significant in most cases. The estimated coefficients of the squared market returns are negative and not statistically significant in the dataset of opportunistic purchases, whereas they have a positive sign in the dataset of opportunistic sales.

To further assess the validity of the results, out-of-sample validation was performed. Specifically, I used 80% of the time series as an in-sample estimation period. The remaining 20% was used as the out-of-sample forecast evaluation period. The mean squared error, MSE, and mean absolute error, MAE, were calculated for each model and dataset. The mean squared error is calculated as the average of the squared differences between the forecasted and the real values of $CSAD$ and $CSSD$. The mean absolute error was calculated as the average of the absolute differences between the forecasted and the real values of $CSAD$ and $CSSD$. Table 3 presents the values of MSE and MAE for all models and datasets. As it can be clearly observed, models with $CSAD$ as the dependent variable exhibit lower values of MSE and MAE, which indicates that they are more accurate relative to those with $CSSD$ as the dependent variable (Brooks, 2014, p. 252). Specifically, for the models with $CSAD$ as the dependent variable, the values of MSE and MAE are less than 0.41, whereas for models with $CSSD$ as the dependent variable, the values of MSE and MAE exceed the value of 1, reaching the maximum value of 3.52 in most cases. The low values of MSE and MAE indicate that the predicted values of $CSAD$ do not deviate largely from their real values.

Table 3. Values of MSE and MAE.

Model	Dataset of Opportunistic Purchases		Dataset of Opportunistic Sales
	MSE	MAE	MSE	MAE
${CSAD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (5th/95th cutoffs)	0.2047	0.3352	0.1902	0.3329
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (5th/95th cutoffs)	1.4148	0.4836	3.0854	0.5704
${CSAD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)	0.3061	0.4105	0.2503	0.3514
${CSSD}_t=\alpha +{\beta }^L{D}_t^L+{\beta }^U{D}_t^U+{\epsilon }_t$ (1st/99th cutoffs)	1.4816	0.5574	2.7238	0.5451
${CSAD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$	0.0620	0.0695	0.0424	0.0728
${CSSD}_t=\alpha +{\gamma }_1\left|R_{m,t}\right|+{\gamma }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t$	1.2522	0.3319	2.9699	0.4162
${CSAD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+$ ${\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$	0.0023	0.0297	0.0045	0.1156
${CSAD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+$ ${\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$	0.0737	0.0774	0.0495	0.0754
${CSSD}_t^{VOL-HIGH}={\alpha }^{VOL-HIGH}+{\gamma }_1^{VOL-HIGH}\left|R_{m,t}^{VOL-HIGH}\right|+$ ${\gamma }_2^{VOL-HIGH}{\left(R_{m,t}^{VOL-HIGH}\right)}^2+{\epsilon }_t$	1.0532	0.1875	0.2004	0.2587
${CSSD}_t^{VOL-LOW}={\alpha }^{VOL-LOW}+{\gamma }_1^{VOL-LOW}\left|R_{m,t}^{VOL-LOW}\right|+$ ${\gamma }_2^{VOL-LOW}{\left(R_{m,t}^{VOL-LOW}\right)}^2+{\epsilon }_t$	1.2940	0.3581	3.5169	0.4494

This table presents the values of the mean squared error (MSE) and mean absolute error (MAE) of the out-of-sample forecasts. The mean squared error is calculated as the average of the squared differences between the forecasted and the real values of $CSAD$ and $CSSD$. The mean absolute error is calculated as the average of the absolute differences between the forecasted and the real values of $CSAD$ and $CSSD$. The 5th/95th and 1st/99th cutoffs are the percentiles of the market return distribution.

4. Discussion

In this paper, I examined the relation between the deviation of stocks traded by opportunistic insider traders from the market returns with the absolute and market returns as an indicator of herding behaviour by applying regression methods based on the cross-sectional absolute and standard deviation of asset returns from the market return. The period covered is from 2014 to 2024. I found no evidence to support that stock prices are concentrated around the returns of the market portfolio in both opportunistic purchases and sells. In other words, I did not find a statistically significant and negative relation between the cross-sectional deviation of stock prices from the market return and the absolute or squared returns of the market portfolio. Based on the assumption that herding behaviour has a substantial impact on stock prices (Christie & Huang, 1995), the results imply the absence of herding behaviour in stock prices around the date that opportunistic insiders traded. This result is important for policy makers who are dedicated to regulating insider trading. Since there are indications that insider trading does not result in herding behaviour, regulators should keep in mind that the impact of using material non-public information on stock prices will not spread among other stocks. For this reason, external traders cannot make conclusions on price movements by observing the insider movements of a specific company.

An important limitation of this study is that conclusions regarding the herding behaviour of insider traders are based on the cross-sectional absolute and standard deviation of asset returns from the market returns. Specifically, in this study, the methodologies of Christie and Huang (1995), Chang et al. (2000), Gleason et al. (2004), and Tan et al. (2008) led to the implication of an absent herding behaviour of insider traders. Future research may adopt methodologies based on different assumptions to examine the existence of herding behaviour. For instance, Mansi et al. (2025) used a portfolio strategy to test herding behaviour based on the assumption that company insiders identify and take advantage of mispricing generated by the trading activity of retail investors. Overlapping industry trade effects and event windows can be taken into consideration.

Moreover, future research may shield more light on the herding behaviour of insider traders. Insiders follow trading plans under Rule10b5-1. The 10b5-1 plan is adopted when the executive is not aware of the MNPI, and it limits the insiders’ trading liability regarding illegal insider trading. Even though there is legislation that prohibits insiders from illegal trading, insiders act strategically using Rule 10b5-1 plans and follow patterns that benefit from the MNPI of their companies. Herding behaviour can be studied in cases of pre-planned insider trading under Rule 10b5-1.