State-Dependent Dynamics of Overconfidence in Frontier Equity Markets: A Transfer Entropy Approach from Bangladesh

Abstract

The study investigates the state-dependent dynamics of overconfidence in the Bangladesh equity market by exploring the relationship between market returns and trading volume within a nonlinear information-theoretic framework. Building up on the traditional return–volume literature, the study differentiates between total market returns and unexpected returns, with the latter representing unexpected information shocks obtained using the Market Index Model. Transfer Entropy with bootstrap inference estimates the directional and asymmetric information flows across five different market states, namely: bullish, bearish, crisis, extended crisis, and COVID-19. The evidence suggests that the overconfidence biases in aggregate market returns are small and intermittent and are reflected in poor and unstable information flow between market returns and trading volume. In comparison, unexpected market returns have a directionally significant impact on trading behavior, which supports the behavior of state-dependent overconfidence. The findings also reveal that overconfidence is higher in normal and bullish market situations but drops significantly in crisis-based situations. The asymmetric analysis indicates increased trading responses to negative returns shocks, as it is more evident that investors are more sensitive to losses and recovery expectations. The research adds to behavioral finance literature on frontier markets through an unexpected return decomposition with nonlinear causality model. The results have serious implications on market surveillance, assessment of investor behavior and design of regulatory policies.

1. Introduction

Behavioral finance presumes that investors are not necessarily rational and are subject to psychological biases that influence investment decisions and market outcomes. Overconfidence is among the most significant behavioral biases, exerting a substantial influence on investor trading behavior and equity market dynamics (De Bondt & Thaler, 1995). Overconfident investors tend to overestimate the accuracy of their private information and forecasting ability, leading to exaggerated trading that may lead to market inefficiency. This behavioral bias is not driven by the factors in the equity markets, but rather it is induced by the characteristics of market participants (Odean, 1998). The previous literature has predominantly focused on the interaction between market return and trading volume, suggesting that an upward movement is related to heightened trading volume.

Nevertheless, most empirical studies on overconfidence have been done using developed and emerging stock markets through linear econometric models such as Vector Autoregression (VAR) and Granger causality models. Although these models offer useful insights on the relationship between returns and volume, they cannot fit the nonlinear and asymmetric behavioral patterns of equity markets. Financial markets are highly complex environments in which dependencies between market return and trading activity become nonlinear, information transmission acts in multiple ways, and investor reactions to the market signals are heterogeneous. Thus, using only linear methods can result in incomplete knowledge of the behavior of equity markets.

The theoretical justification of using Transfer Entropy for examining overconfidence behavior derives from the characteristics of information transmitted in financial markets. Overconfidence occurs when investors react to market signals and heavily rely on past market performance while making trading decisions. This type of activity creates directional information flow from market return to subsequent trading activity. Transfer Entropy is an appropriate model, since it is used to measure nonlinear and directional transfer of information between variables without any constraining assumptions of linearity or normality. A statistically significant information flow between market returns and trading volume is thus seen as an indication that investors overreact to market signals in an overconfidence behavioral fashion.

Another weakness of the current literature is that it extensively uses the total market returns as the main indicator to study overconfidence bias. But behavioral responses tend to be driven by unanticipated information shocks rather than predictable market movements. Unexpected returns are new information that can change the investors’ moods and lead to overconfidence in trading. The phenomenon of unexpected return has not received much attention in the literature, especially in a nonlinear analytical framework, and largely remains unexplored to assess its potential impact on overconfident trading behavior.

Furthermore, previous research on overconfidence is highly dominated by the developed and emerging markets, leaving frontier equity markets relatively under-researched. Frontier markets are structurally different, with less market efficiency, higher information asymmetry, a higher level of speculative trading and weaker institutions. These features can lead to a greater intensity of investor behavioral biases and result in different investor responses in different market scenarios. Even though the investor behavior under bullish, bearish, crisis, extended crisis and COVID-19 market regimes is likely to vary significantly, there is limited systematic empirical data on state-dependent overconfidence dynamics in frontier equity markets.

All these gaps prompt the need to adopt a nonlinear, information-theoretic Transfer Entropy model to examine overconfidence in the Bangladesh equity market. This methodology captures the asymmetric and directional information flows between market returns and trading volume and provides more insightful and accurate information on investor behavior than traditional linear approaches. The study further investigates the influence of unexpected information shocks in driving trading activity by comparing the total market returns with those found under unexpected market returns. This analysis is also carried out in a state classification framework of the market to determine overconfidence dynamics of state-dependency in structurally different market environments.

The study contributes to the literature in multiple ways. Firstly, it adds an unexpected market return to the behavioral finance literature as one of the behavioral triggers of overconfidence. Secondly, it employs Transfer Entropy to analyze the nonlinear and directional information flow between returns and trading volume and surpasses the long-established drawbacks of the conventional linear econometric methods. Thirdly, it offers novel evidence on the conditional character of investor overconfidence and its consequences to financial market development and efficiency with a special emphasis on a frontier market in five market conditions.

The study is organized as follows. Section 2 reviews the literature, Section 3 describes the data and methodology, Section 4 represents the empirical results, Section 5 highlights the discussion of results, and Section 6 concludes the study.

2. Literature Review

2.1. Overconfidence Theory and Lead-Lag Return–Volume Relationship

The behavioral finance literature has widely reported that investors are prone to overconfidence bias and the behavior leads to overestimation of the accuracy of their own information and overtrading. The analysis of causality between the past market returns and the trading volume is one of the most popular methods to detect overconfidence in financial markets. Good market performance tends to boost the confidence of investors in their capacity to invest, thus driving up the trading activity.

Empirical research has documented that overconfident investor trade frequently, which leads to the high levels of trading in the financial market (De Bondt & Thaler, 1995; Odean, 1998, 1999; Gervais & Odean, 2001; Barber & Odean, 2001). Overconfidence is a multidimensional cognitive bias that comes in a number of behavioral tendencies. These are miscalibration, i.e., over-estimating their knowledge and forecasting capabilities; illusion of control, i.e., over-estimating their ability to affect the outcomes, mostly through chance; self-attribution bias, i.e., over-estimating the correctness of their judgment as compared to others; and the better-than-average effect, i.e., over-estimating the accuracy of their judgments as compared to others. These psychological biases can produce various sub-optimal investment patterns, such as overtrading, under-diversifying, engaging in high-risk, low-reward projects, and eventually leading to poor investment performance (Barber & Odean, 2000, 2001).

A number of empirical research findings indicate that overconfidence in equity markets does exist. Chuang and Lee (2006) found overreaction to private information, over-volatility and underestimation of risks as key overconfidence behaviors in the financial market. Statman et al. (2006) examined the relationship between market returns and trading volume in the U.S. market to examine overconfidence and found its evidence. Equally, Metwally and Darwish (2015) analyzed the Egyptian stock market through VAR, Granger causality and impulse response analysis and found that historical returns have positive impacts on modern day trading turnover as they confirmed overconfidence and self-attribution theories predictions. Similar results were reported by Zia et al. (2017); Mushinada and Veluri (2018) who established that investors will respond aggressively after a positive performance in the market leading to increased activity.

Overconfidence has also been found to exist in a number of international and emerging markets. Phan et al. (2020) discovered that there were high overconfidence levels in Vietnam and Singapore, but Thai investors were found to be rather underconfident. Similarly, Boussaidi (2022) found a positive unidirectional relationship between trading volume and market returns in MENA markets, which shows that investors attribute positive returns to their own skills. Ganesh et al. (2022), Podvorec (2023) and Rabbani et al. (2024), also reported the presence of overconfidence bias in various equity market conditions.

Although the evidence on overconfidence bias is quite general, previous research indicates that the behavior of investors does not occur uniformly across markets and time. The existence of differences in institutional structures, maturity of the market, efficiency of information and composition of investors may play an important role in the intensity of overconfidence behavior. As a result, results within the markets are varied and context-specific.

2.2. State-Dependent Perspective of Overconfidence Behavior

Recent literature is giving an ever-growing indication that overconfidence behavior is not consistent irrespective of market settings and economic environments. The sentiment of investors, uncertainty, and risk perception can frequently vary significantly in bullish, bearish, crisis, and pandemic periods, which suggests that behavioral biases can be state-dependent.

According to several studies, the existence of favorable market conditions increases overconfidence behavior. As illustration, Kumar and Prince (2022) had discovered that investors’ overconfidence in pre-crash periods but the bias declined in crisis and post-crisis periods as a result of the increased uncertainty and risk aversion. In a similar manner, Mahjoubi and Henchiri (2024) have stated that the most significant crises like the subprime crisis, Eurozone crisis and the COVID-19 pandemic lowered investor confidence and undermined the strength of overconfidence in market efficiency.

But the empirical results are inconclusive. Unlike in these studies where confidence in times of crisis reduced, Shrotryia and Kalra (2021) found a high level of overconfidence in various international markets at the time of COVID-19. Similarly, Rabbani et al. (2024) reported that the Italian market had a considerable overconfident behavior during the pandemic. These conflicting results indicate that the psychology of investors might not be the same when they face different market conditions and institutions are placed in different settings.

Moreover, the majority of the available literature categorizes market regimes into normal and crisis regimes in broad strokes and does not take into account specific market regimes like bullish, bearish, prolonged crisis and pandemic-induced market regimes. Consequently, the dynamics of overconfidence in various market contexts and settings are not sufficiently examined, especially in frontier equity markets where informational inefficiencies and speculative trading activity are relatively more pronounced.

2.3. Methodological Perspectives and Limitations

The literature available has used many different econometric methods to analyze overconfidence in financial markets. The majority of the studies are primarily dependent on the conventional linear models like Vector Autoregression (VAR), Granger causality tests, impulse response functions, and GARCH-based models. Studies such as Alsabban and Alarfaj (2020); Azam and Baig (2023); Ganesh et al. (2022), Metwally and Darwish (2015); Musah et al. (2023); Mushinada and Veluri (2018); Phan et al. (2020); and Zia et al. (2017) utilized these linear methods and reported that there are significant interactions between market returns and trading volume. Kuranchie-Pong and Forson (2022) used GARCH (1,1) and GJR-GARCH (1,1) in the Ghana equity market to examine overconfidence.

Even though the approaches are useful in detecting the linear associations, they might not be entirely effective in detecting the nonlinear and asymmetric behavioral biases. Complex interactions, feedback and evolving market sentiments often impact investor psychology, and may change differently in other market conditions. Linear models, therefore, may not uncover the directional and nonlinear flow of information between market returns and trading volume, particularly in frontier equity markets with structural instability and shifting investor sentiment.

In the wake of these shortcomings, more recent research has begun to include nonlinear methods in behavioral finance work. In an example, Bouteska et al. (2023) utilized a multilayer feed-forward neural network-based nonlinear Granger causality model and discovered that there was an overconfidence in the U.S. equity market. However, information-theoretic approaches are still not extensively used in overconfidence literature.

Specifically, Transfer Entropy offers a number of benefits over traditional econometric techniques by offering nonlinear, directional, and asymmetric information flow, without the need to assume strict linearity. Although these methodological benefits exist, there are extremely few studies that have used Transfer Entropy to study the behavior of overconfidence, particularly in frontier market settings.

2.4. Evidence from Frontier Equity Markets

Frontier equity markets may have distinct behavioral characteristics from developed and emerging markets are reflected in the informational efficiency, the dominance of speculative trades, the institutional weaknesses and market depth. Short-term sentiment and rumors, along with unofficial information channels, can have an impact on investors in developing countries who may be more prone to behavioral risks and nonlinear market response. Empirical studies on overconfidence behavior in a frontier market are limited, especially in different market states and crisis conditions, although these are unique features of the market. Empirical research on the existence of overconfidence bias in frontier equity markets is relatively limited, with studies concentrated in only a few countries. Tunisia (Zaiane & Abaoub, 2009), Pakistan (Zia et al., 2017; Rahim et al., 2020), Ghana (Kuranchie-Pong & Forson, 2022), and Sri Lanka (Shantha, 2024) have been reported to have evidence on behavioral dynamics in the frontier market setting.

2.5. Research Gap and Novelty of the Study

Despite the vast amount of literature on overconfidence bias in financial markets, there are a number of significant gaps that have not been addressed. To start with, there is a relative lack of empirical data regarding frontier equity markets in comparison to developed and emerging markets. Low informational efficiency, speculative trading and weak institutionalization are the primary characteristics of frontier markets, rendering them particularly vulnerable to the study of behavioral finance. Second, the prevailing literature mainly uses linear econometric models like VAR and Granger causality, which might not be sufficient to reflect nonlinear and asymmetric flow of information between market returns and trading activity. Further information-theoretic frameworks have not been widely used in the literature.

Third, most of the studies study overconfidence with aggregate market conditions without sufficiently addressing the state-dependent behavior of investor psychology in bullish, bearish, crisis, extended crisis, and COVID-19 market conditions. As a result, the dynamic development of overconfidence in the alternative market states is not well comprehended.

To fill these gaps, this study explores the state-dependent overconfidence dynamics in the Bangladesh equity market, based on a Transfer Entropy framework. In particular, the research focuses on the directional information flow between market returns and trading volume under bullish, bearish, crisis, extended crisis and COVID-19 market conditions. The combination of a frontier market view with a nonlinear information-theoretic approach provides a contribution to the literature on behavioral finance by shedding more light on how investor overconfidence changes in various market conditions.

3. Data and Methodology

3.1. Data

The dataset was manually compiled from the trade files of the Dhaka Stock Exchange, as no centralized database, such as Bloomberg or DataStream, is available for the Bangladesh equity market. Data collection involved obtaining the daily closing prices and turnover values of all the listed securities during the sample period from 1 January 2010 to 31 December 2021. An equally weighted daily market return is used to build a market-wide return series to capture the aggregate price movements by taking an average of the individual adjusted stock returns of all stocks on each day. The daily aggregate trading volume of the market is estimated by adding daily market turnover of all the listed securities. The logarithm of the daily turnover series is used for empirical estimation to account for scale effects, heteroscedasticity and long-term structural growth trends in market activity.

A systematic checking of the observations was conducted to ensure consistency in the data and for missing data or duplicate observations, missing trading days, and potential inconsistencies in data input, with the aim of improving transparency and data reliability. Furthermore, the construction of adjusted returns, market turnover and the classification into market-states was verified in order to assure the consistency and reproducibility of the empirical analysis across the sample period. The resulting set of data creates a holistic high-frequency market-wide database that can be analyzed for nonlinear information transmission and behavioral dynamics, via the Transfer Entropy framework.

3.2. Methodology

The standard Granger causality test assumes a linear functional form in which the causes and effects are determined and are implemented by fitting autoregressive models (Granger, 1969; Wiener, 1956). Transfer Entropy, proposed and applied by Schreiber (2000) is treated as an essential tool of assessing causal relationships in nonlinear systems (Hlaváčková-Schindler et al., 2007). It quantifies the directional and dynamical information flow between two interacting time series (Montalto, 2016) without assuming any functional form.

Transfer Entropy is developed relying on the concept of Kullback–Leibler distance under the assumption that the underlying series are Markov Process. A stationary Markov Process is a stochastic process used in time series analysis in which statistical properties remain constant over time, and the probability distribution of the future state depends on its current state, not on the sequence of preceding states.

Entropy definitions can be explained in terms of Shannon and Renyi entropies with a slight variation in their properties. Shannon entropy possesses all desired properties of an information measure that seems to be most appropriate for the distributions of financial variables (Hlaváčková-Schindler et al., 2007). Assume that X is a discrete random variable, can take values $x_1,x_2,\dots \dots \dots ,x_m$ with corresponding probability $p_i,i=1,2,3,\dots \dots \dots \dots \dots \dots \dots \dots ,m$. The Shannon entropy is an average amount information gained from a particular investment value,

$$\mathrm{H}(X)=-{\displaystyle \sum _{i=1}^m{p}_i}\log p_i$$

(1)

The joint entropy $\mathrm{H}(X,Y)$ of the random variable is defined as

$$\mathrm{H}(X,Y)=-{\displaystyle \sum _{i=1}^{m_X}{\displaystyle \sum _{j=1}^{m_Y}p(x_i}},y_j)\log (p(x_i,y_j))$$

(2)

where $x_i,i=1,2,\dots \dots \dots ,m_X$ the values of the discrete variable X,

$y_j,j=1,2,\dots \dots \dots ,m_Y$ the values of the discrete variable Y, and

$p(x_i,y_j)$ the joint probability that X is in state $x_i$ and Y is in state $y_j$.

The joint entropy is expressed in terms of conditional entropy $\mathrm{H}(Y\left|X)\right.$:

$$\mathrm{H}(Y\left|X)=\mathrm{H}(X,Y)-\mathrm{H}(Y)\right.$$

(3)

In discrete case, the conditional entropy is equal to:

$$\mathrm{H}(Y|X)={\displaystyle \sum _{i=1}^{m_X}{\displaystyle \sum _{j=1}^{m_Y}p(x_i}},y_j)p(y_j\left|x_i\right.)$$

(4)

where $p(y_j\left|x_i\right.)$ denotes conditional probability.

• Mathematical Development of Transfer Entropy:

Schreiber (2000) describe the Shannon transfer entropy model for given two time series $X_t$ and $Y_t$ to measure information from X to Y as:

$$T_{X\to Y}={\displaystyle \sum _{y_{t+1,}{y}_{t,}{x}_t}p(y_{t+1,}{y}_{t,}{x}_t})\log {\displaystyle \frac{p(y_{t+1}\left|y_{t,}{x}_t)\right.}{p(y_{t+1}\left|y_t)\right.}}$$

(5)

where,

• $p(y_{t+1,}{y}_{t,}{x}_t$) is the joint probability distribution of the future state $y_{t+1}$, the current state $y_{t,}$ and $x_t$
• $\rho \left(y_{t+1}|y_{t,}{x}_t\right)$ is the conditional probability of $y_{t+1}$ given the past information $y_t$, and $x_t$.
• $\rho \left(y_{t+1}|y_t\right)$ is the conditional probability of $y_{t+1}$ given the past information $y_t$.

Transfer entropy measures the amount of uncertainty in $Y_{t+1}$ that can be reduced by knowing the past information of $X_t$ in addition to $Y_t$. If X has a causal effect on Y, knowing $X_t$ should significantly reduce the uncertainty about $Y_{t+1}$, producing a higher transfer entropy value.

To measure the direction of causality from equity market return to market trading volume, we can present the Transfer Entropy model as

$${\mathrm{T}}_{\mathrm{M}\mathrm{R}\to \mathrm{T}\mathrm{V}}={\sum }_{{\mathrm{T}\mathrm{V}}_{\mathrm{t}+1,}{\mathrm{T}\mathrm{V}}_{\mathrm{t},}{\mathrm{M}\mathrm{R}}_{\mathrm{t}}}{\mathrm{P}(\mathrm{T}\mathrm{V}}_{\mathrm{t}+1,}{\mathrm{T}\mathrm{V}}_{\mathrm{t},}{\mathrm{M}\mathrm{R}}_{\mathrm{t}})\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{\mathrm{P}\left({\mathrm{T}\mathrm{V}}_{\mathrm{t}+1}|{\mathrm{T}\mathrm{V}}_{\mathrm{t},}{\mathrm{M}\mathrm{R}}_{\mathrm{t}}\right)}{\mathrm{P}\left({\mathrm{T}\mathrm{V}}_{\mathrm{t}+1}|{\mathrm{T}\mathrm{V}}_{\mathrm{t}}\right)}}$$

(6)

$${\mathrm{T}}_{\mathrm{T}\mathrm{V}\to \mathrm{M}\mathrm{R}}={\sum }_{{\mathrm{M}\mathrm{R}}_{\mathrm{t}+1,}{\mathrm{M}\mathrm{R}}_{\mathrm{t},}{\mathrm{T}\mathrm{V}}_{\mathrm{t}}}{\mathrm{P}(\mathrm{M}\mathrm{R}}_{\mathrm{t}+1,}{\mathrm{M}\mathrm{R}}_{\mathrm{t},}{\mathrm{T}\mathrm{V}}_{\mathrm{t}})\mathrm{l}\mathrm{o}\mathrm{g}{\displaystyle \frac{\mathrm{P}\left({\mathrm{M}\mathrm{R}}_{\mathrm{t}+1}|{\mathrm{M}\mathrm{R}}_{\mathrm{t},}{\mathrm{T}\mathrm{V}}_{\mathrm{t}}\right)}{\mathrm{P}\left({\mathrm{M}\mathrm{R}}_{\mathrm{t}+1}|{\mathrm{M}\mathrm{R}}_{\mathrm{t}}\right)}}$$

(7)

Equation (6) describes the causality from market return to trading volume; whereas, Equation (7) defines the causality from trading volume to market return. The other representations mentioned in equation remain same.

Transfer Entropy is capable of accommodating an asymmetric relationship, i.e., MR → TV $\ne$ TV → MR and thus it enables us to quantify the directional coupling between two variables. The net information flow can be defined as

$$TE=(\mathrm{M}\mathrm{R}\to \mathrm{T}\mathrm{V})-(\mathrm{T}\mathrm{V}\to \mathrm{M}\mathrm{R})$$

(8)

This quantification represents the dominant direction of information flow. This means a positive Transfer Entropy value indicates a dominant information flow from market return to trading volume compared to the other direction or similarly which variable provides more predictive information about other variables in the system (Michalowicz et al., 2013).

3.2.1. Empirical Implementation Process of Transfer Entropy Model

Despite the Transfer Entropy framework having a well-defined theoretical foundation to identify the nonlinear directional dependence of market returns on trading volume, the model needs to be implemented carefully with numerous parameters being specified to achieve reproducibility and stability of the findings. This part provides a description of the practical implementation procedures that were taken in this study.

Lag Selection Criteria

Lag length selection is a very important aspect of the estimation of Transfer Entropy since it defines the amount of past information that is factored into the analysis. The Transfer Entropy estimation employs a first-order Markov Process with a lag length of one trading day (k = 1), implying that current information transfer depends on the immediately preceding state of the variables. A short lag is also chosen in line with the high-frequency characteristics of the daily financial data and is consistent with the behavioral assumption that the overreaction and self-attribution effects of investors are more likely to be found in short-term trading decisions. Alternative lag structures (k = 2 and k = 3) were also considered in order to make it robust. The qualitative nature of the results is also consistent with various lag specifications, which supports the information flow as not being dependent on the choice of lag.

Discretization Process

Because Transfer Entropy is calculated using probability distributions of time series, continuous financial variables have to be converted to discrete states. In this analysis, unexpected market returns as well as series of trading volume are both discretized by a quantile-based discretization method. In particular, every time series is partitioned into three discrete states namely low, medium and high regimes using the 33rd and 66th percentile thresholds. The number of bins chosen is appropriate, as there are three bins that provide some representation of the states and good probability estimation without being too sparse in the probability distributions. Furthermore, the use of quantile-based discretization results in a relatively uniform distribution of observations within states, and minimizes the effects of extreme observations.

Stationarity Test

Transfer Entropy estimation is based on the assumption that the underlying stochastic processes are weakly stationary. To guarantee the fulfillment of this condition, every time series variable (unforeseen returns and trading volume) is subjected to a standard unit root test to determine whether the variable is stationary or not. The findings affirm that the transformed series are stationary in their transformed form. Moreover, this is further enhanced by the fact that the unexpected returns (as opposed to the raw price levels) minimize non-stationarity issues since the unexpected returns remove deterministic trends and structural movement of the market. Since the Bangladesh equity market has had structural breaks throughout the sample (crisis and COVID-19 effects), the return-based and differenced measures will allow the analysis to be sound to time-varying market conditions.

Probability Distribution Estimation

The joint and conditional probability distributions required for Transfer Entropy estimation are computed empirically from the observed frequency distributions of the discretized time series. Probability estimation is based on relative frequency occurrence within the selected state partitions and lag structures. This nonparametric estimation approach is particularly appropriate for financial time series because it avoids imposing restrictive distributional assumptions and allows the detection of nonlinear and asymmetric information flows.

Robustness

A number of robustness checks are carried out to achieve reliability and reproducibility of the Transfer Entropy results. We analyze how the results are sensitive to other lag lengths (k = 1 to 3), and the results confirm that market returns and trading volume information flow in the same direction are stable. Second, some other discretization schemes are also tested, such as binary state partitioning (median split), and their findings are qualitatively similar. Third, sub-sample tests are conducted in various market states (bullish, bearish, crisis, extended crisis, and COVID-19) to ensure that the observed relationships are not due to a single structural regime. Lastly, the fact that unexpected returns are used rather than total returns is a strength of its own because it isolates information shocks and eliminates bias due to predictable elements of market movements. Overall, these checks confirm that the empirical use of the Transfer Entropy framework is consistent, sound and well-suited to capturing nonlinear directional dependence in frontier equity markets.

To reduce the potential upward bias commonly associated with entropy estimation in finite samples, Effective Transfer Entropy (ETE) is employed as a bias-corrected measure of information transfer. The bias correction procedure involves comparing the estimated Transfer Entropy values with randomized or shuffled versions of the original series, thereby removing spurious information flows arising from finite sample effects. The use of Effective Transfer Entropy improves the reliability and robustness of the estimated directional information transfer between market returns and trading volume.

3.3. Determination of Unexpected Market Returns Applying the Market Index Model

Existing literature primarily emphasized the relationship between trading volume and the total market returns to examine overconfidence bias. This thesis shifts focus from the total market returns to the unexpected market returns to precisely measure the existence of overconfidence across diverse market states in the Bangladesh equity market. Investigation of this bias focusing on the unexpected market returns better reflects the surprise or unanticipated component of market returns, which are more likely to trigger investor psychology.

3.3.1. Market Index Model Framework

The component of unexpected return is extracted from the Market Index Model, a prominent and widely used approach followed in securities pricing and event studies (Fama, 1976; Brown & Warner, 1985). The Market Index Model presumes the linear relationship between the return of individual stock and its sensitivity to the broad equity market index, can be modeled as follows:

$$R_t=\alpha +\beta R_{m,t}+{\epsilon }_t$$

(9)

$R_t$ represents the actual return on each stock at time t.

$R_{m,t}$ represents actual return on a benchmark equally weighted market return at time t.

$\alpha$ and $\beta$ are model parameters estimated through Ordinary Least Squares (OLSs).

${\epsilon }_t$ refers to the residual of the model representing the unexpected or idiosyncratic component of the market returns.

This model is estimated for each stock using historical data over the 2010–2021 period to derive the fitted values from the regression analysis. The expected and the unexpected components of the market returns are estimated with the following model specifications:

$$\widehat{R_t}=\alpha +\beta R_{m,t}$$

(10)

$${UR}_t=R_t-\widehat{R_t}$$

(11)

where $\widehat{R_t}$ represents the expected return on each stock at time, and ${UR}_t$ represents the unexpected return for each stock at time t.

3.3.2. Estimation Process of the Market Index Model

The parameters of the Market Index Model are estimated independently on each of the listed securities under Ordinary Least Squares (OLSs) regression over the entire sample period of January 2010 to December 2021. The full-sample estimation window is suitable in the current study since the goal is to identify the systematic and unsystematic portions of the stock returns across different market states, such as bullish, bearish, crisis, extended crisis and COVID-19. The use of a long enough estimation horizon enhances the efficiency of the parameters and minimizes the effects of short-term noise and transient market changes on the estimated coefficients.

The estimated alpha and beta coefficients are the average sensitivity of the stock returns of individual stocks to the aggregate market movements within the sample period. As the Bangladesh equity market is relatively less liquid and more volatile than developed markets, a long estimation window gives more stable estimates of the parameters and reduces the excessive volatility that would be caused by thin trading and ad hoc trading speculations. The Market Index Model was estimated separately on each stock in order to guarantee methodological reliability instead of using homogeneous market sensitivity to firms. This firm-level estimation incorporates heterogeneity in terms of systematic risk exposure and enhances the accuracy of estimation of expected returns. The residual part of the model indicates the unexpected part of the stock returns that is left over after eliminating a systematic market-related part of stock returns.

In addition, the study uses the equal-weighted aggregation of single unexpected returns to build the market-wide unexpected return series. The noise reduction policy reduces the amount of firm-specific idiosyncratic noise and allows the resulting series to reflect more of the unexpected fluctuations in aggregate market expectations and investor sentiment. The application of unexpected returns as opposed to total market returns is especially significant when analyzing behavioral finance since investor overconfidence is more apt to be provoked by unexpected information shocks as opposed to foreseeable elements of returns. The study isolates the element of surprise in stock returns, leading to a more behaviorally relevant measure of studying how nonlinear transmission of information occurs in returns and trading volume.

Moreover, the Transfer Entropy framework itself offers a further degree of robustness since it does not make strong linearity assumptions, and can represent nonlinear and asymmetric information flows between variables. This is particularly a critical aspect in frontier equity markets where the dynamics of structural instability and nonlinear interactions tend to dominate investor behavior and markets.

3.4. Market States Classification

The sample period of this study spans January 2010 to December 2021, over which the equity market is classified into five distinct states: bullish, bearish, crisis, extended crisis, and COVID-19. The classification criteria and procedures for each state are detailed below.

3.4.1. Identification of Bullish and Bearish Market States Using Dow Theory

The Dow Theory, one of the oldest and most widely applied frameworks for determining equity market trends (Dow, 1884; Hamilton, 1922; Rhea, 1932), is employed to identify bullish and bearish market states. The following explicit rules are applied to the daily closing values of the Dhaka Stock Exchange Broad Index (DSEX).

Primary Trend Identification: A primary uptrend (bullish market) is confirmed when the market index exhibits a sustained pattern of successively higher peaks (higher highs) and successively higher troughs (higher lows). Conversely, a primary downtrend (bearish market) is confirmed when the index records successively lower peaks (lower highs) and successively lower troughs (lower lows). To be classified as a distinct market state, the primary trend must persist for a minimum of three consecutive months, consistent with the Dow Theory requirement that primary trends be differentiated from secondary corrective movements.

Secondary Reaction Filter: Counter-trend secondary reactions, defined as movements retracing between one-third and two-thirds of the preceding primary movement, are recognized but are not considered reversals of the primary trend. A trend reversal signal is only considered when a secondary reaction is followed by a failure to establish a new primary trend high in a bull market or a new primary trend low in a bear market.

Trend Reversal Confirmation: A reversal from a bullish to a bearish state is confirmed when (a) following a primary uptrend, the index fails to establish a new higher high, and (b) a subsequent decline breaks below the most recent higher trough. Symmetrically, a reversal from a bearish to a bullish state is confirmed when, (a) following a primary downtrend, the index fails to establish a new lower low, and (b) a subsequent rally surpasses the most recent lower peak. This double-confirmation rule is applied to minimize the risk of false reversal signals.

3.4.2. Classification of Crisis-Driven Market States

Crisis-driven market states are identified based on documented episodes of systemic financial disruption in the Bangladesh equity market during the sample period.

Crisis Market (1 July 2010–30 June 2011): This period captures the acute equity market crash during which the DSE Broad Index declined by approximately 60% from its peak value, representing the most severe domestic market collapse in recent decades. The classification is based on the magnitude of the index decline, the systemic nature of the correction, and the regulatory interventions undertaken by the Bangladesh Securities and Exchange Commission (BSEC).

Extended Crisis Market (1 January 2010–31 December 2011): The extended crisis is constructed as a symmetrically expanded window around the acute crisis period, extending six months before its onset and six months after its conclusion. This design follows an event-study window logic, encompassing the pre-crash speculative buildup phase as well as the post-crash aftermath period characterized by residual market dislocations, damaged investor confidence, and ongoing regulatory restructuring. The extended crisis window, therefore, provides a broader analytical perspective from which to examine the full behavioral impact horizon of the crash episode, covering the pre-crash, during-crash, and post-crash periods.

COVID-19 Market (8 March 2020–31 December 2021): The COVID-19 market state begins on the date from which pandemic-related disruption became systematically observable in DSE trading data. Following the national lockdown declaration, the Dhaka Stock Exchange suspended trading from 26 March to 30 May 2020; this suspension period is excluded from all Transfer Entropy estimations. The COVID-19 state extends through 31 December 2021, the end of the sample period, capturing both the acute shock phase and the subsequent uncertain recovery environment shaped by ongoing pandemic developments and global supply chain disruptions.

3.5. Treatment of Missing Values, Thin Trading, and Stock Entry and Exit

Missing daily return observations are treated as non-trading days and assigned a return of zero, consistent with standard practice in thin market research (Dimson, 1979; Maynes & Rumsey, 1993). Stocks with five or more consecutive missing observations not attributable to market-wide holidays or the COVID-19 trading suspension are excluded from the cross-sectional average on the affected days but retained for days on which valid return data are available. The official trading suspension period, from 26 March to 30 May 2020, is excluded entirely from all estimation and Transfer Entropy calculations.

To mitigate thin trading bias, stocks with a trading frequency below 60% of available trading days over the full sample period are excluded from the estimation sample. For remaining stocks with episodic thin trading, the Dimson (1979) aggregated coefficient approach is applied to obtain adjusted beta estimates. The equal-weighted aggregation of stock-level unexpected returns further ensures that the market-wide series is not dominated by a small number of actively traded large-capitalization securities.

Stock entry and exit are handled through a dynamic sample construction approach to avoid survivorship bias (Brown et al., 1992). Each stock is included in the cross-sectional computation only for the period during which it is actively listed and trading on the DSE. Stocks entering the market after January 2010 are included from their first available trading date, and stocks exiting the market before December 2021 are excluded from their last available trading observation. Consequently, the number of stocks contributing to the equal-weighted aggregate varies across trading days, appropriately reflecting the actual cross-section of available stocks on each day.

3.6. Treatment of Structural Breaks and Justification of Full-Sample Estimation Window

Firm-level structural break testing is conducted to assess parameter instability over the crisis and COVID-19 periods, using the Chow test (Chow, 1960) and the Quandt–Andrews unknown breakpoint test (Andrews, 1993) applied at the onset of the crisis period (July 2010) and the onset of the COVID-19 period (March 2020). Where statistically significant structural breaks are detected, dummy interaction terms for the affected sub-periods are introduced into the firm-level OLS regression, allowing both the intercept and the market sensitivity coefficient to differ across structurally distinct episodes. Unexpected returns are then derived as the residuals of this augmented specification, ensuring that the idiosyncratic surprise component is cleanly isolated across all market states.

The full-sample estimation window spanning January 2010 to December 2021 is retained as the baseline approach for three reasons. First, the objective of the Market Index Model in this study is return decomposition rather than forecasting, for which a longer estimation window yields more stable and efficient parameter estimates. Second, the frontier market characteristics of the Bangladesh equity market—including thin trading, limited analyst coverage, and episodic liquidity—make short rolling-window beta estimation prone to instability; the full-sample window mitigates this by providing a larger effective sample for each stock-level regression. Third, since the variable of interest is the model residual rather than the raw return, modest variation in beta estimates across sub-periods has only a marginal effect on the unexpected return series, particularly after equal-weighted cross-sectional aggregation. The targeted break-robust specification described above provides an additional layer of protection against parameter instability for the specific episodes identified in the data.

3.7. Hypothesis Development

Overconfident investors are more likely to believe that their information is accurate, and they are prone to reacting to their market signals, which results in increased trading. This behavior has typically been explained in empirical finance by examining the correlation between market return and trading volume after significant prices change in ways that confirm investors’ belief that they are gaining additional information to trade. Although the existing studies mainly emphasize the impact of the total market returns on trading activity, overconfidence behavior is more represented by how the investor reacts to the unexpected information shocks. It is, therefore, important to make a distinction between total market returns and returns that are unexpected to understand the behavioral underpinnings of the trading decision. Accordingly, this study investigates the total market returns and unexpected market returns as possible drivers of trading volume. Unexpected market returns are unanticipated market shocks obtained from the Market Index Model, and isolate investor responses to unexpected information from normal market movements to provide a more behaviorally relevant measure.

The study also takes a state-dependent approach and analyzes overconfidence dynamics in bullish, bearish, crisis, extended crisis, and COVID-19 market conditions, acknowledging the possibility of variations in investor behavior across market states. Dow Theory classifications are used to determine market trends. This study uses Transfer Entropy with bootstrap inference to model the asymmetric, nonlinear and directional nature of the flow of information between returns and trading activity. In this context, the important flow of information from market returns to trading volume is taken as being evidence of behavior that is consistent with overconfidence. The following hypotheses are suggested on the basis of these theoretical statements.

The hypotheses that are proposed to test the direction, magnitude and state-dependence of investors’ behavioral response in the Bangladesh equity market are as follows:

H1. 

The aggregate market returns have a substantial impact on the volume of market trading to assess whether it is overconfidence-based trading.

H2. 

The unexpected market returns have a considerable impact on the trading volume as overconfidence may better reflect in reaction to the unexpected information.

H3. 

The information flow between returns (total market return or unexpected returns) and trading volume could vary in magnitude and direction depending on the market state (bullish, bearish, crisis, extended crisis, and COVID-19), which is a state-dependent overconfidence.

4. Empirical Results

4.1. Examining the Relationship Between Market Return and Trading Volume Using Transfer Entropy Model

Transfer Entropy intends to estimate the direction of information flow shared between two time series variables. The higher Transfer Entropy value confirms a stronger amount of information flow meaning that the predictive information flow from one variable to another is quantitatively stronger.

To be consistent in all empirical estimations, MR → TV represents the direction flow of information in market return to trading volume, TV → MR is the directional information flow between trading volume and market return. TE and ETE refer to Transfer Entropy and Effective Transfer Entropy, respectively, where ETE is the bias-corrected Transfer Entropy measured by comparing the estimated Transfer Entropy values with the estimated ones of the shuffled versions of the original series using 300 bootstrap replications. A statistically significant Transfer Entropy coefficient from MR → TV demonstrates the evidence of overconfidence hypothesis, suggesting that past market returns affect future trading activity.

Table 1. Transfer Entropy results for the overall market.

Information Flow Direction	TE	ETE	Standard Error		p-Value
MR → TV	0.0058	0.0030	0.0012		0.010 **
TV → MR	0.0145	0.0115	0.0013		0.002 ***
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.001	0.002	0.003	0.007
TV → MR	0.000	0.002	0.002	0.003	0.008

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively.

reports the Transfer Entropy results for the overall equity market period. The findings show that market returns and trading volume have a bi-directional information flow. Nevertheless, the directional information flow of trading volume on the market return seems to be relatively more powerful than the other way round. Though the strong information flow between market return and trading volume is not much evidence to support the hypothesis of overconfidence, the information flow in the other direction implies that even the trading activity possesses the information predictive of market movements.

Table 2. Trend-driven equity market phases.

Panel A: Transfer Entropy Results for Bearish Market
Information Flow Direction	TE	ETE	Standard error		p-value
MR → TV	0.002	0.000	0.001		0.820
TV → MR	0.013	0.009	0.001		0.000 ***
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.003	0.004	0.005	0.00
TV → MR	0.001	0.002	0.004	0.005	0.01
Panel B: Transfer Entropy Results for Bullish Market
Information Flow Direction	TE	ETE	Standard error		p-value
MR → TV	0.017	0.011	0.002		0.000 ***
TV → MR	0.018	0.010	0.002		0.030 **
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.001	0.005	0.006	0.008	0.019
TV → MR	0.001	0.004	0.005	0.007	0.013

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively.

presents the results for the trend-driven market phases, which are determined by applying Dow Theory to uncover the significant differences in information transfer patterns. The results indicate that there is a strong directional movement of information between the market returns and trading volume in the bullish market but the same is not true of the bearish market. This implies that there is a variation in the relationship between market returns and trading volume in these two market states.

The findings from

Table 3. Crisis-driven equity market phases.

Panel A: Transfer Entropy Results for Crisis Market
Information Flow Direction	TE	ETE	Standard Error		p-value
MR → TV	0.0128	0.0000	0.0087		0.5133
TV → MR	0.0097	0.0000	0.0083		0.5433
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.009	0.013	0.018	0.054
TV → MR	0.002	0.011	0.015	0.021	0.052
Panel B: Transfer Entropy Results for Extended Crisis Market
Information Flow Direction	TE	ETE	Standard error		p-value
MR → TV	0.007	0.000	0.004		0.720
TV → MR	0.019	0.000	0.004		0.500
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.007	0.009	0.012	0.025
TV → MR	0.002	0.007	0.010	0.013	0.026
Panel C: Transfer Entropy Results for COVID-19 Market
Information Flow Direction	TE	ETE	Standard error		p-value
MR → TV	0.006	0.000	0.006		0.806
TV → MR	0.017	0.003	0.005		0.170
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.001	0.007	0.010	0.015	0.040
TV → MR	0.002	0.008	0.011	0.015	0.039

reveal that there is a low level of directional flow of information between market returns and trading volume in the crisis, extended crisis and COVID-19 periods. The transmission of information observed is relatively weak in the face of increased uncertainty in the market. This conveys that market participants may have the tendency to shift their focus from past market behavior to other external issues like macroeconomic shocks, political tensions, global events, which dilutes the influence of historical market return on trading activity.

4.2. Examining Asymmetric Response of Market Return to Trading Volume: Up-Market Conditions

This section examines the asymmetric impact of overconfidence hypothesis under up- and down-market returns conditions across various market states.

The results of Transfer Entropy between market return and trading volume in

Table 4. Trend-driven equity market phases under up-market conditions.

Panel A: Transfer Entropy Results for Overall Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.008	0.003		0.002	0.150
TV → MR	0.007	0.002		0.002	0.113
Bootstrapped Transfer Entropy Quantiles (300 replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.003	0.004	0.005	0.013
TV → MR	0.001	0.003	0.005	0.006	0.014
Panel B: Transfer Entropy Results for Bearish Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.011	0.012		0.004	0.213
TV → MR	0.017	0.002		0.004	0.036 **
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.006	0.008	0.011	0.029
TV → MR	0.001	0.007	0.009	0.012	0.025
Panel C: Transfer Entropy Results for Bullish Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.012	0.015		0.004	0.216
TV → MR	0.013	0.000		0.004	0.090 *
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.007	0.010	0.012	0.026
TV → MR	0.001	0.006	0.008	0.011	0.025

Notes: * and ** indicate significance at the 10% and 5% levels, respectively.

and

Table 5. Crisis-driven equity market phases up market.

Panel A: Transfer Entropy Results for Crisis Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.014	0.000		0.008	0.520
TV → MR	0.014	0.000		0.009	0.483
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.008	0.018	0.028	0.099
TV → MR	0.001	0.018	0.016	0.028	0.142
Panel B: Transfer Entropy Results for Extended Crisis Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.008	0.000		0.009	0.823
TV → MR	0.011	0.000		0.007	0.763
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.001	0.009	0.013	0.019	0.063
TV → MR	0.003	0.011	0.014	0.019	0.058
Panel C: Transfer Entropy Results for COVID-19 Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.014	0.000		0.009	0.506
TV → MR	0.014	0.000		0.008	0.513
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.009	0.014	0.021	0.062
TV → MR	0.004	0.011	0.014	0.020	0.056

show that there is no statistically significant directional information flow in either of the trend-driven or crisis-driven market states in either rising market returns. The fact that there were no substantial Transfer Entropy coefficients indicates that positive market movements do not produce an informational impact persistent enough to influence further trading activity in the case of up-market conditions. This result can suggest that positive market dynamics are quickly absorbed into the market expectations, and hence restrict the level of discernible directional reliance among returns and trading volume. On the whole, the findings suggest that the flow of information between returns to trading activity is relatively weak in the times of the positive market performance in various market settings.

4.3. Examining Asymmetrical Response of Market Return to Trading Volume: Down-Market Conditions

In contrast to positive market returns, investors often exhibit heightened anxiety and risk aversion. The study also attempts to explore the robustness of Transfer Entropy model to investigate whether information flows from market return to trading volume persist or change during down market returns across different market states.

Table 6. Trend-driven equity market phases down market.

Panel A: Transfer Entropy Results for Overall Market
Information Flow Direction	TE		ETE	Standard Error	p-value
MR → TV	0.011		0.017	0.002	0.000 ***
$T{E}_{TV\to R_m}$	0.040		0.004	0.002	0.046 **
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.002	0.004	0.005	0.012
TV → MR	0.001	0.003	0.004	0.005	0.013
Panel B: Transfer Entropy Results for Bearish Market
Information Flow Direction	TE		ETE	Standard Error	p-value
MR → TV	0.009		0.001	0.002	0.130
TV → MR	0.015		0.010	0.002	0.053 **
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.001	0.004	0.005	0.007	0.016
TV → MR	0.001	0.005	0.006	0.007	0.014
Panel C: Transfer Entropy Results for Bullish Market
Information Flow Direction	TE		ETE	Standard Error	p-value
MR → TV	0.011		0.000	0.004	0.520
TV → MR	0.055		0.043	0.005	0.052 **
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.008	0.010	0.014	0.035
TV → MR	0.000	0.007	0.010	0.013	0.037

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively.

and

Table 7. Crisis-driven equity market phases down market.

Panel A: Transfer Entropy Results for Crisis Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.019	0.000		0.013	0.520
TV → MR	0.019	0.000		0.015	0.356
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.002	0.014	0.020	0.029	0.082
TV → MR	0.004	0.012	0.016	0.024	0.131
Panel B: Transfer Entropy Results for Extended Crisis Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.020	0.002		0.007	0.233
TV → MR	0.016	0.001		0.006	0.276
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.004	0.010	0.014	0.019	0.063
TV → MR	0.001	0.009	0.013	0.017	0.051
Panel C: Transfer Entropy Results for COVID-19 Market
Information Flow Direction	TE	ETE		Standard Error	p-value
MR → TV	0.022	0.003		0.011	0.240
TV → MR	0.014	0.000		0.007	0.513
Bootstrapped Transfer Entropy Quantiles (300 Replications)
Information Flow Direction	0%	25%	50%	75%	100%
MR → TV	0.000	0.007	0.014	0.022	0.065
TV → MR	0.005	0.012	0.014	0.018	0.064

show that the Transfer Entropy values are only significant when information flows in a direction, i.e., from market return to trading volume in the overall market when the market returns are negative. This observation would imply that unfavorable market movements have relatively more formidable informational content on the future trading in the aggregate market structure. Contrastingly, the Transfer Entropy coefficients are statistically insignificant in the rest of the trend-driven and crisis-driven market conditions when the market is in a down-market. This minimal information transfer in these market states can be indicative of the effects of increased uncertainty, risk-aversion in trading and reduced information responsiveness during poor market conditions. Taken together, the results suggest that the relationship between returns and trading volume of the negative market conditions differs significantly in response to alternative market conditions.

4.4. Examining the Relationship Between Unexpected Market Returns and Market Trading Volume Using Transfer Entropy Model: Under Normal Market Conditions

The unexpected market performance may be viewed as a handy behavioral indicator in overconfidence research since it encapsulates the aspect of market performance that cannot be attributed to systematic market data and thus indicates unforeseen market trends and information shocks.

The Transfer Entropy findings regarding unexpected market returns and trading volume in the various market states in normal market conditions are reported in

Table 8. Transfer Entropy results for unexpected market returns.

Overall Market				Bearish Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.013	0.009	0.000 ***	MR → TV	0.007	0.002	0.080 *
TV → MR	0.006	0.004	0.000 ***	TV → MR	0.011	0.005	0.000 ***
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.002	0.003	0.004	MR → TV	0.0043	0.0054	0.0067
TV → MR	0.001	0.002	0.003	TV → MR	0.0030	0.0042	0.0053
Bullish Market				Crisis Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.012	0.030	0.050 **	MR → TV	0.015	0.000	0.443
TV → MR	0.021	0.020	0.000 ***	TV → MR	0.018	0.000	0.313
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.004	0.006	0.007	MR → TV	0.009	0.014	0.020
TV → MR	0.005	0.006	0.008	TV → MR	0.101	0.014	0.020
Extended Crisis Market				COVID-19 Market
Direction	TE	ETE	p-value	Direction	TE	ETE	p-value
MR → TV	0.011	0.000	0.410	MR → TV	0.020	0.007	0.053 **
TV → MR	0.004	0.000	0.960	TV → MR	0.026	0.013	0.033 **
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.008	0.010	0.013	MR → TV	0.006	0.011	0.014
TV → MR	0.007	0.009	0.013	TV → MR	0.009	0.113	0.038

Notes: *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively.

. The results show considerable directional flow of information between unexpected returns and trading volume in the overall and bullish market states but the transfer of information seems to be stronger in the overall market. Conversely, there is no statistically significant information flow in bearish, crisis, extended crisis, and COVID-19 market conditions. In general, the findings imply that unpredictable market dynamics have a comparatively more significant informational impact on trading in stable and positive market conditions than negative market conditions.

4.5. Examining the Asymmetrical Relationship Between Unexpected Market Returns and Market Trading Volume Using Transfer Entropy Model: Under Up-Market Conditions

Table 9. Transfer Entropy results for unexpected market returns under up market condition.

Overall Market				Bearish Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.009	0.006	0.051 **	MR → TV	0.009	0.000	0.387
TV → MR	0.017	0.011	0.000 ***	TV → MR	0.015	0.003	0.130
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.003	0.005	0.006	MR → TV	0.006	0.008	0.010
TV → MR	0.004	0.006	0.007	TV → MR	0.007	0.010	0.013
Bullish Market				Crisis Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.008	0.000	0.457	MR → TV	0.032	0.007	0.237
TV → MR	0.042	0.031	0.000 ***	TV → MR	0.039	0.012	0.137
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.006	0.008	0.011	MR → TV	0.008	0.018	0.030
TV → MR	0.007	0.009	0.012	TV → MR	0.011	0.017	0.028
Extended Crisis Market				COVID-19 Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.006	0.000	0.933	MR → TV	0.026	0.008	0.147
TV → MR	0.015	0.000	0.377	TV → MR	0.013	0.000	0.583
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.010	0.014	0.019	MR → TV	0.010	0.015	0.021
TV → MR	0.010	0.013	0.019	TV → MR	0.011	0.014	0.020

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively.

displays the Transfer Entropy values between unexpected market returns and trading volume in situations of up-market movement. The results indicate that there is no statistically significant directional flow of the unexpected returns to the trading volume of any of the market states under the conditions of positive market returns. The findings indicate that unexpected market movements have relatively less informational impact on trading activity in increasing market conditions, reflecting less strong dependence on the return volumes in up-market conditions.

4.6. Examining the Asymmetrical Relationship Between Unexpected Market Returns and Market Trading Volume Using Transfer Entropy Model: Under Down-Market Conditions

The Transfer Entropy results between the unexpected market returns and the trading volume under down-market conditions are presented in

Table 10. Transfer Entropy Results with unexpected market returns under down-market conditions.

Overall Market				Bearish Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.016	0.010	0.000 ***	MR → TV	0.009	0.002	0.180
TV → MR	0.012	0.007	0.000 ***	TV → MR	0.018	0.010	0.003 **
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.004	0.005	0.007	MR → TV	0.005	0.006	0.008
TV → MR	0.003	0.004	0.005	TV → MR	0.006	0.008	0.009
Bullish Market				Crisis Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.029	0.017	0.000 ***	MR → TV	0.0185	0.000	0.543
TV → MR	0.017	0.002	0.210	TV → MR	0.0165	0.000	0.503
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.009	0.012	0.016	MR → TV	0.013	0.020	0.030
TV → MR	0.008	0.011	0.141	TV → MR	0.010	0.016	0.026
Extended Crisis Market				COVID-19 Market
Information Flow Direction	TE	ETE	p-value	Information Flow Direction	TE	ETE	p-value
MR → TV	0.018	0.001	0.240	MR → TV	0.040	0.022	0.050 **
TV → MR	0.017	0.000	0.280	TV → MR	0.029	0.005	0.233
Bootstrapped Transfer Entropy Quantiles				Bootstrapped Transfer Entropy Quantiles
Information Flow Direction	25%	50%	75%	Information Flow Direction	25%	50%	75%
MR → TV	0.010	0.014	0.018	MR → TV	0.014	0.020	0.028
TV → MR	0.009	0.013	0.078	TV → MR	0.009	0.013	0.022

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively.

. A strong directional flow of information, in both cases, is found to flow from unexpected market returns to the trading volume in both overall and bullish market states but relatively weaker information flow is observed during the COVID-19 period. These findings indicate that when unexpected adverse market movements occur, they have a greater informational impact on the trading activity in specific market conditions, especially in the overall and bullish market states. In general, the results show that the correlation between unexpected market returns and trading volume in down-market conditions is different across various equity market states.

4.7. Robustness Analysis

To make sure that the key inferences of this study are not the result of certain Transfer Entropy estimation decisions, we run two groups of robustness tests: (i) different lag structures, and (ii) different discretization schemes.

4.7.1. Alternative Lag Structures

The baseline estimation uses a first-order Markov Process (k = 1), which is consistent with the high-frequency of daily financial data and the behavioral hypothesis that the effects of overreaction and self-attribution are only encountered in short-term trade choices. We re-estimate all Transfer Entropy models with lag length of k = 2 and k = 3 trading days to evaluate the sensitivity of the results to this choice.

The findings in

Table 11. Robustness of Transfer Entropy estimates under alternative lag structures: overall and trend-driven market states.

Market State	Information Flow Direction	k = 1 (Baseline) TE	k = 2 TE	k = 3 TE	Inference
Overall Market	MR → TV	0.004 ** (0.020)	0.003 ** (0.023)	0.001 ** (0.020)	Stable
	TV → MR	0.021 *** (0.000)	0.020 *** (0.000)	0.020 *** (0.000)	Stable
Bullish Market	MR → TV	0.001 *** (0.000)	0.001 *** (0.000)	0.001 *** (0.000)	Stable
	TV → MR	0.008 ** (0.036)	0.007 ** (0.031)	0.007 ** (0.024)	Stable
Bearish Market	MR → TV	0.022 (0.400)	0.020 (0.319)	0.020 (0.349)	Stable
	TV → MR	0.020 ** (0.034)	0.008 ** (0.038)	0.007 ** (0.032)	Stable

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively. p-value is given in parentheses.

and

Table 12. Robustness of Transfer Entropy estimates under alternative lag structures: crisis-driven market states.

Market State	Information Flow Direction	k = 1 (Baseline) TE	k = 2 TE	k = 3 TE	Inference
Crisis Market	MR → TV	0.003 (0.662)	0.003 (0.657)	0.003 (0.672)	Stable
	TV → MR	0.006 (0.615)	0.006 (0.595)	0.006 (0.566)	Stable
Extended Crisis	MR → TV	0.004 (0.623)	0.004 (0.566)	0.004 (0.543)	Stable
	TV → MR	0.005 (0.544)	0.007 (0.516)	0.007 (0.567)	Stable
COVID-19	MR → TV	0.002 (0.634)	0.002 (0.667)	0.003 (0.671)	Stable
	TV → MR	0.004 (0.551)	0.004 (0.543)	0.005 (0.433)	Stable

Notes: Transfer Entropy results are not significant. p-value is given in parentheses.

affirm that the direction, magnitude and statistical significance of the Transfer Entropy estimates are qualitatively the same when lag length, k = 2 and k = 3, are used. The bullish market still reports statistically significant bidirectional transfer of information flow, while the bearish market exhibits unidirectional flow of information from trading volume to the market return, and the crisis-driven market phases (crisis, extended crisis, and COVID-19) consistently reveal statistically insignificant transmission of information flow. These results indicate that the observed state-specific dynamics of overconfidence are not responsive to the alternative lag structure choice and the first-order Markov formulation employed in the baseline is not influencing the results.

4.7.2. Alternative Discretization Schemes

The baseline analysis discretizes market returns and trading volume into three states (low, medium, high) using quantile-based partitioning at the 33rd and 66th percentiles. To verify that the conclusions are not sensitive to this binning choice, we re-estimate the models using: (i) a binary (two-state) discretization based on a median split, and (ii) a four-state discretization using the 25th, 50th, and 75th percentile thresholds.

The results in

Table 13. Robustness of Transfer Entropy (TE) estimates under alternative discretization: overall and trend-driven market states.

Market State	Information Flow Direction	3-State Discretization TE (Baseline)	2-State Discretization TE	4-State Discretization TE	Inference
Overall Market	MR → TV	0.003 ** (0.021)	0.002 ** (0.023)	0.002 ** (0.021)	Stable
	TV → MR	0.011 *** (0.000)	0.011 *** (0.000)	0.010 *** (0.000)	Stable
Bullish Market	MR → TV	0.002 *** (0.000)	0.003 *** (0.000)	0.002 *** (0.000)	Stable
	TV → MR	0.009 ** (0.036)	0.008 ** (0.037)	0.008 ** (0.031)	Stable
Bearish Market	MR → TV	0.011 (0.560)	0.010 (0.550)	0.010 (0.623)	Stable
	TV → MR	0.010 ** (0.011)	0.009 ** (0.021)	0.009 ** (0.012)	Stable

Notes: ** and *** indicate significance at the 5% and 1% levels, respectively. p-value is given in Parentheses.

and

Table 14. Robustness of Transfer Entropy (TE) estimates under alternative discretization: crisis-driven market states.

Market State	Information Flow Direction	3-State Discretization TE (Baseline)	2-State Discretization TE	4-State Discretization TE	Inference
Crisis Market	MR → TV	0.002 (0.545)	0.002 (0.522)	0.001 (0.513)	Stable
	TV → MR	0.003 (0.499)	0.003 (0.481)	0.003 (0.501)	Stable
Extended Crisis	MR → TV	0.001 (0.601)	0.001 (0.587)	0.002 (0.589)	Stable
	TV → MR	0.002 (0.498)	0.002 (0.512)	0.001 (0.524)	Stable
COVID-19	MR → TV	0.001 (0.551)	0.001 (0.512)	0.000 (0.544)	Stable
	TV → MR	0.003 (0.611)	0.003 (0.615)	0.002 (0.675)	Stable

Notes: Transfer Entropy results are not significant. p-value is given in parentheses.

demonstrate that the main empirical conclusions are robust to alternative discretization procedures. Whether a two-state median split or a four-state quartile-based partition is employed, the pattern of state-dependent information transfer remains consistent with the baseline three-state results. Specifically, significant overconfidence-driven information flow from market return to trading volume is observed in the bullish and overall market phases, while the crisis-driven market phases (crisis, extended crisis, COVID-19) continue to show statistically insignificant information transfer across all discretization schemes. This consistency across binning strategies confirms that the quantile-based three-state discretization used in the baseline is neither an artifact of the chosen partition nor unduly influenced by the treatment of extreme observations.

5. Discussion of Results

The study aims to explore the overconfidence dynamics in the Bangladesh equity market by applying the Transfer Entropy framework to assess the direction of the nonlinear relationship between market returns and trading volume. The findings indicate that the return–volume relationship is nonlinear, asymmetric, and highly state-dependent when it comes to market states and the informational content of returns. The results broadly support behavioral explanations based on overconfidence and self-attribution bias, but a systematic and careful analysis must account for other mechanisms, such as liquidity dynamics, feedback trading, market microstructure effects, and speculative trading, in addition to behavioral explanations, in each market state. The following discussion combines both points of view.

5.1. Overall Market

The results of the aggregate market analysis using total returns indicate that there exists a two-way relationship between market returns and trading volume. The quantitative strength of the information flow from trading volume to market returns, however, is stronger than the flow from market returns to trading volume. This is an asymmetry that needs to be interpreted. This direction flow from return-to-volume is consistent with the over-confidence hypothesis, that past performance builds trust among investors, which in turn drives more trading in the market, while the more dominant direction, volume-to-return, means that trading activity is an indicator of future market performance. This is more of a feedback trading pattern and liquidity-induced price pattern than overconfidence (Sentana & Wadhwani, 1992; Chordia & Swaminathan, 2000). Frontier markets in Bangladesh, where institutions play a relatively small role and retail investors dominate, can be characterized by periods of high trading volume, which can stem from a sense of herd mentality, from liquidity shocks, or from momentum trading, rather than from processes of ‘self-attribution’ within overconfidence theory. The evidence from the aggregate market with total returns is thus mostly indirect, and limited support for the overconfidence hypothesis can be extracted. The primary direction of information flow seems to be from volume to return, and this is better explained by feedback trading and market microstructure.

5.2. Trend-Driven Market States

The state-dependent analysis provides a more complex picture of different phases of the trend-driven market. The bullish market yielded a statistically significant bidirectional information flow from market return to trading volume information transfer, a result more consistent with the overconfidence hypothesis. Positive market performance seems to boost investors’ confidence, leading to more trading activity, because traders are more likely to believe that they are predicting markets correctly than that they are benefiting from good luck, aligned with self-attribution bias (Gervais & Odean, 2001; Daniel et al., 1998). This behavioral assertion is feasible in the context of Bangladesh, where the market upswing is supported by the high participation of retail investors with well-documented speculative trading.

However, even in a positive market, the direction of volume and return remains significant, indicating that there are liquidity influences and feedback trading processes present together, along with behavioral influences. Increased trading volume during bullish phases may exaggerate price through liquidity-forced demand pressure, independent of investor psychology (Kyle, 1985). The observed information transfer in the bullish market is thus likely to be a result of both overconfidence-related behavioral responses and liquidity feedback effects.

The bearish market, by contrast, has a one-way flow of information from trading volume to market returns, without any significant influence from return-to-volume flow. This does not follow the prediction of the overconfidence hypothesis, but rather better fits the predictions of market microstructure explanations. In bearish markets, trades are more likely to be motivated by liquidity, stop-loss trades, portfolio rebalancing, and risk-aversion rather than by over optimistic trades on speculation (Avramov et al., 2006). The volume to return information flow in this state is likely to be a price impact of the forced or reactive trading rather than any behavioral self-reinforcement mechanism. The results point out that the overconfidence-consistent behavioral dynamics are mainly a bullish market effect in the Bangladesh equity market and are not universal across trend-driven market states.

5.3. Crisis-Driven Market States

The Transfer Entropy estimates are not statistically significant when the market is in a crisis state, or the extended crisis window, or the COVID-19 crisis window. The absence of significant information in these market phases reveals a fundamental failure of the systematic return–volume relationship under extreme conditions of uncertainty and structural disruption. This result aligns with the theory of investor behavior during a crisis period that investors are less likely to be influenced by behavioral biases like overconfidence and more likely to be affected by macroeconomic uncertainty, liquidity constraints, risk aversion, and trading in response to external shocks (Barberis & Thaler, 2003).

During the crisis and extended crisis periods, a lack of information transfer could also be caused by a deterioration in the market micro-structure, such as increased price impact, reduced market depth, and widened bid-ask spreads, which interfere with the systematic relationship between the return signals and trading responses (Roll, 1984). The official suspension of trading from 26 March to 30 May 2020, due to COVID-19, further confused the information environment; whereas, the still-to-be-normalized recovery period was driven by exogenous information, including news about the pandemic, policy changes, and global supply chain disruptions, without any systematic signal of recovery. In these markets, the return-to-volume information channel is further compromised by speculative trading, based on sentiment or rumor, rather than return information.

These findings collectively suggest that the behavioral dynamics underlying overconfidence are muted during systemic disruption, while the alternative explanations of the return–volume dynamics, including liquidity constraints, risk aversion, deterioration in market microstructure, and exogenous trading shocks, are more satisfactory in these crisis-driven market states.

5.4. Asymmetric Analysis

The asymmetric analysis under up-market and down-market return conditions gives additional insights into the results. Information flow from market returns to trading volume is, in general, weak and statistically insignificant under up-market conditions in most market states. This demonstrates that positive return realizations are quickly incorporated in market expectations, as there does not seem to be an informational feedback loop between returns and volume, but rather a momentum-driven trading process in which returns trigger automatic purchase reactions. Lack of a persistent return-to-volume information transfer under rising market conditions may also be due to the presence of passive and index-linked trading strategies that react to the level of the price, but not to an information signal, further reducing the behavioral content of the return–volume relationship.

In contrast, for down-market conditions, the information transfer from return-to-volume is statistically significant in the overall and bullish market states. These larger informational responses to negative return shocks are in line with the behavioral finance literature that shows investors are more sensitive to losses than gains (Kahneman & Tversky, 1979). But this differential reaction to negative returns is also in line with non-behavioral explanations such as forced selling due to margin calls, stop-loss induced liquidations or the liquidity spiral of price declines, leading to a surge in volume and hence further declines in prices (Brunnermeier & Pedersen, 2009). The combination of these explanations of the down-market asymmetry from behavioral and non-behavioral perspectives highlights the need to view the Transfer Entropy results in a wider context of the trading dynamics of frontier markets and not only as an overconfidence theory.

5.5. Perspective of Unexpected Market Returns

The strong and most direct evidence for the overconfidence hypothesis comes from using unexpected market returns, instead of total returns, as the measure of return. By eliminating the predictable systematic component of market returns that investors can reasonably expect and discount from their investment decisions, unexpected returns isolate the idiosyncratic surprise component of market returns that is most closely related to the psychological response of investors. The substantial increase in return-to-volume information transfer during unexpected returns in the overall and bullish market state, and during the COVID-19 period to a lesser extent, offers more behaviorally specific evidence that unexpected positive market signals promote trading activity in a manner that is consistent with self-attribution bias and overconfidence dynamics.

However, even in this specification, the volume-to-return direction remains significant for a number of market states, suggesting that liquidity-driven and feedback trading mechanisms still prevail over the behavioral impacts. The application of unexpected market returns narrows but does not discard the effect of alternative explanations, and the findings should be viewed as evidence of a behavioral phenomenon that becomes persuasive when considered together with state-dependent and asymmetric behavior rather than in isolation.

5.6. Synthesis: Overconfidence vs. Alternative Explanations

Overall, our results suggest multiple explanations for the findings of this study; overconfidence and self-attribution bias are the most plausible primary explanation for the return-to-volume information transfer in bullish and overall market conditions, especially under unexpected market returns and down-market return realizations, while other explanations such as feedback trading, liquidity dynamics, market microstructure effects, and speculative trading are equally or more plausible in explaining the most pervasive volume-to-return information transfer across multiple market states and conditions. This holistic interpretation aligns with the greater behavioral finance literature, which views the investor behavior in frontier equity markets as being the result of a mix of psychological biases, institutional constraints, liquidity conditions and structural characteristics of the market, and cannot be attributed to any single theoretical framework (Barberis & Thaler, 2003; Sewell, 2011). The Transfer Entropy approach employed in this study is ideally effective in detecting the state-dependent, nonlinear, and complex market dynamics and contributes to the existing literature, confirming that behavioral and structural mechanisms together shape the information environment of frontier equity markets.

5.7. Comparison with Previous Empirical Studies Across Developed, Emerging, and Frontier Equity Markets

The state-dependent pattern observed in this study—overconfidence dynamics are stronger in bullish and normal market conditions, while behavioral effects are muted during crisis periods,—is aligned with the theory of behavioral finance and previous literature from developed, emerging, and frontier markets.

For developed markets, Statman et al. (2006) and Chuang and Lee (2006) offer basic evidence from the U.S. market that there is a positive relationship between past market returns and subsequent trading volume, and that such a relationship is more significant in bull markets than bear markets. Glaser and Weber (2007) also describe more pronounced overconfidence symptoms when the performance of the individual investors’ portfolios is positive, which is gathered from German individual investors. Our study findings are supportive of this developed market evidence, regarding the bull-market enhancement of return-to-volume information transfer and the enhanced behavioral signal in unexpected returns compared to total returns.

In emerging markets, where retail investors dominate and informational efficiency is likely to be lower, Chen et al. (2007) and Metwally and Darwish (2015) report strong evidence of overconfidence, mostly in bull markets for the Chinese and Egyptian equity markets, respectively. The same trend is observed in the Pakistani equity market by Zia et al. (2017). The results of the current study broadly agrees with this growing market evidence and further contributes by using a nonlinear Transfer Entropy framework, which exhibits state-contingent and asymmetric dynamics that have not been detected in the majority of previous studies using linear Granger causality models.

There is still limited evidence from frontier markets, but Prosad et al. (2015) and Victor et al. (2019) report that the manifestations of overconfidence are particular to the upswing episodes of a trend and that they can be significantly reduced during periods of macroeconomic stress, which is directly comparable to the findings of this study. This study contributes to this stream of literature by providing the first systematic state-dependent overconfidence dynamics in the Bangladesh equity market using a nonlinear framework.

The theoretical explanation for the presence of the state-dependent overconfidence pattern can be explained by three complementary mechanisms. First, the self-attribution bias mechanism of Daniel et al. (1998) implies that during periods of positive market performance investors become overconfident, and this overconfidence creates a dynamic feedback loop between returns and trading behavior, and this feedback is strongest when markets are in an extended uptrend. Second, the sentiment mechanism of Baker and Wurgler (2006) suggests that when the market is bullish, the risk appetite and speculative tendency of investors increase and the behavioral biases become more salient; and when the market is in crisis, they decrease due to fear and uncertainty. Third, Epstein and Schneider (2008) describe the “ambiguity aversion” mechanism in their theory, which explains the complete attenuation of behavioral dynamics during crisis periods: when facing deep uncertainty, such as the market crash in 2010–2011 and the COVID-19 pandemic, investors do not rely on their own assessment but on external cues, and this mechanically suppresses the self-attribution processes that underlie overconfidence-consistent return-to-volume information transfer. This theoretical prediction is completely confirmed by the statistically insignificant Transfer Entropy estimates for all three crisis-driven market states.

Based on the comparison with the previous evidence, it is concluded that the state-dependent overconfidence phenomenon captured in the context of the Bangladesh equity market is actually a systematic behavioral pattern, that is, it is not a unique phenomenon of the Bangladesh market and is already theoretically predicted as well as empirically documented in various markets. The present study adds to this literature by offering solid nonlinear evidence with a state-specific specificity not attainable by earlier linear studies.

6. Conclusions

This study examines the state-dependent dynamics of overconfidence in the Bangladesh equity market by investigating the nonlinear directional relationship between market returns and trading volume within a Transfer Entropy framework. By distinguishing between total and unexpected market returns, the study provides deeper insight into how behavioral responses vary across different market environments. The results demonstrate that overconfidence behavior in the Bangladesh equity market is strongly state-dependent and asymmetric. While total market returns yield relatively weak and inconsistent overconfidence signals, unexpected market returns generate statistically significant directional information flows to trading volume, particularly in overall and bullish market conditions. Conversely, the behavioral effect diminishes substantially during bearish, crisis, and extended crisis periods, indicating that heightened uncertainty and negative market sentiment suppress speculative confidence. The findings further establish that investor behavior differs systematically across up-market and down-market conditions, reflecting the nonlinear and asymmetric nature of behavioral dynamics in frontier equity markets.

The study makes several important contributions to the literature on behavioral finance. First, it extends overconfidence research to a frontier market context in which empirical evidence remains relatively scarce. Second, it demonstrates that investor behavior varies considerably across distinct market states, underscoring the importance of state-dependent analysis in behavioral finance research. Third, the application of Transfer Entropy provides richer and more precise information than traditional linear econometric models by capturing the nonlinear and directional nature of information flow between market returns and trading activity.

6.1. Research Limitations and Future Study

Regardless of these contributions, the study has several limitations that should be acknowledged. First, the analysis is confined to a single frontier market, which may limit the generalizability of the findings to other institutional and market contexts. Second, although Transfer Entropy is effective in capturing nonlinear information flows, macroeconomic, political, and policy-related variables that may influence investor behavior are not directly incorporated into the framework. Third, while logarithmically transformed aggregate market turnover is employed as the primary proxy for trading activity, alternative volume-based measures—such as the turnover ratio, abnormal trading volume, detrended volume, and standardized trading activity—may provide additional insights into investor behavior across varying market conditions. Future research could extend the current framework by incorporating these alternative volume measures to further examine the robustness of state-dependent behavioral dynamics in frontier equity markets.

Future studies may also expand this framework in several productive directions, including cross-country comparisons across frontier and emerging markets, sector-level behavioral analysis, integration of macroeconomic and investor sentiment variables, and comparison with alternative nonlinear and machine learning-based causality models to further illuminate the dynamics of investor behavior in financial markets.

6.2. Research Implications

The findings carry several significant implications for regulators, policymakers, and market participants in frontier equity markets. First, the stronger behavioral responses elicited by unexpected returns relative to anticipated market movements suggest that investors in the Bangladesh equity market are highly sensitive to information shocks and market uncertainty. Accordingly, the Bangladesh Securities and Exchange Commission (BSEC) should prioritize improvements in disclosure quality, market transparency, and the timely dissemination of financial information to reduce information asymmetry and mitigate speculative responses to unanticipated market signals.

Second, the stronger evidence of overconfidence during bullish and normal market conditions indicates that speculative trading behavior is likely to intensify during periods of market optimism. Regulators are therefore advised to strengthen market surveillance mechanisms during sustained market upswings to detect and deter excessive speculation, irregular trading patterns, and potential price distortions before they escalate into systemic instability. Third, the asymmetric investor responses observed under negative return conditions highlight the need for enhanced awareness of behavioral biases and improved risk management practices among market participants. Investor education initiatives focused on behavioral decision-making, risk diversification, and the identification of irrational trading behavior can strengthen market discipline and reduce the prevalence of emotionally driven trading activity.

Finally, the findings demonstrate the analytical value of nonlinear information-theoretic methods in identifying behavioral market dynamics that are not adequately captured by standard linear econometric models. Incorporating such frameworks into regulatory monitoring and surveillance systems could enhance the early detection of abnormal market behavior, contributing to the development of more robust, transparent, and efficient frontier financial markets.