PCA-Based Investor Attention Index and Its Impact on the KSE-100 Excess Returns

Abstract

The study employs principal component analysis (PCA) to construct an investor attention index derived from seven key variables: abnormal trading volume, extreme returns, past returns, nearness to the 52-week high, nearness to the historical high, Google search volume, and mutual fund inflows. Subsequently, the research examines the impact of the investor attention index on the KSE-100 index excess returns. The analysis covers monthly data from January 2004 to December 2024. The PCA identified four components and constructed attention indices: $A^{PCA1}$ has highest weights of nearness to the 52-week high, abnormal trading volume, past returns, and mutual funds inflows; $A^{PCA2}$ has major weights of abnormal trading volume, extreme returns, past returns, and Google search volume; $A^{PCA3}$ has nearness to the 52-week high, nearness to the historical high, extreme returns, and mutual funds inflows; and $A^{PCA4}$ has nearness to the historical high, extreme returns, Google search volume, and mutual funds inflows. The $A^{PCA1}$ and $A^{PCA4}$ have a positive and significant impact on the excess returns of the KSE-100 index. This suggests that when investors are more motivated to invest, herding behavior increases, leading to improved index performance and higher returns. Subsequently, $A^{PCA3}$ has a negative but significant impact on index returns, indicating that a lack of investor interest leads to reduced trading activity and weaker index performance. The findings of this study have important implications for policymakers, investors, and mutual fund managers to understand the patterns of investor attention, creating policies and procedures to make the financial markets more transparent and protect the investor’s rights.

1. Introduction

Investor attention has long been a subject of interest in financial research, particularly as markets increasingly exhibit patterns that deviate from traditional rational models. One such deviation arises from the concept of investor attention, a limited cognitive resource that shapes how individuals process information and make investment decisions. Contrary to the Efficient Market Hypothesis (Fama, 1970), which assumes that all available information is fully and instantly reflected in asset prices, behavioral finance suggests that investors often rely on selective attention, shaped by information overload, media signals, and cognitive limitations (Kahneman, 1973; Barber & Odean, 2008; Peng & Xiong, 2006). This limited attention can lead to disproportionate focus on certain stocks or market-wide events, resulting in price fluctuations that are not entirely justified by fundamentals. While a growing body of literature supports the link between investor attention and predictability of stock return in developed markets (Da et al., 2011; J. Li & Yu, 2012), evidence from emerging economies remains fragmented. This study contributes to the discourse by examining the impact of investor attention on Pakistan’s KSE-100 index performance in a context where structural reforms, evolving investor attention, and heightened volatility create a compelling environment for such analysis.

In Pakistan, initially, there were three stock exchanges: the Karachi Stock Exchange (KSE), the Lahore Stock Exchange (LSE), and the Islamabad Stock Exchange (ISE) (Jamal & Ashraf, 2024; Sharif, 2018). The existence of multiple stock exchanges created conflicts of interest and frustration for investors, as none of the exchanges coordinated with one another and operated independently regarding trading interfaces, indexes, and listing criteria (Ali & Sharif, 2022). Hence, the government of Pakistan introduced the Stock Exchanges Act in 2012, integrated all three stock exchanges into one operation, and formed the “Pakistan Stock Exchange” (PSX) on 11 January 2016 (Ali & Sharif, 2022). It became operational at the beginning with 559 listed companies across 35 sectors, including domestic and foreign companies (Pakistan Stock Exchange, 2024). The history of PSX has witnessed a significant improvement over time. It started with just five listed companies with a total paid-up capital of Rs 37 million (Pakistan Stock Exchange, 2024). Then, in the 1960s, 81 companies were added with a free float capitalization of Rs 1.8 billion (Pakistan Stock Exchange, 2024). The PSX witnessed an aggregate market capitalization of Rs 10.37 trillion as of 30 June 2024 (Pakistan Stock Exchange Annual Report, 2024).

Among the indices operating under the PSX, the performance of the KSE-100 index is reflected as a barometer to evaluate the country’s economic progress. In a report PSX on KSE 100 Index, it is mentioned that the KSE-100 index was brought into effect in November 1991, and the base value was set at 1000 points. As the number in the index suggests, it comprises 100 blue-chip companies. The criteria for selecting companies for the KSE 100 index are based on two main components: Sectorial Representation and companies with the highest free float market capitalization (Pakistan Stock Exchange, 2025). Initially, 35 companies are selected from 36 available sectors (one from each sector) based on the highest free float capitalization (the Open-End Mutual Fund Sector is excluded). The remaining 65 companies are chosen based on the highest free float capitalization, irrespective of their sector. Hence, the KSE-100 index comprises about 80% of the total free float market capitalization of all listed companies on the Exchange (Pakistan Stock Exchange, 2025). The rationale for selecting the KSE 100 Index includes the broad market coverage, sectoral diversity, and economic importance. In addition to reflecting the collective movements of major publicly traded firms in Pakistan, it serves as a barometer of national economic performance and a critical tool for investors, analysts, and policymakers. With its comprehensive composition, researchers can draw insightful and meaningful inferences about macroeconomic trends, investor behavior, and the movement of the financial market in the Pakistani context.

Figure 1 shows the KSE-100 price index data from January 2004 through December 2024. The data was extracted from LSEG (Formerly Refinitiv and Thomson Reuters) DataStream. The figure shows that the Index experienced a significant financial downturn in 2008, following a minor crash in 2005, during which the market stopped functioning for four months. The military rule ended in 2008, and power was transferred to a civilian democratic government. Following the 2008 financial crisis, numerous discussions were held to implement changes in the stock market. Finally, the Corporatization, Demutualization, and Integration Stock Exchanges Act was enacted in 2012. Reflecting this milestone, Bloomberg ranked the Pakistani index among the five best stock performers in 2016 (Mangi, 2016). The FTSE also considers it an emerging secondary market. In 2017, it was again classified by MSCL (Morgan Stanley Capital International) and NBSP as an emerging market. The economy experienced a boom, with the PSX performing best due to high Chinese Investment in CPEC projects from 2013 to 2018. However, in May 2017, the market showed a bearish trend, and the Index dropped by 28% after an association of China purchased 40% of the shares for $85 million.

Interestingly, in 2020, among the 61 stock exchanges worldwide, the PSX ranked fourth best, and fourth in Asia, despite the COVID-19 outbreak. In addition, PSX is recognized as one of the premier emerging markets globally, characterized by a high growth rate and a highly liquid environment. However, this market is also culturally sensitive and unstable due to macroeconomic differences and political instability (Jaffri et al., 2025; Zahid & Saleem, 2025; Ghani et al., 2022; Joyo & Lefen, 2019). Factors such as political instability, economic crisis, and fluctuating policy significantly impacted the KSE 100 index, which remained volatile from 2021 to 2024. Moreover, the change in government in 2022, ongoing inflation, and the climate-induced floods of 2022 led to a decline in investor confidence. Recovery began in FY 2024, as macroeconomic indicators improved following the successful completion of the IMF program, which led the KSE 100 to achieve a remarkable return of 89.24%.

The current structure of Pakistan’s financial market offers opportunities for conducting a wide range of interesting research, but it also poses several problems. Although significant strides have been made to enhance the depth and stability of the market, further research is needed to compare the PSX with developed markets. This gap provides the necessary background to analyze the role of behavioral factors, such as investor attention, in the historically volatile market surrounding the stocks. Research shows that Pakistan’s stock market is highly sensitive to macroeconomic shocks. Therefore, it is anticipated that greater effort is needed to understand investors’ behavior in this regard.

There is also evidence of heightened investor attention to stock returns due to mirror-neighbors, decision heuristics, and self-organizing map information available in Pakistan’s capital market. Mirror-neighbors refers to the imitation of peers’ trading behavior with geographical and social proximity, leading to effects known as localized herding and information clustering (Banerjee, 1992; Bikhchandani et al., 1992). While decision heuristics—mental shortcuts used in judgment—help make investment decisions in uncertain environments, they sometimes introduce the risk of systematic biases. The use of such heuristics in decision-making, as proposed by Tversky and Kahneman (1973, 1974), corroborates the idea that individuals assess probabilities based on how readily instances come to mind. In other words, recent events and the emotions associated with them in an investor’s life significantly influence their decision making. It challenges objectivity and rationality in decision making. The use of decision heuristics can, therefore, represent a distorted perception, especially in retail-dominated markets like Pakistan (Abideen et al., 2023; Shah et al., 2018). Furthermore, Self-Organizing Map (SOM), a neural network–based unsupervised learning method, is increasingly used in financial analysis to detect hidden patterns and cluster investor behaviors, offering a data-driven lens on market segmentation and volatility (Resta, 2016). Generally, extant finance theories rely on assumptions about self-interest and wealth maximization. However, as obtained from the behavioral finance theory, investors act in ways that can be deemed irrational due to psychological factors and the inability to control their emotions, such as overconfidence, fear, and greed (Gill & Bajwa, 2018). In Pakistan’s case, these behavioral factors, such as heuristics, the herding effect, and market variables, have a meaningful influence over the investment decision.

The main motivation behind this study is to shed light on the growing and significant impact of investor attention in the Pakistani stock market by systematically analyzing attention proxies that affect future stock returns. In Pakistan, a few studies on investors’ attention are available. This study adds valuable insights to the existing body of knowledge by addressing the investor’s attention constructed from the context of the KSE-100 index and its effects on subsequent returns. It builds upon prior research in the following ways: The PCA methodological technique is used to construct the attention index. It will help policymakers understand the patterns of investor attention, creating policies and procedures to make the financial markets more transparent and protect the investors’ rights. From this study, market participants could identify key strategic directions that could assist them in understanding market conditions. In addition, appropriate investment decisions could be of considerable benefit and a competitive advantage in the market. It would help academic scholars in behavioral finance and open a new perspective. Besides this, the researcher would examine the signals that affect the performance of the KSE-100 index, thereby effectively managing their portfolios and risk.

The remaining study is structured as follows. Section 2 covers the existing literature. Section 3 discusses the methodology. Section 4 presents the empirical analysis and discussion, and Section 5 concludes the study.

2. Literature Review

Information must first attract investor attention before it can be processed and incorporated into asset prices through trading. Therefore, understanding how investor attention influences asset price formation is of significant importance (Z. Li et al., 2024, 2025). As attention is a finite cognitive resource that an individual possesses, researchers and industry experts have a keen interest in studying the theoretical and empirical significance of investors’ attention on the prices of stocks. Two ways are identified in the theories through which prices are affected. Informed traders are the first path through which the market learns (Hirshleifer & Teoh, 2003; Huang & Liu, 2007; Peng & Xiong, 2006). The second path is when attention fascinates uninformed traders (Barber & Odean, 2008). The authors documented that an individual investor requires more attention towards stock prices than institutional investors. A buy decision requires an average investor to gauge the worthiness of thousands of instruments before making a final decision, whereas a selling decision need a smaller evaluation.

Da et al. (2011) identified that one of the major limitations in empirically testing attention theories is the unavailability of a direct measure of investor attention. Hence, the researchers must take indirect proxies such as extreme returns, trading volume, news and headlines, advertising expenses, and price limits. Building on these foundations, the literature of this study is organized around three central themes. The first theme presents the theoretical discussion, and the second theme presents studies that elaborate on the proxies or methodologies used to construct the attention index. The third part of the same studies examines the impact of investor attention on stock returns.

2.1. Theoretical Discussion

Economist Herbert A. Simon, in 1955, proposed the Bounded Rationality Theory, which posits that decision-makers have cognitive and informational limitations (Simon, 1955). They “satisfice”—therefore making decisions that are adequate in the light of available cognitive abilities, time, and information. Merton (1987) emphasized that individual investors save resources by seeking only portions of the financial information. On this premise, Kahneman (1973) and Pashler et al. (2001) posited that, given their low cognitive abilities, investors were able to apprehend a simple take on attention. Hence, attention paid by investors is a link between bounded cognition and securities’ price determination. Information that targets this short span of attention from investors can skew their decision-making, thus producing consequences in the market that can include short-run changes in prices, volatility, and returns. Thus, this theory of bounded rationality can be used to explain why investor attention is not distributed evenly and how the process of selective attention contributes to nonrandom patterns of stock returns, especially in the less-developed emerging markets.

Miller’s (1977) Heterogeneous Beliefs Theory states that the correlation between heterogeneity of beliefs and the risk of stock is direct. He states that “in practice, uncertainty, disagreement over a security’s return, and risk correlate.” Therefore, ‘high-risk, low volume stocks are also high information uncertainty stocks; hence, the market clearing price for a high-risk stock will be higher than that for a low-risk stock. Miller also opines that the overvaluation of high-risk stocks is attributed to short sale constraints among the heterogeneous investors.

Prospect Theory (Kahneman & Tversky, 1979), the foundational theory in behavioral finance, helps to explain the impact that attention has on stock returns in emerging markets due to investor psychology. The theory deviates from the rational expectations model by stating that investors compare economic outcomes to a reference level and are characterized by systematic decision-making biases about risk. There are three types: (1) Loss aversion speaks of why investors respond more aggressively to negative signals: when attention is given to the potential of a loss, the suffering felt is always more than that resulting from an equivalent amount of profit, which we sell off more aggressively, a factor that occurs in emerging markets, due to increased volatility and information asymmetry (Barberis & Huang, 2001). (2) Probability weighting explains why investors overestimate the stock that provides ‘lottery-like’ investments, a finding supported by theoretical (Tversky & Kahneman, 1992) and empirical research (Da et al., 2011). (3) The editing phase of Prospect Theory discusses how investors employ attention as an information filter and base their choices on easily recognizable but potentially irrelevant cues in situations of uncertainty (Peng & Xiong, 2006). This dilemmatic-heuristic behavior results in short-run mispricing, with prices rising in conditions of increased focus and then experiencing a backlash. Theoretical frameworks predict that such shocks equate to short-term outperformance and subsequent underperformance for the stocks receiving the attention boost (Hong & Stein, 1999). Such patterns are particularly pronounced in markets where institutions are immature and where more retail investors trade, such as the emerging markets suggested by Seasholes and Wu (2007). The combination of Prospect Theory and investor attention explains these return anomalies, hence shedding light on how behavioral prejudice plays out in structural imperfections in these markets. Limited Attention Theory by Peng and Xiong (2006) studies theoretically the outcome of inadequate investor attention on asset–price dynamics. However, this study is based on Prospect Theory.

2.2. The Measurement of Investor Attention

Barber and Odean (2008) studied the New York Stock Exchange equity market and tested attention-driven buying by sorting stocks based on events that capture investor attention. These include abnormal trading volume, extreme one-day returns (positive or negative), and news coverage. Aboody et al. (2010) have taken top percentile stocks, ranked based on prior 12-month price performance, as a proxy measure for observing investor attention from 1971 to 2005. J. Li and Yu (2012), motivated by the psychological evidence on limited investor attention, considered two proxies to test whether attention plays its role in the U.S. stock market. The two proxies were nearness to the Dow 52-week high and nearness to the Dow historical high. W. Zhang et al. (2013) advocate the search frequency of stock names in Baidu Index (the largest search engine in China) as a novel and direct proxy for investor attention. Aouadi et al. (2013) studied the French equity market and considered abnormal trading volume as a proxy measure of investor attention. Hirshleifer et al. (2013) used Analyst Coverage as a substitute measure to gauge investor attention. Lou (2014) also took advertising spending as a proxy measure of investor attention.

Choi and Choi (2019) discovered the influence of trading volume on investor attention in the Korean market. For measuring investor attention, the top 30 stocks were considered, and they were discussed online frequently on the message board from 2010 to 2014 using Daum (a widely used internet portal in Korea). Chemmanur and Yan (2019) studied the US stock market from 1996 to 2005. In the first hypothesis, they tested the relationship between advertising and stock returns. Then, in the second hypothesis, their research investigated whether advertising predicts future stock returns. Another study by Düz Tan and Taş (2019) examined whether firm-specific investor attention predicts future stock returns for the Borsa Istanbul All Shares Index, Turkey. The researchers developed the Abnormal Google Search Volume index (ASVI) as a direct measure of investor attention, which quantifies investor interest based on abnormal search volumes. Their data spanned from 2013 to 2017. Moreover, Subramaniam and Chakraborty (2020) explored whether investor attention influences the prices of cryptocurrencies. They used the daily Google Search Volume index as a proxy for attention. In their work, they analyze Bitcoin, Ethereum, Ripple, and Litecoin from January 2013 to March 2018 and utilize a quantile causality approach to consider effects through various market phases. Ibikunle et al. (2020) investigated whether high investors’ attention disturbs the price discovery process of Bitcoin. For this, they used two data sources: First, 30.5 million trades from Bitstamp between 13 September 2011 and 10 April 2019, including time, price, and volume. The second measure of investor attention is calculated using Google Trends data for the keyword “Bitcoin”, which is the most popular search term for potential investors.

The COVID-19 pandemic represents an unparalleled disruption in the modern era, having an impact on global markets and institutions, including the financial sector. Unlike past pandemics, it leads to unprecedented volatility, liquidity shocks, and market instability (S. R. Baker et al., 2020). The epidemic triggered widespread sell-offs, increased systemic risks, and pressurized central banks to use aggressive monetary and fiscal policies to stabilize economies (D. Zhang et al., 2020). COVID-19 intensifies the profit gaps between banks and non-financial markets, undermining the development of the real economy (Guan et al., 2021). The pandemic set the finest example of analyzing market response to variations in investors’ attention. According to Smales’ (2021) research, GSV for the keyword “coronavirus” rose sharply from late February, peaked in mid-March, and then declined significantly. Therefore, he attempted to explain the changing dynamics of market response by considering Google Search Volume (GSV) as a proxy measure for investor attention. Similarly, recent research by Yahya et al. (2021) examined the impact of various factors, including the outbreak of novel COVID-19, investor attention as assessed by the Google search volume index, social isolation, and investor sentiments, on stock returns in the German Stock Market. The study investigated whether social isolation influences the investor’s attentiveness to the stock market amid fluctuating investor sentiments.

2.3. The Impact of Investor Attention on Stock Markets

Barber and Odean (2008) suggest that individual investors exhibit attention-driven buying behavior. They tend to be net buyers on high-volume days, reacting to both extremely negative and positive one-day returns, and when stocks receive media coverage. The results of Aboody et al. (2010) showed that strong past returns attract individual investors’ attention, particularly before earnings announcements. Another study by J. Li and Yu (2012) found that, due to scarce attention, future stock returns are positively predicted by nearness to the 52-week high, whereas this is the opposite for nearness to the historical high. According to W. Zhang et al. (2013), attention could be the new barometer for information in financial markets due to the heterogeneous behavior of investors. Consequently, investor attention is the major factor in predicting abnormal stock returns and exhibits contemporary relationships with it. Aouadi et al. (2013) identified a positive and significant relationship between investor attention and abnormal trading volume at the market level. Hirshleifer et al. (2013) found that stock returns tend to be high for those firms that are efficient in research and development. Furthermore, the authors identified it because such firms’ earnings per share (EPS) tend to increase in the future. Lou (2014) concluded that if a firm increases advertising spending, the stock price will grow simultaneously, followed by a complete return reversal.

Choi and Choi (2019) concluded that when investors paid high attention to the stocks, the trading volume of such stocks increased suddenly and unexpectedly on that day. Thus, due to short-sell constraints, high investor attention results in low future returns through active trading. Chemmanur and Yan (2019), in the first hypothesis, found that more investor attention is drawn to firms if firms invest heavily in advertising. Then, in the second hypothesis, the results showed that advertising significantly increases investors’ attention to the firms’ stocks and negatively affects their future returns. The study of Düz Tan and Taş (2019) found that firms attracting high ASVI tend to generate higher returns. The study emphasized that ASVI outperforms indirect proxies of investor attention, such as abnormal turnover, excess returns, and news volume, in predicting stock returns, as it is more closely linked to actions or decisions made by investors. These findings demonstrate the significant impact of investor attention (constructed by ASVI) on stock prices in Turkey, particularly in the context of the All-Shares Index. Moreover, Subramaniam and Chakraborty (2020) concluded that retail/individual investors pay high attention to highly ranked cryptocurrencies such as Bitcoin and Ethereum. Therefore, the returns of that cryptocurrency increase. However, the prices of new cryptocurrencies such as Ripple are influenced by investor attention, but only at the time of their superior performance. Ibikunle et al. (2020) concluded that irrational, uninformed trading activity increases when attention is given to the bitcoin market. However, attention is unaffected by fully rational and informed traders. It implies that only uninformed traders paid high attention, leading them to participate more in the bitcoin market, which is unrelated to any increase in informed trading (Ibikunle et al., 2020).

The study findings of Smales (2021) suggest that as news events or other information drew investors’ attention, the prices responded by incorporating the same news or information. So, it was proved that stock returns are marginally low and that price volatility grew strong as the news or certain information drew investors’ attention. Moreover, Yahya et al. (2021) showed a significant impact of the coronavirus on the Frankfurt Stock Exchange after considering all the anomalies, such as weather disruptions, calendar variations, and oil price volatility. Furthermore, the higher stock returns during the social isolation period resulted from investors’ attention to buying underpriced stock. Thus, a temporary lockdown helped increase investors’ precision in decision making, leading them to make better investment decisions.

Principal component analysis (PCA) is a widely used technique for simplifying complex multivariate systems with high dimensionality. PCA reduces the large number of variables to a concise representation without compromising the characteristics of the original data. Thus, brevity is achieved through the PCA model, but not at the cost of clarity in the data. PCA is used in numerous prominent studies on investors’ attention and stock return predictability (Ludvigson & Ng, 2007; M. Baker & Wurgler, 2006; Neely et al., 2014; B. Wang et al., 2018; He et al., 2021; J. Chen et al., 2022; Chu et al., 2022; Song et al., 2023), among many others. Resultantly, this study has been finalized to use the PCA prediction technique. Through PCA, market-level measures were aggregated into a single index. By doing so, this study first aggregates firm-level measures into measures at the market level whenever needed. Thus, an aggregated attention index would employ all information on the proxies and stock market returns.

3. Methodology

3.1. Data Sources and Variables

This study uses monthly time-series data from January 2004 to December 2024 to construct an investor aggregate attention index. The time period is selected based on the data availability for all the constituents of the KSE-100 index, thereby eliminating survivorship bias. Also, this time period captures significant market cycles and regulatory changes in the Pakistan stock market, impacting investors’ sentiments. The data is collected from Refinitiv Eikon and DataStream. We collect mutual funds’ data from the Mutual Funds Association of Pakistan (MUFAP) website, and Google search volume from Google Trends. The stock’s closing price is used for the calculations of company-specific returns. We follow the literature and use principal component analysis (PCA) to construct the investor attention index (Ludvigson & Ng, 2007; M. Baker & Wurgler, 2007; Neely et al., 2014; B. Wang et al., 2018; He et al., 2021; J. Chen et al., 2022; Chu et al., 2022; Song et al., 2023). Based on the behavioral finance theories and empirical evidences of attention proxies, this study has taken seven major individual attention proxies, namely $A^{AT{V}_{it}}$—abnormal trading volume and $A^{E{R}_{it}}$—extreme returns (Barber & Odean, 2008), $A^{P{R}_{it}}$—past returns (Aboody et al., 2010), $A^{NK52W{H}_t}$—nearness to the 52-week high and $A^{NKIH{H}_t}$—nearness to the historical high (J. Li & Yu, 2012), $A^{GS{V}_t}$—google search volume (Da et al., 2011; Aouadi et al., 2013; Ding & Hou, 2015; Yao et al., 2017), and $A^{NAVEM{F}_t}$—mutual funds inflow (J. Chen et al., 2022). These seven proxies were first used to construct individual investor indexes at the firm level; then, this research aggregated them to the market level by following the J. Chen et al. (2022) methodology. At first, the variables are computed using the formulas provided in

Table 1. Definition and Operationalization of Variables.

Variables	Symbol and Operationalization		Definition
Abnormal Trading Volume	$A^{AT{V}_{it}}={\displaystyle \frac{T{V}_{it}}{\overline{T{V}_{it}}}}$	(1)	In Equation (1), $A^{AT{V}_{it}}$ is the equal-weighted abnormal trading volume ($AT{V}_{it}$) at time $t$ across all stocks. It is calculated as a ratio of the stock’s trading volume ($T{V}_{it}$) at time $t$ to its average trading volume ($\overline{T{V}_{it}}$) over the previous year. According to Barber and Odean (2008), when abnormally heavy trading volumes are observed in the stock market, investors are more attracted to these shares than usual. Hence, it is a measure of the market-level attention index.
Extreme Returns	$A^{E{R}_{it}}={\displaystyle \frac{E{R}_{it}}{E{R}_{it-1}}}$	(2)	According to Barber and Odean (2008), investors notice extreme one-day returns, positive or negative, mostly when news about the company occurs. Hence, extreme returns play a significant role in measuring investors’ attention. In Equation (2), $A^{E{R}_{it}}$ is ratio of extreme returns ($E{R}_{it}$) at the end of each month to the average of extreme returns over the previous one year for each stock ($E{R}_{it-1}$). Hence, it $A^{E{R}_{it}}$ is the equal-weighted extreme returns at time $t$ across all stocks.
Past Returns	$A^{P{R}_{it}}={\displaystyle \prod _{s=t-12}^{t-1}(1+r_{i,s}})-1$		Aboody et al. (2010) highlighted that stocks with sharp past returns attract investors’ attention. Also, the company’s earnings announcements grab attention; hence, there is a need to include a past returns proxy in the investors’ attention index. $A^{P{R}_{it}}$ is the cumulative monthly returns for the past twelve months for each stock $i$ at time $t$ is calculated which is the equally weighted past return across all stocks (J. Chen et al., 2022).
Nearness to the KSE-100 Index 52-Week High	$A^{NK52W{H}_t}={\displaystyle \frac{p_t}{p_{52W{H}_t}}}$	(3)	To empirically test psychological anchoring and limited investor attention, J. Li and Yu (2012) used Nearness to the Index 52-week high ($A^{NK52W{H}_t}$) and historical high proxies. Furthermore, the authors stated that $A^{NK52W{H}_t}$ helps in measuring the extent of underreaction and in predicting the aggregate market returns. In Equation (3), $A^{NK52W{H}_t}$ is the ratio of the current level of KSE-100 index ($p_t$) at the end of month $t$ to its 52-week high ($p_{52W{H}_t}$) at month $t$.
Nearness to the KSE-100 Index Historical High	$A^{NKIH{H}_t}={\displaystyle \frac{p_t}{p_{{\max }_t}}}$	(4)	J. Li and Yu (2012) used Nearness to the KSE-100 index historical high ($A^{NKIH{H}_t}$) specifically to examine when the current price is far from the historical high price, which is the time when investors react to the bad news. The authors stated that investors overreact because there has been a series of bad news in the past, and prolonged news has a negative impact on future market returns. In Equation (4), $A^{NKIH{H}_t}$ is the ratio of the current KSE-100 index ($p_t$) at the end of the month $t$ to its historical high ($p_{{\max }_t}$) at the end of month $t$. The $p_{{\max }_t}$ is the maximum index value of KSE-100 price index dataset from January 2004 to December 2024.
Google Search Volume	$A^{GS{V}_t}$		Da et al. (2011) proposed Google aggregate search frequency as a direct measure of investors’ attention. $A^{GS{V}_t}$ is the monthly aggregate search frequency of companies listed on KSE-100 index from Google Trends using their stock ticker. The data is available from January 2004 onwards.
Equity Mutual Funds Inflow	$A^{NAVEM{F}_t}$		$A^{NAVEM{F}_t}$ denotes the net asset value of mutual fund inflow for each equity mutual fund $i$ at the end of the month $t$. Like J. Chen et al. (2022), we computed the equal-weighted mutual funds inflow as a proxy for the market level.
KSE 100 Index Returns	$KSE{100}^{M{R}_t}=\ln ({\displaystyle \frac{I{P}_t}{I{P}_{t-1}}})$	(5)	$KSE{100}^{M{R}_t}$ is the index returns, $I{P}_t$ is the KSE-100 index price at time $t$ and $I{P}_{t-1}$ is the index price at time $t-1$.
KSE 100 Index Excess Returns	$KSE{100}^{EM{R}_t}=KSE{100}^{M{R}_t}-R{F}_t$	(6)	$KSE{100}^{EM{R}_t}$ is the KSE-100 index excess market returns. It is the difference of $KSE{100}^{M{R}_t}$ and $R{F}_t$ (three-month treasury bill rate)

. Hence, Table 1 exhibits the variables, their definitions, and operationalization.

3.2. Aggregate Attention Index and Principal Component Analysis (PCA)

The aggregated attention index is created using all seven proxies together. A factor structure is developed in Equation (5).

$$A_{it}={\eta }_{i,0}+{\eta }_{i,1}{A}_t^{*}+{\eta }_{i,2}{E}_t+e_{it}$$

(7)

In Equation (7), $A_t^{*}$ is the true but unobservable investor attention (J. Chen et al., 2022), $A_{it}$ is the proxy of attention sensitivity to $A_t^{*}$ which is the true attention, and is summarized by factor loadings, that is ${\eta }_{i,1}$, the common error term of all the proxies is $E_t$, while $e_{it}$ denotes the idiosyncratic noise solely associated with $i$. The estimation of $A_t^{*}$ helps in identifying investor attention impact in the stock market, mainly to impose factor structure and reduce $E_t$ (the common approximation error) and $e_{it}$ (estimation idiosyncratic noise).

According to J. Chen et al. (2022), PCA is the simplest but popular method that helps in extracting the principal component $A_{it}$, the aggregate attention index measure. It represents the maximum total variation in the seven proxies used in this study. Furthermore, this approach apprehends the information in an index and separates $A_t^{*}$ from $e_{it}$. Researchers have widely used PCA in the literature, specifically in forecasting stock returns (M. Baker & Wurgler, 2006; Ludvigson & Ng, 2007; Neely et al., 2014; J. Chen et al., 2022; and others). The main rationale for using PCA for constructing an index is that it reduces dimensionality, transforming high-dimensional data into a low dimension while retaining total variance or information. Furthermore, it creates components that reduce noise and explain the most variance, helps in removing multicollinearity, and constructs orthogonal components. Also, it compresses the dataset and retains the components with the most variance. In short, to ensure that no a priori weighting is imposed, the PCA allows for an endogenous data-driven scheme based on the variance–covariance among the standardized variables. The PCA approach follows established practice in financial economics for aggregating indicators into latent constructs (M. Baker & Wurgler, 2006; Ben-Rephael et al., 2017). The main steps in PCA methodology and in constructing an index are as follows: It computes the covariance matrix, mainly to understand how factors vary with each other. Then it computes and sorts eigenvalues and eigenvectors to define the direction of principal components.

Similarly, the rationale for this methodological choice and its significance are supported by the literature. The classical PCA technique is effective for high-dimensional datasets, particularly correlated variables, and successfully reduced the feature space while retaining the maximum variance, enabling clear interpretation of the underlying patterns without the overfitting risks associated with more complex models. Jolliffe and Cadima (2016) emphasized the importance of PCA, which remains a cornerstone in exploratory data analysis mainly due to its simplicity, interpretability, and robustness across diverse sets of applications. The results of this study demonstrate that PCA adequately captures the essential structure of the data, aligning with the study’s aim to construct an investors’ attention index derived from seven key proxies. Hair (2009) highlighted that PCA is particularly valuable when the goal is to identify key components driving variability in a dataset without unnecessary complexity. However, hybrid or novel models may introduce assumptions that could obscure insights or limit generalizability, especially given our dataset’s characteristics in developing an index.

Abdi and Williams (2010) stated that PCA often outperforms more complex hybrid models in scenarios where linear relationships dominate, as observed in our dataset. Moreover, in many contexts, the primary drivers of financial phenomena can be well-approximated by linear structures, making PCA a robust and parsimonious tool for initial dimension reduction and factor identification. For instance, PCA has been successfully applied to analyze yield curve dynamics, market risk factors, and portfolio construction, where the lending principal components often correspond to well-understood market movements such as level, slope, and curvature (X. Wang, 2006; Oprea, 2022). Wold et al. (1987) specified that PCA’s value lies in its ability to uncover meaningful patterns, which this study achieves to minimize risk and promote efficient financial management.

In summary, the findings of this study are grounded in PCA, providing actionable insights directly applicable to researchers, portfolio managers, and financial analysts in gauging investors’ herding behavior, specifically in the KSE-100 benchmark index. Based on this, it constructs the matrix and predicts the data. J. Chen et al. (2022) used an equally weighted (EW) aggregation approach and normalized all the proxies; however, according to the authors, the EW fails to eliminate the common observation errors and only captures the maximum common variations in predictors. Hence, we have not used this technique.

The STATA software version 17.0 is employed for index construction and empirical testing. We standardize and normalize all the variables using z-score ($z={\displaystyle \frac{X-\mu }{\sigma }}$). Please note that the descriptive statistics and correlation matrix of standardized variables are provided in Appendix A and Appendix B. Additionally, to examine whether all the standardized series are stationary, the Augmented Dickey–Fuller (ADF) test was run (See Appendix C). All the variables are significant except for $A^{NKIH{H}_t}$; hence, by taking the first difference, it is converted into stationary ($A^{DNKIHH}$) and is used in the index. The line graphs of each variable in Appendix D give the graphical presentation of the index variables. Through PCA, four indices are constructed; mainly, these indices have eigenvalues approximately equal to 1 or greater than 1. Please see screeplot of eigenvalues in Appendix E. The scoreplot and loadings of components are shown in Appendix F. The loadings are estimated, and based on the loadings, four indices are created, mainly because all the components explain 12% to 26% and cumulatively 73% of the variations. Then, Kaiser–Meyer–Olkin (KMO) is run to examine the sampling adequacy. The line graphs and ADF results of all the four attention indices are provided in Appendix G. The authors examine the linearity assumption of OLS regression through a scatter plot (see Appendix H). The OLS regression and its four assumptions (heteroscedasticity, autocorrelation, multicollinearity, and normality) empirical test results are shown in Appendix I. As some of the assumptions are not fulfilled, we have to use GLS regression. Based on the attention index, the forecasting regression Equation (8) mentioned below is considered for the current research.

$$KSE{100}^{EM{R}_{t+1}}={\alpha }_i+{\beta }_i{A}_{it}+{\epsilon }_{t+1}$$

(8)

where $KSE{100}^{EM{R}_{t+1}}$ is KSE-100 index excess return, ${\beta }_i$ denotes the slope of regression on the $i_{th}$ attention proxy $A_{it}$ at time $t$, and ${\epsilon }_{t+1}$ is the noise term. The primary aim of this study is to examine the impact of investor attention index on KSE 100 stock returns while keeping all other factors constant; therefore, the univariate forecast model is empirically tested. To estimate the model above, the GLS regression is used in line with the literature to examine the impact of investor attention on excess stock market returns, also known as market risk premium.

4. Results and Discussion

4.1. Descriptive and Correlation Analysis

This study uses monthly data comprising 252 observations (months) as shown in

Table 2. Descriptive statistics of investors’ attention proxies and KSE-100 index returns.

Variables	Obs	Mean	SD	Min	Max	P1	P99	Skew	Kurt
$A^{NK52WH}$	252	0.861	0.115	0.395	1	0.552	1	−0.974	3.628
$A^{NKIHH}$	252	0.241	0.164	0.041	1	0.044	0.772	1.061	4.872
$A^{ATV}$	252	0.996	0.365	0.004	2.361	0.212	2.013	0.58	3.707
$A^{GSV}$	252	10.442	2.862	1.373	19.529	2.451	18.049	−0.22	3.967
$A^{ER}$	252	0.08	0.021	0.001	0.233	0.041	0.157	2.585	18.498
$A^{PR}$	252	0.238	0.346	−0.56	1.397	−0.529	1.19	0.269	2.965
$A^{NAVEMF}$	252	2404.885	659.002	1258.838	4666.711	1306.07	4163.147	1.257	4.088
$KSE{100}^{EMR}$	252	−0.088	0.081	−0.483	0.167	−0.297	0.107	−0.504	5.309

Note. Obs represents the number of observations, Mean is the average of investors’ index proxies, SD is the standard deviation, Min is the minimum value, Max is the maximum value in the data series, P1 is the first percentile, P99 is the ninety-ninth percentile, Skew represents skewness, and Kurt is kurtosis. The Table exhibits the descriptive statistics of key variables: $A^{NK52WH}$ (Nearness to KSE-100 Index 52-Week High), $A^{NKIHH}$ (Nearness to KSE-100 Index Historical High), $A^{ATV}$ (Abnormal Trading Volume), $A^{GSV}$ (Google Search Volume), $A^{ER}$ (Extreme Returns), $A^{NAVEMF}$ (Equity Mutual Funds Inflow), $A^{PR}$ (Past Returns), and $KSE{100}^{EMR}$ is the KSE 100 index excess returns. The data frequency is monthly, and the period is from January 2004 to December 2024.

.

The mean of Nearness to KSE-100 Index 52-Week High ($A^{NK52WH}$) is 0.861 with SD of 0.115, a minimum value of 0.395, maximum of 1, p1 of 0.552, and p99 of 1; skewness is −0.974, showing negatively skewed data, kurtosis is 3.628, which is greater than 3, meaning the data is leptokurtic. Nearness to KSE-100 Index Historical High ($A^{NKIHH}$) has a mean of 0.241, SD of 0.164, minimum and maximum are 0.041 and 1, p1 of 0.044, p99 of 0.772, positively skewed with 1.061, and 4.872 is kurtosis, showing leptokurtic data. The mean of Abnormal Trading Volume ($A^{ATV}$) is 0.996, SD is 0.365, the minimum value is 0.004, the maximum value is 2.361, p1 is 0.212, and p99 is 2.013. The variable has positively skewed data with skewness of 0.58, and kurtosis of 3.707, which is greater than 3, representing leptokurtic data.

The mean value of Google Search Volume ($A^{GSV}$) is 10.442, with an SD of 2.862, a minimum search of 1.373, and a maximum of 19.529. It has p1 of 2.41 and p99 of 18.049, along with the skewness of −0.22, and kurtosis of 3.967, indicating the data is leptokurtic. Extreme Returns ($A^{ER}$) represents extreme returns with a 0.080 mean value and 0.021 SD, minimum extreme returns of 0.001 and 0.233 with maximum extreme returns, p1 of 0.041, p99 of 0.157, skewness of 2.585, and kurtosis of 18.498, showing leptokurtic data series. The mean value of Past Returns ($A^{PR}$) is 0.238 with SD of 0.346, −0.56 of minimum past returns and 1.397 maximum returns, with p1 of −0.529 and p99 of 1.19, skewness of 0.269, and kurtosis of 2.965, showing data is platykurtic. Equity Mutual Funds Inflow ($A^{NAVEMF}$) mean value is 2,404.89, SD of 659.002, a minimum of 1258.84, a maximum of 4666.71, p1 of 1306.07, and p99 of 4163.15, with skewness of 1.257, and kurtosis of 4.088. $KSE{100}^{EMR}$ descriptive statistics show that the index has produced average −0.088 excess returns along with a SD of 0.081. The index produced a minimum excess return of −0.483, and a maximum of 0.167, during the period of study. The lowest percentile p1 is −0.297, and the largest percentile p99 is 0.107, with −0.504 skewness, and kurtosis of 5.309 showing leptokurtic behavior.

4.2. Attention Index Construction Through PCA and Its Impact on Stock Market Returns of KSE-100 Index

For the construction of an attention index, it is important to have relationship among the variables.

Table 3. Pairwise correlation matrix of investors’ attention proxies.

Variables	$\mathit{K}\mathit{S}\mathit{E}{100}^{\mathit{E}\mathit{M}\mathit{R}}$	${\mathit{A}}^{\mathit{N}\mathit{K}52\mathit{W}\mathit{H}}$	${\mathit{A}}^{\mathit{D}\mathit{N}\mathit{K}\mathit{I}\mathit{H}\mathit{H}}$	${\mathit{A}}^{\mathit{A}\mathit{T}\mathit{V}}$	${\mathit{A}}^{\mathit{G}\mathit{S}\mathit{V}}$	${\mathit{A}}^{\mathit{E}\mathit{R}}$	${\mathit{A}}^{\mathit{P}\mathit{R}}$	${\mathit{A}}^{\mathit{N}\mathit{A}\mathit{V}\mathit{E}\mathit{M}\mathit{F}}$
$KSE{100}^{EMR}$	1.000
$A^{NK52WH}$	0.387 ***	1.000
	(0.000)
$A^{DNKIHH}$	0.566 ***	0.123 *	1.000
	(0.000)	(0.052)
$A^{ATV}$	0.112 *	0.382 ***	0.107 *	1.000
	(0.077)	(0.000)	(0.091)
$A^{GSV}$	−0.288 ***	−0.051	0.083	0.117 *	1.000
	(0.000)	(0.420)	(0.188)	(0.065)
$A^{ER}$	−0.176 ***	−0.160 **	−0.010	0.094	0.143 **	1.000
	(0.005)	(0.011)	(0.877)	(0.137)	(0.023)
$A^{PR}$	0.271 ***	0.187 ***	0.049	0.229 ***	−0.335 ***	−0.095	1.000
	(0.000)	(0.003)	(0.442)	(0.000)	(0.000)	(0.131)
$A^{NAVEMF}$	0.163 ***	0.131 **	0.021	0.264 ***	0.043	−0.089	0.327 ***	1.000
	(0.009)	(0.038)	(0.737)	(0.000)	(0.497)	(0.160)	(0.000)

Note. Table 3 illustrates the relationship between $KSE{100}^{EMR}$ and seven attention index proxies. *** p < 0.01, ** p < 0.05, * p < 0.1.

showed a negative and weak to moderate correlation of $A^{GSV}$, and $A^{ER}$ of −0.288, and −0.176 with the dependent variable $KSE{100}^{MR}$. The variables $A^{NK52WH}$, $A^{DNKIHH}$, $A^{ATV}$, $A^{PR}$, and $A^{NAVEMF}$ have positive but weak to moderate correlations of 0.387, 0.566, 0.112, 0.271, and 0.163 with $KSE{100}^{EMR}$. The results showed that the variables are significant and do not have the problem of multicollinearity.

Table 4. Principal components eigenvalue shows total variance explained by variables/factors.

Component	Eigenvalue	Difference	Proportion	Cumulative
Comp1	1.831	0.498	0.262	0.262
Comp2	1.334	0.303	0.191	0.452
Comp3	1.030	0.107	0.147	0.599
Comp4	0.924	0.040	0.132	0.731
Comp5	0.883	0.363	0.126	0.857
Comp6	0.520	0.042	0.074	0.932
Comp7	0.478	0.000	0.068	1.000

shows eigenvalues for each component. As per the rules of PCA, if eigenvalues are greater than and/or equal to one (eigenvalues >= 1), such components should be included for further analysis. The eigenvalue suggested by (Cattell, 1966) stated that four components should be retained for factor analysis of this research. The eigenvalue for Comp1 is 1.831, Comp2 is 1.334, Comp3 is 1.030, and Comp4 is 0.924. The eigenvalues show the total variance each factor accounts for (Mooi et al., 2018). The proportion of Comp1 explains 26.2%, Comp2 explains 19.1%, Comp3 explains 14.7%, and Comp4 explains 13.2% of the overall variance. Based on the PCA results, four attention indices are predicted; Comp1 is the first attention index denoted by $A^{PCA1}$, Comp2 is the second index $A^{PCA2}$, Comp 3 is the third index $A^{PCA3}$, and Comp 4 is the fourth index $A^{PCA4}$. Please note that for the construction of indices standardized values are used.

The eigenvectors of each variable of each component of PCA are mentioned in

Table 5. Principal components (eigenvectors).

Variable	Comp1	Comp2	Comp3	Comp4	Unexplained
$A^{NK52WH}$	0.479	0.111	−0.363	−0.017	0.427
$A^{DNKIHH}$	0.161	0.291	−0.582	0.470	0.287
$A^{ATV}$	0.484	0.417	0.133	0.049	0.320
$A^{ER}$	−0.170	0.411	0.559	0.596	0.073
$A^{PR}$	0.510	−0.309	0.261	0.248	0.271
$A^{GSV}$	−0.150	0.679	−0.025	−0.440	0.164
$A^{NAVEMF}$	0.447	0.062	0.362	−0.408	0.341

. According to Mooi et al. (2018) PCA eigenvectors comprise factor weights that help in obtaining the maximum variance until a significant part of the variables’ variance is explained. The unexplained column in Table 5 shows the unexplained variance of four components.

The aggregate attention index is constructed using a combination of factor weights of the individual attention proxies available in Table 5:

$$\begin{array}{l}{A}^{PCA1}=0.479A^{NK52WH}+0.161A^{DNKIHH}+0.484A^{ATV}-0.170A^{ER}+0.510A^{PR}-0.150A^{GSV}\\ +0.447A^{NAVEMF}\end{array}$$

(9)

$$\begin{array}{l}{A}^{PCA2}=0.111A^{NK52WH}+0.291A^{DNKIHH}+0.417A^{ATV}+0.411A^{ER}-0.309A^{PR}+0.679A^{GSV}\\ +0.062A^{NAVEMF}\end{array}$$

(10)

$$\begin{array}{l}{A}^{PCA3}=-0.363A^{NK52WH}-0.582A^{DNKIHH}+0.133A^{ATV}+0.559A^{ER}+0.261A^{PR}-0.025A^{GSV}\\ +0.362A^{NAVEMF}\end{array}$$

(11)

$$\begin{array}{l}{A}^{PCA4}=0.427A^{NK52WH}+0.287A^{DNKIHH}+0.320A^{ATV}+0.073A^{ER}+0.271A^{PR}+0.164A^{GSV}\\ +0.341A^{NAVEMF}\end{array}$$

(12)

The coefficients of eigenvalues of each variable in each component are provided in

Table 6. The coefficients of eigenvalues results.

Variable	Comp 1 (PCA1)	Comp 2 (PCA2)	Comp 3 (PCA3)	Comp 4 (PCA4)	Unexplained
$A^{NK52WH}$	0.4792		−0.3634		0.4267
$A^{DNKIHH}$			−0.5816	0.4700	0.287
$A^{ATV}$	0.4836	0.4168			0.3195
$A^{ER}$		0.4108	0.5585	0.5958	0.0728
$A^{PR}$	0.5095	−0.3087			0.2707
$A^{GSV}$		0.6793		−0.4397	0.1642
$A^{NAVEMF}$	0.4465		0.3621	−0.4084	0.3407

. In order to identify which factors load the most in the respective index, the coefficients below 0.3 are removed for graphical representation of Table 6.

According to the results of Table 6, the following proxies contribute higher to the indices $A^{PCA1}$, $A^{PCA2}$, $A^{PCA3}$, and $A^{PCA4}$. Hence, the major contributions are of these factors:

$$A^{PCA1}=0.4792A^{NK52WH}+0.4836A^{ATV}+0.5095A^{PR}+0.4465A^{NAVEMF}$$

(13)

$$A^{PCA2}=0.4168A^{ATV}+0.4108A^{ER}-3087A^{PR}+0.6793A^{GSV}$$

(14)

$$A^{PCA3}=-{0.3634}^{NK52WH}-0.5816A^{DNIKHH}+0.5585A^{ER}+0.3624A^{NAVEMF}$$

(15)

$$A^{PCA4}=0.4700A^{DNKIHH}+0.5958A^{ER}-0.4397A^{GSV}-0.4084A^{NVEMP}$$

(16)

The attention indices loadings are estimated, and the indices are constructed based on the loadings. The Kaiser–Meyer–Olkin (KMO) results are used to analyze the adequacy of samples because the correlations and partial correlations between variables are compared by KMO value in

Table 7. KMO measure of sampling adequacy.

Variable	KMO
$A^{NK52WH}$	0.5595
$A^{DNKIHH}$	0.6101
$A^{ATV}$	0.5368
$A^{ER}$	0.4403
$A^{PR}$	0.5400
$A^{GSV}$	0.4170
$A^{NAVEMF}$	0.5693
Overall	0.5248

.

The KMO value for this study is 0.5248, which indicates a middling sample and highlights that correlations are high compared to partial correlations (Field, 2024). We examine the data pattern and stationarity of $A^{PCA1}$, $A^{PCA2}$, $A^{PCA3}$, and $A^{PCA4}$ through line graphs and ADF tests (Appendix E). All the indices are stationary. The descriptive statistics of the aforementioned variables are shown in

Table 8. Descriptive statistics.

Variables	Obs	Mean	Std. Dev.	Min	Max	p1	p99	Skew.	Kurt.
$A^{PCA1}$	251	0	1.353	−5.408	3.188	−3.393	2.859	−0.388	3.797
$A^{PCA2}$	251	0	1.155	−3.866	3.736	−2.487	3.454	0.336	4.042
$A^{PCA3}$	251	0	1.015	−3.505	4.62	−2.102	3.904	0.919	6.316
$A^{PCA4}$	251	0	0.961	−3.232	4.544	−2.201	3.267	0.683	6.118

. The mean value of all the four indices is equal to zero and standard deviation (SD) is in the range of 0.961 and 1.353, indicating higher volatility in $A^{PCA1}$, with the main index explaining 26.2% of variations (see Table 4). $A^{PCA1}$ descriptive statistics show the minimum value is −5.408, maximum is 3.188, p1 is −3.393, p99 is 2.859, skewness is −0.388, and kurtosis is 3.797, showing non-normal and leptokurtic pattern. The second index is $A^{PCA2}$ which explains the 19.1% variations (see Table 4) has SD of 1.155, minimum is −3.866, maximum is 3.736, p1 is −2.487, p99 is 3.454, skewness is 0.336, and kurtosis is 4.042. These statistics show that it has relatively fewer variations as compared to the first index. The third index $A^{PCA3}$ explains 14.7% of variations (see Table 4), has a comparatively lower SD of 1.015, minimum of −3.505, and maximum of 4.62 along with p1 of −2.102, p99 of 3.904, skewness of 0.919, and kurtosis of 6.316, showing leptokurtic curve. The fourth and the last index is $A^{PCA4}$, which explains 13.2% of total variance (see Table 4), has lowest SD of 0.961, minimum of −3.232, maximum of 4.544, p1 of −2.201, p99 of 3.267, skewness of 0.683, and kurtosis of 6.118 showing positively skewed and leptokurtic curve. All these four indices cumulatively explain the total variance of 73.1% (see Table 4).

Table 9. Pairwise correlations.

Variables	$\mathit{K}\mathit{S}\mathit{E}{100}^{\mathit{E}\mathit{M}\mathit{R}}$	${\mathit{A}}^{\mathit{P}\mathit{C}\mathit{A}1}$	${\mathit{A}}^{\mathit{P}\mathit{C}\mathit{A}2}$	${\mathit{A}}^{\mathit{P}\mathit{C}\mathit{A}3}$	${\mathit{A}}^{\mathit{P}\mathit{C}\mathit{A}4}$
$KSE{100}^{EMR}$	1.000
$A^{PCA1}$	0.451 ***	1.000
	(0.000)
$A^{PCA2}$	−0.061	0.000	1.000
	(0.335)	(1.000)
$A^{PCA3}$	−0.415 ***	0.000	0.000	1.000
	(0.000)	(1.000)	(1.000)
$A^{PCA4}$	0.288 ***	0.000	0.000	0.000	1.000
	(0.000)	(1.000)	(1.000)	(1.000)

*** p < 0.01.

shows the correlation of $A^{PCA1}$, $A^{PCA2}$, $A^{PCA3}$, and $A^{PCA4}$ with $KSE{100}^{EMR}$. The results show $A^{PCA1}$ and $A^{PCA4}$ have a positive moderate and significant relation with $KSE{100}^{EMR}$. $A^{PCA2}$ has a negative and insignificant relation, and $A^{PCA3}$ shows negative but significant correlation.

Once the components were analyzed, we regressed each of the attention indices with the $KSE{100}^{M{R}_{t+1}}$ to investigate whether the investors’ attention index developed using PCA influences index returns or not. The GLS regression results are presented in

Table 10. Generalized least square regression results of each attention index.

Variables	Coef.	St. Er.	t-Value	p-Value	R2	F-Test	Prob > F	Transformed DW
Model 1: $KSE{100}^{EM{R}_{t+1}}={\alpha }_0+{\beta }_1{A}^{PCA{1}_t}+{\epsilon }_{t+1}$
$A^{PCA1}$	0.361	0.051	7.06	0.000 ***	0.167	49.85	0.000 ***	2.01
Constant	−0.009	0.076	−0.12	0.904
Model 2: $KSE{100}^{EM{R}_{t+1}}={\alpha }_0+{\beta }_1{A}^{PCA{2}_t}+{\epsilon }_{t+1}$
$A^{PCA2}$	0.089	0.066	1.36	0.176	0.007	1.85	0.176	2.10
Constant	−0.012	0.096	−0.12	0.904
Model 3: $KSE{100}^{EM{R}_{t+1}}={\alpha }_0+{\beta }_1{A}^{PCA{3}_t}+{\epsilon }_{t+1}$
$A^{PCA3}$	−0.632	0.046	−13.69	0.000 ***	0.430	187.33	0.000 ***	2.22
Constant	−0.031	0.120	−0.26	0.796
Model 4: $KSE{100}^{EM{R}_{t+1}}={\alpha }_0+{\beta }_1{A}^{PCA{4}_t}+{\epsilon }_{t+1}$
$A^{PCA4}$	0.320	0.069	4.65	0.000 ***	0.080	21.67	0.000 ***	2.05
Constant	−0.008	0.088	−12.38	0.928

Table 10 presents the results of four GLS regressions examining the impact of $A^{PCA1}$, $A^{DPCA2}$, $A^{PCA3}$, and $A^{PCA4}$ attention indices on $KSE{100}^{EM{R}_{t+1}}$. *** shows significance at the 1% level, respectively. DW denotes Durbin–Watson.

:

Table 10 presents the empirical results examining the impact of each attention index on the KSE 100 Index excess returns while holding all other factors constant. The probability values of F-test of $A^{PCA1}$, $A^{PCA3}$, and $A^{PCA4}$ models are significant at 1% significance level except $A^{PCA2}$ which is insignificant. The $R^2$ of model 1 is 0.167, of model 3 is 0.430, and of model 4 is 0.080, explaining 16.7%, 43%, and 8% of the variations in the $KSE{100}^{EM{R}_{t+1}}$ returns. The low $R^2$ supports results of Ben-Rephael et al. (2017) and J. Chen et al. (2022). In model 1 $A^{PCA1}$ is regressed on $KSE{100}^{EM{R}_{t+1}}$, with ${\beta }_1$ of 0.361 and p-value of 0.000 showing positive and significant impact on $KSE{100}^{EM{R}_{t+1}}$. Among all the four models, model 3 ($A^{PCA3}$ regressed on $KSE{100}^{EM{R}_{t+1}}$) has the better explanatory power along with negative but significant ${\beta }_1$ of −0.632 and p-value of 0.000 and 1% significance level. In model 4, the impact of $A^{PCA4}$ is examined, and the results showed ${\beta }_1$ of 0.320 is positive and significant at 1% significance level, meaning an increase in $A^{PCA4}$ would increase $KSE{100}^{EM{R}_{t+1}}$ market returns. Concisely, models 1 and 4 showed that the more investors’ attention, the better the KSE 100 index performs, along with higher returns. However, model 3 showed the negative impact on the index returns. Furthermore, the results support Prospect Theory (Kahneman & Tversky, 1979), which helps to explain the impact of attention on stock returns. Investors make investment decisions and pay attention to stocks that significantly impact stock returns based on their psychology and available information.

From all seven proxies, the results of $A^{PCA3}$ showed four variables that significantly contribute to the attention index along with an $R^2$ of 43%. It comprises $A^{NK52WH}$, $A^{DNKIHH}$, $A^{ER}$, and $A^{NAVEMF}$ proxies, as shown in Table 6. Thus, other factors that affect the attention index can explain the remaining 57% of the variability in $KSE{100}^{EM{R}_{t+1}}$ returns. As J. Chen et al. (2022) mentioned, the sign of beta coefficients can be positive or negative or inconclusive. This study’s results also support their proposition, as the beta coefficient of $A^{PCA3}$ is negative and of $A^{PCA1}$ and $A^{PCA4}$ are positive, showing both negative and positive significant impacts of attention indices on excess stock returns. Furthermore, the results of $A^{PCA1}$ and $A^{PCA4}$ supports Barber and Odean’s (2008) and Peng and Xiong’s (2006) findings that individual investors are more attentive to attention grabbing stocks and are the net buyers, which simultaneously leads to positive pressure on stock prices but lower future stock returns (J. Chen et al., 2022). In addition, the authors created an index using an orthogonal rotation; the results are provided in Appendix J. Figure 2 displays the KSE 100 market returns and the investors’ attention indices. The results show that the 2008 financial crisis had a significant impact in Pakistan, particularly in 2008 and 2009. All four indices, specifically $A^{PCA1}$, showed a sharp decline, indicating lower investors’ interest. Another downturn was observed during COVID-19, from 2019 to 2020. In 2023, a decline in investors’ interest was observed mainly due to a liquidity crunch in the economy. On the other hand, the highest investors’ interest was observed during 2004, 2006, 2008, 2014, 2016, and 2017 as per $A^{PCA1}$. $A^{PCA3}$ shows upper turning points during 2005, 2006, 2007, 2008, 2016, 2017, 2020, and 2024. $A^{PCA4}$ illustrates highest attention in 2004, 2016, 2017, 2020, and 2024.

5. Discussion

The current findings support the studies by Peng and Xiong (2006), Barber and Odean (2008), and J. Chen et al. (2022) which demonstrate that investor attention is a crucial factor in the dynamics of stock markets. The same is true in the Pakistan stock market. The aggregate attention index used in this study performs well, as it incorporates relevant and recent information by using proxies that help measure investors’ true attention to the Pakistan stock market. The findings show that greater investor attention leads to more active trading in the KSE-100 index and higher returns. However, the negative attention index means that the lower investors’ attention leads to poor index performance. Other factors, including expansionary and contractionary monetary and fiscal policies and different phases of the business cycle, may influence the changes in investors’ attention. The empirical findings also support previous literature and underpinned theories.

Some previous studies used different proxies or factors, such as Hirshleifer et al. (2013), who studied Analyst Coverage, and found that stock returns tend to be high for firms that are efficient in research and development and that have increasing expected earnings per share. Lou (2014) used Advertising Spending as a proxy, and the results showed that an increase in advertising spending is associated with a simultaneous increase in stock prices, followed by a complete return reversal. Chemmanur and Yan (2019) found that advertising in the US stock market attracts investors’ attention to the firm’s stocks and affects future returns. Media coverage was also considered an attention measure (Hillert & Ungeheuer, 2015; Zou et al., 2019). Various researchers have already studied the factors above, but in Pakistan, the major limitation was the lack of data on them. In addition, macroeconomic factors and monetary policy also affect investors’ attention. Therefore, Choi and Choi (2019) examined the US equity market and found a negative, significant relationship between investor attention and abnormal trading volume at the market level. Their study concluded that when investors paid close attention to the stocks, the trading volume of those stocks increased suddenly and unexpectedly that day. Thus, due to short-sell constraints, high investor attention leads to lower future returns through active trading. Aboody et al. (2010) identified the top-performing stocks ranked by prior 12-month price performance for the 1971 through 2005 period and showed that strong past returns tend to attract individual investors’ attention, particularly before earnings announcements.

In this study, attention index proxies affect excess returns. The proximity to the 52- historical high in $A^{PCA3}$ has a negative influence on excess returns. The results support J. Li and Yu (2012), who found that heightened attention to this factor adversely affects future stock returns. Chang et al. (2018) investigated the impact of a historically high ratio on stock index returns of G7 countries. The authors found an inverse correlation between the historical high and the stock returns, attributing this to the significant gap. Our findings also support the results as historical high has a negative relationship with KSE 100 index excess returns. Google Search Volume index (GSVI) was used as a proxy for investor attention, as the authors considered it a reliable indicator (Aouadi et al., 2013; Ding & Hou, 2015; Yao et al., 2017). In this study, the Google Search Volume index shows a positive relationship: the more investors that are interested in a stock, the more attention they give it and search for the company’s technical and fundamental analysis on Google.

The findings are consistent with the literature. J. Chen et al. (2022) also concluded that the index had a negative but significant impact on future stock returns of the NASDAQ market. The negative coefficient is consistent with the literature review on the investors’ attention index. Yuan (2015) found that market-wide events that captured investors’ attention led to a decrease in future stock returns.

From the study, market participants could identify key strategic directions to help them understand market conditions. In addition, appropriate investment decisions could be highly beneficial and confer a competitive advantage in the market. It would help academic scholars in behavioral finance and open a new perspective. Besides this, the researcher would examine the signals that affect the performance of the KSE-100 index, enabling effective portfolio management and risk mitigation.

6. Conclusions, Limitations, Implications, and Recommendations

This paper aimed to illuminate the critical and growing phenomenon of investor attention in the Pakistani stock market by systematically analyzing attention proxies affecting stock market returns. For the first time, $A^{NK52WH}$, $A^{NKIHH}$, $A^{ATV}$, $A^{ER}$, $A^{PR}$, $A^{GSV}$, and $A^{NAVEMF}$. These proxies were used to construct the investor attention index using the PCA approach, which is renowned for its predictive capabilities. The findings reveal that $A^{PCA1}$ and $A^{PCA4}$ have a positive and significant impact on KSE-100 index excess returns. However, $A^{PCA3}$ has a negative but significant impact on the index excess returns. The results are consistent with J. Chen et al. (2022) and T. Chen (2017).

This study highlights the importance of investor attention in Pakistan’s equity market and its substantial role in behavioral finance. Two primary economic sources were identified: First, lower investor attention leads to greater future uncertainty, prompting investors to demand higher returns to compensate for increased risk, thereby driving higher stock returns. Second, heightened investor attention can drive a surge in trading volume, particularly through active trading and short-sell constraints, ultimately leading to lower future returns. Furthermore, this research underscores two significant points: investor attention substantially influences the aggregate stock market, both statistically and economically, and individual attention measures understate the true predictive power of investor attention in Pakistan’s stock market when analyzed using PCA. In conclusion, this study has provided valuable insights into investor attention in Pakistan’s stock market, paving the way for future research to build on these findings and explore new dimensions of behavioral finance.

However, this research encountered several limitations, including fluctuations in advertising expenditures, media coverage, analyst coverage, and other economic and firm-specific variables, which were excluded due to data unavailability in Pakistan. The study period was limited from 1 January 2004 to 31 December 2024, due to the availability of Google Search Volume data from 2004. J. Chen et al. (2022) also used the dataset from January 2004. The analysis was also confined to the KSE-100 index, which was assumed to represent the Pakistani stock market. Additionally, due to time constraints and the COVID-19 pandemic, the research was limited to market-based variables and in-sample analysis, with data analysis conducted solely using STATA. Furthermore, in this study, 30% to 40% of the variation is unexplained, and the KMO of 0.5248 highlights limitations and opportunities for future research. We have examined the impact of Investor’s Attention Index only and used bivariate model. The variance remains unexplained, mainly due to other factors influencing investor sentiment, such as political instability, the application of capital gains taxes, terrorist attacks, the US–Afghanistan war, COVID-19, Sino–US trade war, natural disasters such as earthquakes and floods, and other socio-political issues. We have not accounted for exogenous factors that directly affect investors’ sentiment.

In addition, we have considered bivariate regression, resulting in lower $R^2$. To improve explanatory power, multivariate regression analysis can be conducted, including macroeconomic variables and other proxies, depending on data availability. Furthermore, it would be valuable to analyze the impact on other indices and conduct comparative analyses.

The major implications of this study are the need for greater financial literacy and a better understanding of investment strategies to earn higher returns. Policymakers can develop and implement transparent policies and procedures to increase effective trading in the stock market. Furthermore, they can offer incentives to attract more investors to equity trading, thereby increasing market liquidity, making it more transparent, and motivating both national and international investors to participate. Policymakers can also plan a capital gains tax, which would increase their revenues and not hurt investor sentiment, a crucial factor for sustainable growth. Furthermore, understanding investors’ attention patterns would help reduce the risk of a bubble that could lead to a financial crisis in the future and eliminate speculation. Individual investors can also increase returns by understanding the market sentiments and information. Mutual fund managers and practitioners can design portfolios based on individual investors’ behavior and risk appetite to maximize future returns. Scholars and academicians can conduct further research studies to understand investors’ attention behavior in different market scenarios and contribute to strengthening knowledge of behavioral finance.

In this study, a few recommendations are given to researchers and financial institutions who are highly inspired to conduct research, especially in this domain. The authors can consider economic variables for constructing an investor attention index and investigate their impact on returns. The authors can use firm-specific variables such as dividend-to-price ratio, earnings-to-price ratio, dividend payout ratio, book-to-market ratio, and the like. One of the limitations of this study is that PCA does not capture nonlinear relationships; it is still often preferred by researchers because of its greater transparency and ease of application. However, in future studies, the extension of PCA is Kernel PCA could provide additional information on potential nonlinear dependencies. Furthermore, it is recommended to perform comparative analysis on emerging or frontier markets like Turkey, China, India, and alike, and can explain how Pakistan’s unique institutional context adds new insights. Also, researchers can predict in-sample and out-of-sample stock returns using different forecast models including ARIMA and SARIMA forecasts. The researchers may consider specific industries in which investor attention is analyzed, including health, manufacturing, energy, telecommunications, etc. Moreover, future studies may compare this study with other studies that used different methodologies.