# Subjective Well-Being of Chief Executive Officers and Its Impact on Stock Market Volatility During the COVID-19 Pandemic in Poland: Agent-Based Model Perspective

Marcin Rzeszutek, Jørgen Vitting Andersen, Adam Szyszka, Szymon Talaga

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## To cite this version:

Marcin Rzeszutek, Jørgen Vitting Andersen, Adam Szyszka, Szymon Talaga. Subjective Well-Being of Chief Executive Officers and Its Impact on Stock Market Volatility During the COVID-19 Pandemic in Poland: Agent-Based Model Perspective. Journal of Happiness Studies, 2024, 25 (7), pp.89. 10.1007/s10902-024-00800-4. hal-04723512

HAL Id: hal-04723512

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Submitted on 7 Oct 2024

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# Subjective Well-Being of Chief Executive Officers and Its Impact on Stock Market Volatility During the COVID-19 Pandemic in Poland: Agent-Based Model Perspective

Marcin Rzeszutek¹ Ⓒ · Jorgen Vitting Andersen² · Adam Szyszka³ · Szymon Talaga⁴

Accepted: 7 August 2024
© The Author(s) 2024

## Abstract

This study aimed to connect the behavioral corporate finance perspective (micro level) with complexity theory via agent-based modeling to analyze the impact of selected psychological factors of chief executive officers (CEOs) on stock market volatility (macro level). Specifically, we wanted to explore whether Polish CEOs' subjective well-being (SWB) influenced their managerial decisions during the COVID-19 pandemic and how it might be related to the volatility of stock prices during this critical period in Poland. Our study was based on a survey of Polish CEOs who managed companies listed on the Warsaw Stock Exchange. In particular, 255 CEOs completed the Satisfaction with Life Scale, the Positive and Negative Affect Scale, and a business survey on the impact of the COVID-19 pandemic on company management. Using the results of this survey, we built an agent-based model to investigate how CEOs' decision-making, stemming from their SWB levels, influences the perception of prices by individual traders and, in turn, how it is translated into aggregate stock market volatility. The results indicate the pathways through which the microscopic-level SWB of CEOs influences market price formation at a macroscopic level. The findings obtained from our model may shed new light on the rational expectations theory applied to stock market volatility during the financial crisis.

**Keywords** Subjective well-being · CEO · COVID-19 · Stock market volatility · Rational expectations theory · Agent-based model

## 1 Introduction

Decades of studies on behavioral economics have proven the need to incorporate psychological insights for a better understanding of many research topics in economics (e.g., Akerlof & Schiller, 2009; Kahneman, 2012; Kahneman & Tversky, 1979). One such area deals with the bounded rationality of investors and the existence of so-called stock market anomalies, which has led to the field of behavioral finance (e.g., De Bondt & Thaler, 1987; Thaler, 2005, 2015). Extensive studies conducted by behavioral finance proponents have provided an accurate picture of stock market investors and the market at the aggregate level, countering the classic finance paradigm based on the expected

<footnote>Extended author information available on the last page of the article</footnote>
utility theory (Von Neumann & Morgenstern, 1944), the rational expectations theory (Muth, 1961), and the related efficient market hypothesis (Fama, 1965, 1970). However, until now, behavioral finance has focused predominantly on behavioral biases among stock market investors and their influence on the valuation of stock-market securities (e.g., Baddeley, 2013; Costa et al., 2019). Therefore, some research gaps within the behavioral finance school are yet to be filled. One area is behavioral corporate finance, which concentrates on the bounded rationality of corporate managers and its relationship with the quality of company management (Baker & Wurgler, 2013; Szyszka, 2013). Specifically, some authors found that managers are only human beings, and despite being generally well-educated in economics, they may also display bounded rationality in decision-making, which may negatively impact the process of corporate management (Boulton & Campbell, 2016; Rzeszutek & Szyszka, 2020a, 2020b). Thus, our study was intended to fill this research gap by investigating the role of Polish CEOs' subjective well-being (SWB; Diener et al., 1985, 2016) in the context of their business decisions in management and investment policy during the COVID-19 pandemic.

The COVID-19 pandemic was associated with a sharp economic recession and severe turbulence in financial markets globally (e.g., Li et al., 2021; Sharif et al., 2020). For companies' management, the pandemic has been linked to a high level of uncertainty in business activity and significant challenges due to numerous uncontrollable factors, such as significant supply chain disruptions, inflationary pressures, banks' tightening of lending policies toward consumers and firms, and constant uncertainty and fear over the spread of COVID-19, which resulted in numerous limitations in social activities (e.g., Bairoliya & Imrohoroglu, 2020; Kushwaha et al., 2023). One unique aspect of the COVID-19 crisis that made it particularly stressful for CEOs is that it was based on noneconomic health factors, so the traditional tools of economic stimulation against financial crisis were largely powerless (Sharma et al., 2020). These global stressors may have had an undisputable negative impact on subjective well-being (SWB) and economic decisions among various business entities (Kushwaha et al., 2023), including CEOs (Rzeszutek et al., 2023). Nevertheless, to the best of our knowledge, no studies have examined the potential interconnection between managerial SWB levels regarding company management and stock market volatility during the COVID-19 pandemic. This goal can be reached by applying an agent-based modeling (ABM) framework.

ABM is a relatively new simulation tool that behavioral economics proponents are increasingly using since it may provide the missing association between the micro and macro behaviors of various economic agents (see, e.g., Andersen & Nowak, 2013; Caverzasi & Godin, 2015; LeBaron, 2006; Rekik et al., 2014). Historically, the interest in ABMs describing financial markets has been because they can be used to reproduce the quantitative empirical statistical properties of real markets, such as the autocorrelation of price returns, the autocorrelation of volatility, and the marginal distribution of price changes (Levy et al., 2000; Lux & Marchesi, 1999; Poledna et al., 2023). The central assumption of ABM concerns the existence of heterogeneous, bounded rational agents that mutually interact, the aggregation of which at the micro level may generate unexpected structures at the macro level (LeBaron, 2006; Poledna et al., 2023). This latter phenomenon reflects the core idea hidden in many behavioral models of financial markets (Thaler, 2015) but not empirically tested due to a lack of appropriate data analysis tools. In contrast, ABM enables us to answer this key research question regarding how well behavioral biases hold up under aggregation (Andersen & Nowak, 2013). Nevertheless, the use of ABM in behavioral finance is a nascent research area with several open questions and opportunities for investigation (Malmendier et al., 2023). In

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particular, using ABM in corporate behavioral finance is rare, with only two studies we know (Rzeszutek et al., 2020a, 2020b; 2021).

Finally, behavioral finance is usually poor at providing a convincing psychological
rationale for explaining the irrational behaviors of investors, managers, and other business
entities (Kushwaha et al., 2023; Sahi, 2017). Putting it differently, although they relied
on selective psychological terms (e.g., heuristics), such studies often did so without thor-
oughly analyzing the psychological theories underlying them concerning their application
in economic behavior, which came under criticism of being atheoretical (Kahneman, 2012;
Thaler, 2015). One of the most significant theoretical models of well-being in psychology
is the tripartite model of subjective well-being (SWB; Diener et al., 1985, 2016), accord-
ing to which SWB is defined as people's satisfaction with their lives as a whole or with
particular domains of their lives and consists of two main elements, which are satisfaction
with life, which is the cognitive aspect of SWB (CWB) and affective well-being (AWB)—
that is, positive and negative emotional reactions to people's life. SWB is the more formal
psychological term for "happiness," and often, these terms are used interchangeably (Step-
toe et al., 2015). Dozens of studies have shown that high levels of SWB are related to good
physical health, personal happiness, and optimal psychosocial functioning in various areas
of life, from intimate relationships to the work environment (for reviews, see, e.g., Diener
et al., 2016; Fredrickson, 2013). Numerous authors discussed the issue of long-term SWB
stability in reaction to various life events (see reviews Eid & Diener, 2004; Lucas, 2007). A
plethora of mixed results have been reported, with several studies favoring SWB's tempo-
ral stability (e.g., Lucas & Donnellan, 2007) while others disagree (e.g., Fujita & Diener,
2005). In particular, although SWB is relatively stable over time, it has also been observed
that some critical life events (e.g., divorce, losing one's job, and retirement) can have a
negative impact on SWB. However, they have a powerful and persistent influence on CWB
components compared to the aforementioned AWB elements (Luhman et al., 2012). Some-
times, such critical events can take the form of global and unexpected phenomena for the
majority, or even the entire population, of the world, as was the case with the COVID-19
pandemic, which was linked to a high level of uncertainty in business activity (Bairoliya
& Imrohoroglu, 2020). In our model, we explored whether Polish CEOs' subjective well-
being (SWB) influenced their managerial decisions during the COVID-19 pandemic and
how it might be related to the volatility of stock prices during this critical period in Poland.

## 2 Agent-Based Model Conceptual Framework

In this section, we introduce a theoretical agent-based modeling (ABM) framework to capture potential pathways through which CEOs' subjective well-being (SWB) can influence the individual decision-making of traders simulated in our model. The aim is to explore how such influence can impact financial markets, particularly in markets with both short- and long-term price volatility. In our study, we introduce a novel ABM framework. Its novelty lies in the fact that rational expectations (RE) agents not only use the price in their decision-making to trade but also the uncertainty of the price calculations themselves. We then link price uncertainty to the SWB levels observed in our survey of Polish CEOs. To our knowledge, such an attitude has never been used in ABMs describing financial markets (Andersen & Nowak, 2013; Poledna et al., 2023). We describe price formation in financial markets in terms of two types of different traders, corresponding to (a) speculative agents
who use information about past price moves to predict the next future price movement and (b) agents who use rational expectations to determine the fundamental price of an asset.

## 2.1 Speculative Agents

Speculative agents are introduced via the so-called $-Game ($G; Andersen & Nowak, 2013) [1], in which single agents make their investment decisions based on past price behavior to maximize their profit payoff function. We can imagine those agents as technical investors (chartists) who neglect fundamental information and focus predominantly on signals generated by the prior formation of prices. The basic $G scheme consists of a repeated game in which players choose one out of two alternatives (buy or sell) at each time step based on past price information. The mathematical definition of the model includes N agents who simultaneously trade in a one-asset financial market over a time horizon of T periods. At each t period, where $t < T$, each agent chooses the best-performing strategy at time t—that is, $S_i^*(t)$ among $S_i$ different strategies assigned at the beginning of the game. The "*" notation indicates the "best" strategy, defined below. It is essential to note the time behavior $t$ in the notation $S_i^*(t)$ because as the market dynamics change over time, the best strategy will also change as a function of time, which will, in turn, change the market, leading to critical feedback loops. We denote the action of the $j$ th strategy of agent $i$ at time $t$ for $a_i^j(t)$. $G$ strategies use the last $M$ price directions to predict the next price move. For example, if $M = 3$, and the last $M$ directions are (0,0,1)—meaning that the last price movement was up, and the two price movements before that were down—then a strategy conditioned on that price pattern will predict whether to buy ($a_i^j(t) = 1$) or sell ($a_i^j(t) = -1$). Because there are $2^M$ different price histories for a fixed $M$, a strategy in the $G$ is a table of size $2^M$, recommending whether to buy or sell for each price history. This means that the total number of $G$ strategies goes like $2^{2^M}$, an astronomically large number even for a relatively small $M$, which shows the game's complexity.

We call the payoff function of the $i$ th agents the $j$ th strategy for $G_i^j(t)$. Agents in the $G$ use their strategies to predict and profit from the next price move. For example, if the $j$ th strategy that agent $i$ uses at time $t - 2$, $a_i^j(t - 2)$ is to issue a market buy order, then the market maker will collect that buy order and deliver it to the agent at a price $p(t - 1)$. However, it is only when we know what happens next (did the price increase or decrease from $t - 1$ and $t$?) that we can say whether the action issued of strategy $a_i^j(t - 2)$ was profitable or not. The change in the payoff function of the $i$ th agent's $j$ th strategy is therefore assumed to be.

$$ \Delta G_i^j(t) = a_i^j(t - 2)R(t), \qquad (1) $$

where $R(t) = \ln(p(t)/p(t-1))$ is the return of the market between time $t - 1$ and $t$. In our ABM, the return is assumed to be determined by the action of all the agents $A(t)$ (speculative and RE agents) divided by the liquidity $\lambda$, as follows:

$$ \Delta G_i^j(t) = a_i^j(t - 2) \frac{A(t - 1)}{\lambda}. \qquad (2) $$

In a game with $G$ agents alone, the cumulative action is given by $A(t) = \sum_{i=1}^{N} a_i^*(t)$. The "*" notation indicates that at each time step $t$, each agent uses their best strategy out of the $S$ possible strategies, meaning the strategy with the most significant cumulative return at that time step. So, for an ABM with only $G$ agents,

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$$ \Delta G_i^j(t) = a_i^j(t-2) \sum_{i=1}^{N} a_i^*(t-1). \qquad (3) $$

## 2.2 Rational Expectation Agents

RE agents are rational in trying to assess an asset's fundamental correct price based on the available information set. In other words, we call them fundamental traders. In our ABM, we assume a certain percentage $\rho$ are RE agents, and the remaining $1 - \rho$ are speculative agents. The RE agents are rational in the sense that when each agent tries to estimate the fundamental price $p_F$, they might not find precisely the right price, but averaging over the estimate of all RE agents gives the right price $p_F$, meaning there is no consistent bias in the decision-making of the RE agents. This is in line with Fama's (1965) understanding of the relationship between fundamental value and market price. Market price does not have to be equal to its fundamental value (which, in the real world, with all its ambiguity, is often unknown). However, it is the best approximation of the fundamental value, and there is equal probability at each given moment that a stock is overvalued or undervalued. RE agents are heterogeneous, and their perception of the current market price versus the fundamental value differs.

Specifically, with $Pr_F$, we denote the probability that a given RE agent thinks the current price $p(t)$ is the right fundamental price $p_F$. We assume that $Pr_F$ is given by

$$ Pr_F = e^{-\gamma^2}; \gamma = \frac{p(t) - p_F}{X}. \qquad (4) $$

An agent will therefore think that the current price is not the right fundamental price, with the probability $Pr_{NF}$, as follows:

$$ Pr_{NF} = 1 - Pr_F. \qquad (5) $$

The factor $X$ in the denominator of $\gamma$ is our new contribution to probing how the SWB of CEOs at the microscopic level can influence market price formation at the macroscopic level. Ultimately, prices in a given market are given by the decision-making of traders acting in that market. The traders, however, watch the decision-making of CEOs, which shapes their expectations of the proper fundamental price and, as we now postulate, the uncertainty $X$ of the fundamental price. Suppose there is significant uncertainty (e.g., due to the erratic behavior of some CEOs, such as in the case of Elon Musk and the former Twitter). In that case, it simply means that traders now have a much more extensive range of prices that they believe should be the right fundamental price. Note that when we take the expectation value of the beliefs of traders, we still get the right fundamental price $p_F$ (there is no bias creating erratic prices). This is also the case in our model; however, as will be shown, what is new is that the larger the price range in the expectations of traders, the more significant the volatility of the market. This is not previously described in the traditional rational expectations theory (Poledna et al., 2023; Sargent, 2008).

The actions of RE agents are now determined. If an RE agent determines (with probability $Pr_F$) that the current price $p(t)$ is the right fundamental price $P_F$, that agent takes no action. If not (probability $Pr_{NF}$), the agent thinks that the price is overvalued (case $p(t) > p_F$) and will sell. If the agent thinks it is undervalued (case $p(t) < p_F$), they will instead buy the asset.
## 3 Study Hypotheses

Regarding the above-mentioned theoretical framework and using the results of Rzeszutek et al. (2023) survey on the subjective well-being (SWB) of 255 Polish CEOs during the COVID-19 pandemic concerning corporate management practices in risk management and investment policy, we formulated the following two main hypotheses:

1. The SWB of CEOs, as operationalized by the level of life satisfaction and the presence of positive and negative affect, influence their managerial decisions during the COVID-19 pandemic (micro level). In particular, the higher the levels of SWB, the more optimal the managerial decisions in the areas of risk management and investment policy.

2. CEOs decisions stemming from their SWB levels impact the stock price volatility on the stock market in Poland at an aggregated level (ABM perspective). This influence happens because the rational expectations (RE) agents observed the CEO's decision-making, which in turn influenced their decision about when to buy or sell an asset. In this way, the joint aggregate action of the RE traders and the speculative agents (SE) can influence the volatility of the whole market as a whole (macro level).

Our agent-based model was created based on the Rzeszutek et al. (2023) survey on the SWB of Polish CEOs during the COVID-19 pandemic. Participants were 255 chief executive officers (CEOs) of companies listed on the primary market of Poland's Warsaw Stock Exchange (WSE). Their age range was 26-63 years (M=48.88; SD=8.17). As far as sex distribution, 200 males aged 26-63 (M=49.44; SD=7.67) and 55 females aged 27-60 (M=46.83; SD=9.61) took part in our survey. Most participants declared being in a stable relationship (n=222; 87.1%). Table 1 presents the characteristics of CEOs' companies analyzed in the final model.

The external company conducted the survey online from September 2021 through June 2022, during the so-called fourth and fifth waves of the COVID-19 pandemic. CEOs were additionally motivated to complete the survey by the promise that a fixed charitable donation would be made for each completed questionnaire. The study questionnaires were sent to participants in electronic format via computer-assisted telephone interviews (CATIs) and computer-assisted web interviews (CAWIs) with the help of a specially designed webpage. The survey was created with unique tokens that enabled complete control of the status of the study's implementation and secured against the same respondents who filled out the measures more than once.

## 4 Subjective Well-Being Measures

SWB was evaluated using the Satisfaction with Life Scale (SWLS) (Diener et al., 1985) and the Positive and Negative Affect Schedule (PANAS-X; Watson & Clark, 1988). The first scale comprises five items evaluated on a 7-point scale ranging from 1 (strongly disagree) to 7 (strongly agree); a higher total score indicates greater satisfaction with life. Positive and negative affect (PA/NA) was measured with 20 descriptions of emotions: 10 for PA (e.g., 'proud,' 'excited') and 10 for NA (e.g., 'depressed,' 'stressed'). In this inventory, participants evaluate their general affective states on a 5-point response scale from 1 (not at all) to 5 (firmly).

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<table><caption>**Table 1** Characteristics of CEOs' companies analysed in the final model</caption><thead><tr><th>Company's management board</th><th>n</th><th>%</th><th>Sector</th><th>n</th><th>%</th></tr></thead><tbody><tr><td>Multi-person, but financial decisions are made by one member of the board in financial affairs</td><td>64</td><td>25.1</td><td>Agriculture, forestry and fishing</td><td>9</td><td>3.5</td></tr><tr><td>Multi-person in which financial decisions are taken collegially</td><td>83</td><td>32.5</td><td>Mining and quarrying</td><td>15</td><td>5.9</td></tr><tr><td>Other</td><td>108</td><td>42.4</td><td>Manufacturing</td><td>78</td><td>30.6</td></tr><tr><td>Position held</td><td></td><td></td><td>Electricity, gas, steam and air conditioning supply</td><td>7</td><td>2.7</td></tr><tr><td>President of the management board</td><td>51</td><td>20.0</td><td>Water supply, waste management and remediation activities</td><td>5</td><td>2.0</td></tr><tr><td>Member of the financial management board</td><td>88</td><td>34.5</td><td>Construction</td><td>8</td><td>3.1</td></tr><tr><td>Financial director but without board membership</td><td>105</td><td>41.2</td><td>Wholesale and retail trade</td><td>30</td><td>11.8</td></tr><tr><td>Other</td><td>11</td><td>4.3</td><td>Transportation and storage</td><td>2</td><td>0.8</td></tr><tr><td>Revenues</td><td></td><td></td><td>Accommodation and food service</td><td>4</td><td>1.6</td></tr><tr><td>Below 500 million PLN</td><td>205</td><td>80.4</td><td>Information and communication</td><td>20</td><td>7.8</td></tr><tr><td>500 million–1 billion PLN</td><td>30</td><td>11.8</td><td>Financial and insurance activities</td><td>19</td><td>7.5</td></tr><tr><td>1–5 billion PLN</td><td>14</td><td>5.5</td><td>Real estate activities</td><td>4</td><td>1.6</td></tr><tr><td>Over 5 billion PLN</td><td>6</td><td>2.4</td><td>Professional, scientific and technical activities</td><td>29</td><td>11.4</td></tr><tr><td>Assets</td><td></td><td></td><td>Administrative and support service</td><td>2</td><td>0.8</td></tr><tr><td>Below 500 million PLN</td><td>199</td><td>78.0</td><td>Education</td><td>1</td><td>0.4</td></tr><tr><td>500 million–1 billion PLN</td><td>38</td><td>14.9</td><td>Human health and social work</td><td>5</td><td>2.0</td></tr><tr><td>1–5 billion PLN</td><td>13</td><td>5.1</td><td>Arts, entertainment and recreation</td><td>12</td><td>4.7</td></tr><tr><td>Over 5 billion PLN</td><td>5</td><td>2.0</td><td>Other service activities</td><td>5</td><td>2.0</td></tr></tbody></table>
# 5 Business Survey

To assess the participants' diagnosis of the COVID-19 pandemic's impact on companies and their subsequent selected corporate management practices in risk management and investment policy, we employed a survey adopted from Szyszka's (2013) study on the behavioral aspects of corporate finance. This survey first gathered basic metrical information on company characteristics (see Table 1) and then asked the participants to diagnose the impact of the COVID-19 pandemic on their company and the entire Polish economy and to describe the measures they took in reaction to the crisis.

# 6 Results

Since our study aimed to describe price formation behavior in general financial markets, we will show results for typical parameter values used in the simulations of the $G in the following without trying to address specific market conditions. We tested the robustness of the X and $\rho$ parameters dependence in a range around the parameter values used in our model (Andersen & Nowak, 2013).

Figure 1 shows some of the price trajectories in our ABM, where there is a certain percentage $\rho$ of the RE agent and a percentage $1 - \rho$ of $G$ agents. The price trajectories show examples of the different price behaviors for the specific choice where $\rho=0.75$ percent of the traders are RE traders. The four different plots correspond to the case of a stock market where the uncertainty $X$ perceived by the RE traders increases (from 0.1 to 100). We remind the reader that we hypothesize that the SWB of the CEOs influences their (rational/erratic) decision-making, which is observed by the RE traders influencing, in turn, their uncertainty in determining the proper price of an asset (via Eq. (4)). As can be seen in Fig. 1 the larger the uncertainty $X$ perceived by the RE traders, the larger the price range is being explored by the financial markets. Clear and rational decisions by the CEOs induce little uncertainty for the RE traders regarding the proper price, e.g., $X=0.1$ leads to prices very close to 100. A significant uncertainty of $X=10$ instead leads to prices that sometimes explore the 94 or 106 price level. The red lines in the figure indicate the price range predicted by Eq. (7); see the explanation further below.

As shown in Fig. 1, there appears to be a tendency for a given fixed $\rho$, the more significant the $X$ factor, the larger the volatility of the market. We can now quantify the observations made in Fig. 1 by looking at the quantiles of many market games generated by the ABM. The idea is that by simulating a large number of examples of price formations in financial markets, we thereby probe the range of price values and its dependence on, in particular, the percentage of RE agent, $\rho$, and the uncertainty $X$ that the RE agents perceive in pricing the asset appropriately. Specifically, we initiate $K=10,000$ different ABM market simulations, each done over $T=100,000$ time periods. Figure 2 shows the 99% and 1% quantiles of those simulations for each period $t$, meaning that only 100 runs at that time $t$ would have price behavior above the indicated (gray circles) 99% quantile. Similarly, only 100 runs would go below the 1% quantile (gray circles).

As can be seen from the figure, there is a general tendency that for a given fixed level of uncertainty $X$, increasing the percentage of RE agents decreases the range of price values that the markets can go through. Similarly, for a given fixed percentage $\rho$ of RE agents, the larger the uncertainty $X$ (assumed to result from more erratic behavior of the CEOs), the
<figure><img src="image_6.png" /><figcaption>**Fig. 1** Examples of Price Time Series. Note The four different plots show an illustrative price time series for our ABM. The parameters used were N=1001, T=1000, ρ = 0.75, λ = 500 N, M=10, and S=5. The plot in **a** corresponds to X=0.1, in **b** to X=1, in **c** to X=10, and in **d** to X=100. (Color figure online)</figcaption></figure>

larger the range of price values. These observations can now be qualitatively understood by
the following argument.

The price range of the market can now be calculated by observing that the range of
Speculative price behavior will attain its maximum/minimum at the precise moment when
there are more RE agents taking action compared to the number of $G agents taking a uni-
fied action (all want to buy or sell). Suppose one calls the price range Δ ≡ p<sup>max/min</sup>(t) − p<sub>F</sub>,
with p<sup>max/min</sup> the maximum (minimum) observable price value. In that case, Δ can be
determined by estimating for which value of Δ it is more likely that an RE agent takes
action compared to a $G agent taking (assumed unified) action. The probability that an RE
agent takes action is the compounded probability that an agent is an RE agent times the
probability that the agent takes action. This is the l.h.s. of Eq. (6). Since unified action is
assumed among $G agents, the probability that the action of a $G agent is the opposite of
that of an RE agent is given by the r.h.s. of Eq. (6). After solving Δ, one obtains Eq. (7).

$$
(1 - e^{-\gamma_*^2}) \rho > (1 - \rho); \gamma_* \equiv \frac{\Delta}{X} \qquad (6)
$$

$$
\Delta = \mp \sqrt{\ln\left(2 - \frac{1}{\rho}\right)} \quad X; 0.5 < \rho < 1 \qquad (7)
$$

As shown in Fig. 2, the price range via the quantiles follows Eq. (7) (red lines), thereby
showing how microscopic uncertainty can have macroscopic consequences. It should be
noted that to test our assumptions and framework, we have only studied a case where X and
P<sub>F</sub> are constant, so we have been able to get results in a steady state. According to rational
expectations, new information influences P<sub>F</sub>, which changes over time. In addition, the
new information impacts not only P<sub>F</sub> but also X, so a proper study within the framework
of rational expectations will require a dual study of the time dependence of both variables.
<figure><img src="image_7.png" /><figcaption>**Fig. 2** Impact of the X factor on the price range. *Note* Each plot shows as functions of time the 99% price quantile (upper gray circles), 50% price quantile (middle gray circles), and 1% price quantile (middle gray circles). The parameters used were N=1001, T=10,000, λ = 500 N, M=10, and S=5. Each column corresponds to simulations done with a fixed value of ρ = 0.55, 0.75, and 0.95, while the different rows correspond to different values of X (from top to bottom: X=0.1, 1, 10, and 100). The thin red lines illustrate the solutions to Eq. (7), showing a generally nice agreement between the theoretically predicted price range and the price range found in our ABM simulations. (Color figure online)</figcaption></figure>

Taking everything into account, we received the confirmation of both of the formulated
study hypotheses.

7 Discussion

In this study, we introduced an ABM framework to capture the impact of changes in CEOs'
SWB levels on the stream of information perceived by traders on financial markets. We
claimed that the *uncertainty* about CEOs' decision-making stemming from their SWB
could directly transpose into the uncertainty of traders concerning how to position them-
selves in the markets, leading to long-term price instability. For example, suppose there
is significant uncertainty in the market (e.g., due to the irrational behavior of CEOs stem-
ming from their low SWB). In that case, it means that traders now have a much larger
range of prices that they believe should be the right fundamental price. As in traditional
rational expectations theory (e.g., Sargent, 2008), traders are rational, so when one takes
the average of what traders think should be the right fundamental price, one gets the right

<figure><img src="image_8.png" /></figure>
(averaged over what they expect) fundamental price. This is also the case in our study. However, what is new in our model is that the larger the price range in the expectations of traders, the larger the market volatility. Therefore, the main novelty of our model is related to the observation that agents' rational expectations are shaped not only by new information about fundamental prices but also by new information about the uncertainty of the market and prices, which are the function of CEO's SWB, which also influences fundamental price changes itself. To the best of our knowledge, such a result has never been found before in ABMs describing the volatility of stock markets (e.g., Andersen & Nowak, 2013; Bazzana et al., 2023; Dosi et al., 2020; Poledna et al., 2023).

The results observed from our model may shed new light on the RE theory applied to stock market volatility during the financial crisis. More specifically, despite the undisputable place that RE theory had in the twentieth century for macroeconomic analysis (Muth, 1961; Sargent, 2008), the large body of empirical studies from that century showed its significant limitations. Thus, alternative models emerged based on the critique of RE, such as the sticky information model of Mankiw and Reis (2002), the noisy information model of Sims (2003), the sticky information model with the uncertainty of Branch (2007), and the hybrid sticky-noisy information model of Andrade and Le Bihan (2013). When briefly summarizing the most important lines of criticism of RE theory described in these models, one may underline that agents do not have perfect information but encounter limited information flows and uncertainty, their expectations are primarily heterogeneous and not rational, they do not update their information sets continuously, and they are not able to distinguish proper information from noisy signals. In other words, if agents are characterized by bounded rationality and are heterogeneous and constantly uncertain about new information flows, these characteristics can manifest in their myopic signal processing and low degree of information rigidity, which should be analyzed for expectation formation in the models.

However, all these models were created before the COVID-19 pandemic, which was a rare and completely unexpected natural shock and aroused a very high level of general uncertainty accompanied by high market volatility and substantial negative market returns across the world (e.g., Li et al., 2021; Sharif et al., 2020). More recently, Baker et al. (2020) developed a novel learning model to simulate expectation formulation following a natural disaster shock, which was the case in this pandemic. In particular, they found two interrelated channels through which this kind of natural shock could impact the formation of expectation—namely, the attention effect (the COVID-19 pandemic shock might induce the immediate and synchronized updating of information for inattentive agents) and the uncertainty effect (attentive agents could raise their acquisition of private information to compensate for higher uncertainty after the shock happened). Put differently; those authors observed that agents are systematically heterogeneous in how often they search for and revise new information and that these differences in the frequency of revision of new information can significantly bias the average economic forecast and change its dynamics. This kind of view on agents' heterogeneity may help explain the information rigidity observed in new expectation models, especially the fact that information rigidity declines during recession periods (Coibion & Gorodnichenko, 2012). Baker et al. (2020) claimed that their model warns that, rather than using the degree of information rigidity as a structural parameter in models, it is more reasonable to apply state-dependent expectation formation in the information flow updating process. This is somewhat in line with the findings obtained by our model, where traders must constantly adjust their expectations about fundamental prices regarding the behavior of CEOs, which translates to the volatility of the market at an aggregated level. Nevertheless, what is underlined above and what is the main
novelty of our model is that rational expectations agents are influenced not only by new information on fundamental prices but also by new information about uncertainty in the market, which can drive price changes. This notion should be considered in future ABM processes for catastrophic and unprecedented events in financial markets (An et al., 2021; Bazzana et al., 2023).

# 8 Limitations

Despite the novelties of our research mentioned above, this study is also not free from limitations. First, our model was calibrated to investigate whether Polish CEOs' subjective well-being (SWB) influenced their managerial decisions during the COVID-19 pandemic and how it might be related to the volatility of stock prices during this critical period in Poland. However, reverse causality in this association could also be underlined, i.e., unsuccessful performance in the Polish stock market might also affect the CEO's SWB during that critical period of the pandemic. Secondly, we could not fully control whether the CEO's SWB during the pandemic was shaped purely by personal or social aspects or their mutual interrelationships. This kind of simplification was inevitable in creating the model, but we realize it may preclude obtaining a thorough picture of the CEO's well-being during the pandemic. Finally, because revealing the actual corporate practices of publicly listed companies is very sensitive, we cannot be sure that all the participants' answers in the business survey, on which we also calibrated our model, were truthful, even though we strongly emphasized the anonymity of our survey.

# 9 Conclusion: Policy Implications and Future Research Avenues

Although our model can be interpreted as being specific to the Polish financial market during the COVID-19 pandemic, a more general policy implication of this paper can also be reached. Overall, the decision-making of CEOs can be closely related to their current levels of subjective well-being, which, on the macro level, may influence aggregate stock market volatility, especially during the economic crisis. More specifically, we noted that introducing an agent-based model (ABM), where rational expectation agents react not only to information but also to information uncertainty, opens up new ways of understanding how information spreads across a population with different agendas in their decision-making. Tools like this are in particular demand in the present period, where fake news often flourish worldwide and drive real economic events (Shiller, 2019).

The findings of our study suggest the necessity for more empirical research on the determinants of CEOs' well-being to create more effective methods of psychological counseling in the future, better tailored to this specific occupational group (Pradenas et al., 2021). On the other hand, the results of our study highlight the need for more empirical investigation within the behavioral corporate finance area, which is still a nascent research area with several open questions and opportunities for investigation in the future (Malmendier et al., 2023). Finally, our paper also draws attention to more rigorous measurement and operationalization of psychological constructs while building ABM of financial markets (Andersen & Nowak, 2013; Rzeszutek et al., 2021).
**Acknowledgements** The authors wish to acknowledge the financial support given for the conduct of this research from the National Science Centre, Poland, under grant no. 2020/39/B/HS4/00032.

**Funding** Narodowe Centrum Nauki, 2020/39/B/HS4/00032, Adam Szyszka.

**Declarations**

**Conflict of interest** The Authors declare no conflict of interest.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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## Authors and Affiliations

Marcin Rzeszutek<fnref n="1" /> Ⓒ · Jorgen Vitting Andersen<fnref n="2" /> · Adam Szyszka<fnref n="3" /> · Szymon Talaga<fnref n="4" />

<figure><img src="image_9.png" /></figure>

Marcin Rzeszutek

marcin.rzeszutek@psych.uw.edu.pl

Jorgen Vitting Andersen

jorgen-vitting.andersen@univ-paris1.fr

Adam Szyszka

aszysz1@sgh.waw.pl

Szymon Talaga

stalaga@uw.edu.pl

<footnote n="1">¹ Faculty of Psychology, University of Warsaw, Stawki 5/7, 00-183 Warsaw, Poland</footnote>

<footnote n="2">² Centre National de Recherche Scientifique (CNRS), Centre d’Économie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Maison des Sciences Économiques, 106-112 Boulevard de l’Hôpital, 75647 Paris, Cedex 13, France</footnote>

<footnote n="3">³ Warsaw School of Economics, Collegium of World Economy, Warsaw, Poland</footnote>

<footnote n="4">⁴ Robert Zajonc Institute for Social Studies, University of Warsaw, Warsaw, Poland</footnote>