Literature review

Behavioral finance has emerged as a significant field of study that challenges traditional finance theories by incorporating insights from psychology and human behavior into the understanding of financial markets. The exploration of behavioral finance, particularly within the context of market anomalies in the US stock market, has led to valuable insights that shed light on why financial markets often exhibit irrational behavior, unexpected price movements and deviations from traditional finance assumptions.

One of the fundamental aspects of behavioral finance is the recognition of behavioral biases that influence investor decisions. Behavioral biases, such as loss aversion, overconfidence and herding behavior, play a substantial role in shaping market anomalies. Research by Merkle (Reference Merkle2020) and Greene (Reference Greene2011) highlights the impact of loss aversion on investor decision-making, where individuals tend to fear losses more than they value equivalent gains. Loss aversion can lead to risk-averse behavior during periods of market volatility, contributing to market anomalies.

Overconfidence, as another predominant cognitive bias, may significantly affect investor decisions and contribute to market anomalies. Research in this area, such as that conducted by Kansal and Singh (Reference Kansal and Singh2018), has demonstrated that individuals often overestimate their own knowledge and abilities. In the context of financial markets, overconfident investors may trade excessively, believing they possess superior information or skills. This overtrading can result in increased transaction costs and suboptimal portfolio performance, thereby contributing to anomalies like the disposition effect, where investors tend to hold on to losing investments for too long in the hope of a rebound.

Another remarkable behavioral bias is herding behavior, which refers to the tendency of investors to follow the crowd rather than making independent decisions. Herding can exacerbate market anomalies by amplifying trends and magnifying market movements. When a large number of investors herd into a particular asset class or investment strategy, it can lead to price bubbles or crashes that deviate significantly from fundamentals. Empirical studies, such as that by Tan et al. (Reference Tan, Chiang, Mason and Nelling2008) and Spyrou (Reference Spyrou2013), have provided insights into the impact of herding behavior on market dynamics, highlighting how this behavioral bias can contribute to market inefficiencies and anomalies.

Investor sentiment and its influence on market anomalies provide another layer of complexity to the field of behavioral finance. Schneider (Reference Schneider2014) highlights the idea that a multitude of factors, including weather, mood and external events, can significantly impact investor sentiment, consequently affecting market behavior. This dynamic relationship between sentiment and market anomalies is multifaceted.

High levels of consumer confidence, as explored by Gormus and Gunes (Reference Gormus and Gunes2010), often lead to a sense of optimism among investors. When consumers are confident about the economy and their financial well-being, they are more likely to invest in the stock market. This influx of positive sentiment can have a cascading effect on the market, driving up prices and contributing to bullish market anomalies (Sruthi and Shijin, Reference Sruthi and Shijin2017). In such situations, investors may become less risk-averse, leading to increased trading activity and potentially the emergence of bubbles in certain asset classes.

Conversely, low consumer confidence can trigger risk aversion and a shift away from equities (Chen, Reference Chen2011). During times of economic uncertainty or external shocks, such as financial crises or geopolitical events, investors tend to become more cautious. They may liquidate their equity holdings in favor of safer assets like bonds or cash, leading to bearish market anomalies. The collective sentiment of fear and pessimism can create a self-fulfilling foresight, where market participants expect downturns, and these expectations are obvious in actual market declines.

Behavioral finance has illuminated a fascinating array of specific market anomalies within the US stock market, each shedding light on the complicated interaction between investor behavior and market dynamics. The momentum effect, as explained by Dhankar and Maheshwari in 2016, reveals how psychological biases can drive market anomalies. This phenomenon contradicts the notion of strict market efficiency theorized by the EMH. It shows that stocks that have performed well in the recent past tend to continue performing well, often challenging rational expectations. The persistence of this anomaly implies how investor sentiment and the propensity to generalize recent trends can overpower fundamental valuation metrics.

Conversely, the value effect, precisely explored by Sharma and Kumar in 2019, challenges traditional market wisdom. This anomaly reveals that stocks with lower price-to-earnings (P/E) ratios can outperform those with higher P/E ratios, contrary to the EMH's assumption that stock prices fully reflect all available information. Investors’ tendency to undervalue stocks with lower P/E ratios due to their perceptions or behavioral biases can trigger market anomalies where these ‘value’ stocks outperform their ‘growth’ counterparts.

The small-cap effect, discussed by Latif et al. (Reference Latif, Arshad, Fatima and Farooq2011), adds another layer to the market anomalies. It demonstrates how smaller companies can outperform their larger counterparts, defying traditional risk-return expectations. This anomaly is often attributed to investor preferences and behavioral biases, where investors may overlook smaller stocks due to their perceived risk, creating opportunities for intelligent investors who recognize this bias.

Several studies, including those by Chang et al. (Reference Chang, Hsieh and McAleer2016) and Wang (Reference Wang2019), have revealed a negative correlation between market volatility and stock market performance. This correlation implies that as market volatility rises, investors tend to become more risk-averse. Such heightened risk aversion can lead to erratic market behavior, potentially amplifying market anomalies. Investors may become overly cautious, leading to under-pricing or overpricing of assets, depending on the direction of volatility. This insight highlights how fluctuations in investor sentiment, triggered by increased volatility, can contribute to the emergence of market anomalies.

CDS, as examined by Bystrom (Reference Bystrom2005) and Mateev and Marinova (Reference Mateev and Marinova2019), offers another intriguing perspective on the interaction between financial derivatives and market anomalies. It is essentially an insurance contract against the default of a particular debt instrument, such as a bond. These instruments are associated with risk aversion and loss aversion due to their nature. When investors purchase CDS, they are essentially betting on the possibility of a default event, indicating a preference for safety over risk-taking. This risk-averse behavior is intertwined with loss aversion, as investors are more concerned about the potential loss from default than the gains from the insurance premium. As a result, there exists a negative relationship between the prevalence of CDS trading and the performance of the stock market. When investors become more inclined to use CDS, it often signifies a heightened sense of caution and fear, potentially contributing to market anomalies as risk perception intensifies.

Figure 1 shows the conceptual framework of this study.

Figure 1. The conceptual framework. Source: Isik Akin and Meryem Akin.

Figure 2. Trend of variables over a 10-year period. Source: Isik Akin and Meryem Akin.

Methodology

This study aimed to investigate the impact of behavioral finance on the performance of the S&P 500. To achieve this, several financial indicators, including the real interest rate (RR), consumer confidence index (CCI), volatility index (VIX) and CDS, were employed as independent variables, with the S&P 500 serving as the dependent variable. The effects of RR, CCI, VIX and CDS on the S&P 500 were analyzed using time-series analysis, specifically the least squares method, within the context of behavioral bias. Data spanning a period of 10 years (2013–2023) for each of the variables were collected from sources such as investing.com, the Statista Database and the OECD Database.

Table 1 presents the variable name, symbol and their source in detail.

Table 1. Variable information

Source: Isik Akin and Meryem Akin.

Least squares method

The least squares method aims to find the best-fitting linear relationship between a dependent variable Y and one or more independent variables X ₁, X ₂, … , X _k. Let's consider the case of simple linear regression, where there is only one independent variable X. The goal is to find the line Y = β ₀ + β ₁X that minimizes the sum of the squared differences between the observed values of Y and the values predicted by the model.

The linear regression model is represented as follows (Miller, Reference Miller2006):

$$Y = \beta _0 + \beta _1X + \varepsilon $$

where Y is the observed dependent variable, X is the observed independent variable, β ₀ is the intercept, representing the value of Y when X is zero, β ₁ is the slope, representing the change in Y for a one-unit change in X, ε is the error term, representing the random variability in Y not explained by the model.

Minimization of squared residuals

The least squares method seeks to minimize the sum of the squared residuals (the vertical distances between each observed Y and the corresponding predicted value):

$${\rm Minimise}\sum\nolimits_{i = 1}^n {\varepsilon _i^2 } $$

where n is the number of data points, $\varepsilon _i$ is the difference between the observed Y _i and the predicted Y _i for the i-th data point:

$$\varepsilon _i = Y_i-\beta \;_1X_i$$

Least squares estimators

To find the best-fitting line, we differentiate the sum of squared residuals with respect to the parameters β ₀ and β ₁ and set the derivatives equal to zero. This leads to the following equations:

$$\displaystyle{\partial \over {\partial \beta _0}}\sum\nolimits_{i = 1}^n {\varepsilon _i^2 = 0} $$

$$\displaystyle{\partial \over {\partial \beta _1}}\sum\nolimits_{i = 1}^n {\varepsilon _i^2 = 0} $$

Solving these equations results in the least squares estimators:

$$\widehat{{\beta _1}} = \displaystyle{{\mathop \sum \nolimits_{i = 1}^n ( X_i-\overline {X) } ( Y_i-\overline {Y) } } \over {\mathop \sum \nolimits_{i = 1}^n ( X_i-{\overline {X) } }^2}}$$

$$\widehat{{\beta _0}} = \bar{Y}-\widehat{{\beta _1}}\bar{X}$$

where $\bar{X}$ and $\bar{Y}$ are the sample means of X and Y, respectively.

These estimators $\widehat{{\beta _0}}$ and $\widehat{{\beta _1}}$ are unbiased and have minimum variance under certain assumptions about the errors, such as independence, constant variance (homoscedasticity) and normality.

Findings

In this section, the findings of the time-series analysis are presented.

The S&P 500 exhibits a generally upward trend. It started at around 1,200 in the year 2013, it steadily increased and reached a value of around 4,800 in the year 2023. This indicates a positive performance of the stock market over the given period. In essence, the overall value of the stocks in the index has increased which reflects the growth and profitability of the companies represented in the index.

The RR fluctuates between −0.4% and 2.0% over the years. It began at around −0.5% in the year 2013 and remained relatively stable until 2020. It stayed negative from the beginning of 2020 to the beginning of 2022. This indicates that low and negative interest rates provided a favorable borrowing and investment climate as it allowed businesses and individuals to access credit at relatively low costs. It encouraged productive economic activity until the beginning of the year 2022. However, the RR started to increase from the beginning of the year 2022 to 2.06%. This conversely discourages borrowing and investment as the cost of borrowing becomes more expensive.

CCI exhibits a gradual increase until 2022. It exceeded 100 basis points after 2014 which means that consumers were more optimistic about economic conditions and their financial prospects. This shows that consumers were more likely to make major purchases, invest and contribute to overall economic activity during this period. However, CCI decreased to under 100 basis points by the year 2022. It typically indicates a decline in consumer confidence. This could be influenced by various factors such as economic challenges, rising inflation, job market concerns or geopolitical uncertainties. A drop in consumer confidence can lead to decreased consumer spending and a more cautious approach to personal finances.

The VIX shows a gradual increase over the years. When the VIX increases, it suggests that investors are becoming more uncertain or anxious about future market movements. It started around 15 in the year 2013, it increased and reached a value of around 53 in the year 2022. This substantial increase in the VIX indicates that market participants perceived increasing levels of uncertainty and potential for price fluctuations during this period. The VIX returned to 15 in the year 2023. This suggests a decrease in market volatility and potentially a calmer market environment.

CDS shows a decreasing trend until 2022. It began at around 38 in the year 2013, it gradually decreased to 9.95. This decline implied a diminishing perception of credit risk and increased confidence in borrowers’ creditworthiness during that period. It started to rise after 2022 and reached 70 in the year 2023. This indicates a growing level of credit risk in the market. The increasing CDS suggests that investors are becoming more concerned about the creditworthiness of borrowers and are demanding higher compensation for taking on credit risk.

Table 2 presents the descriptive statistics for the variables.

Table 2. Descriptive statistics

Source: Isik Akin and Meryem Akin.

The S&P 500 has an average level of around 2838.72, but a slightly lower median at 2688.85 implies potential right-skewness. It spreads a wide range from 1514.68 to 4766.18 which indicates significant volatility. Positive skewness (0.54) and moderate leptokurtosis (kurtosis 2.03) suggest a right-skewed distribution with heavier tails.

RR shows a positive real return with a mean of about 0.5834. The median of 0.5450 implies potential right-skewness, while a standard deviation of 0.5042 indicates moderate variability. Positive skewness (0.4142) and moderate leptokurtosis (kurtosis 3.1854) further suggest a right-skewed distribution with moderately heavy tails.

CCI has an average level of approximately 99.84, with a median of about 100.46, indicating potential left-skewness. It exhibits limited variability within a narrow range of 96.13 to 101.64. Negative skewness (−0.77) and moderate leptokurtosis (kurtosis 2.49) suggest a left-skewed distribution with moderately heavy tails.

VIX represents an average market volatility level (mean 18.21). The slightly lower median (16.25) suggests potential right-skewness. It spreads a wide range from 9.51 to 53.54 which reveals significant volatility. Positive skewness (1.87) and high leptokurtosis (kurtosis 7.99) indicate a right-skewed distribution with heavy tails and significant fluctuations.

CDS indicates an average credit default risk level (mean 20.69). The median (18.70) suggests potential right-skewness, and it spreads from 9.95 to 70.42. This reflects significant credit risk volatility. Positive skewness (2.52) and high leptokurtosis (kurtosis 14.38) imply a right-skewed distribution with extremely heavy tails and extreme fluctuations.

The correlation matrix presented in Table 3 reveals the relationships among the S&P 500, RR, CCI, VIX and CDS. First of all, there is a strong positive correlation (0.581) between the S&P 500 and CCI (Gormus and Gunes, Reference Gormus and Gunes2010). It highlights the significance of consumer sentiment in influencing stock market movements. When consumers are optimistic about economic conditions and their financial prospects, it tends to move with an upward trend in the S&P 500, reflecting increased confidence in investing and spending (Nofsinger, Reference Nofsinger2005; Hadi and Ahmad, Reference Hadi and Ahmad2021). Conversely, the moderate negative correlation (−0.365) between the S&P 500 and VIX points to the impact of market volatility on stock prices (Wang, Reference Wang2019). As the VIX, an indicator of market uncertainty, rises, the S&P 500 tends to dip, highlighting investors’ heightened risk aversion during turbulent periods (Chang et al., Reference Chang, Hsieh and McAleer2016). Regarding RR, a weak negative correlation (−0.069) suggests a nuanced relationship between real interest rates and the S&P 500 (Amarasinghe, Reference Amarasinghse2015). However, the correlation is not statistically significant. Lastly, the moderately strong negative correlation (−0.114) between the S&P 500 and CDS indicates that credit default risk plays a role in stock market movements (Bystrom, Reference Bystrom2005). This correlation is not statistically significant.

Table 3. Pearson correlation matrix

^a Correlation is significant at the 0.01 level (two-tailed).

^b Correlation is significant at the 0.05 level (two-tailed).

Source: Isik Akin and Meryem Akin.

At its original level, the S&P 500 demonstrates a non-stationary behavior with a t-statistic of −0.375495 and a high probability of 0.9087. However, when differenced once (transformed into first differences), the t-statistic significantly drops to −13.5816, and the probability becomes 0.0000, strongly indicating stationarity. RR is non-stationary with a t-statistic of −1.612079 and a probability of 0.4734 at level. Yet, when differenced once, the t-statistic becomes −13.94129 with a probability of 0.0000, providing strong evidence of stationarity. The original CCI data are non-stationary with a t-statistic of −1.107561 and a probability of 0.7114. However, when transformed into first differences, the t-statistic becomes −5.289103 with a probability of 0.0000, indicating stationarity. The VIX data, in its original form, show strong evidence of stationarity with a t-statistic of −4.859170 and a very low probability of 0.0001. CDS is stationary with a t-statistic of −3.843517 and a probability of 0.0112 at the level. Thus, no differencing is required for VIX and CDS.

The F-statistic tests the overall significance of the regression model. In this case, the F-statistic is 28.91, with an extremely low p-value (Prob(F-statistic) = 0.0000). This indicates that the model is statistically significant and that at least one of the independent variables has a significant impact on the S&P 500.

The coefficient for RR (−1) (−403.8172) indicates that a one-unit increase in the lagged real interest rate is associated with an approximate 403-point decrease in the S&P 500, holding other variables constant. The negative coefficient suggests a negative relationship between RR and the S&P 500. This finding is supported by Alam and Uddin (Reference Alam and Uddin2009) and Amarasinghe (Reference Amarasinghse2015).

The coefficient for CCI (−1) (361.6019) indicates that a one-unit increase in the lagged CCI is associated with an approximate 361-point increase in the S&P 500, holding other variables constant. The positive coefficient implies a positive relationship between CCI and the S&P 500. It is similar findings with Gormus and Gunes (Reference Gormus and Gunes2010) and Hadi and Ahmad (Reference Hadi and Ahmad2021).

The coefficient for VIX (−25.75667) suggests that a one-unit increase in the VIX is associated with an approximate 25.76-point decline in the S&P 500, assuming other variables remain constant. This negative relationship implies that as market volatility increases, the S&P 500 tends to decline. This result is supported by Chang et al. (Reference Chang, Hsieh and McAleer2016) and Wang (Reference Wang2019).

The coefficient for CDS (−44.62010) implies that a one-unit increase in the CDS is associated with an approximate 44.62-point decrease in the S&P 500, controlling for other variables. This negative coefficient suggests an inverse relationship between CDS and the S&P 500, indicating that higher credit default risk is associated with lower stock market values. This is supported by Bystrom (Reference Bystrom2005) and Mateev and Marinova (Reference Mateev and Marinova2019).

The Jarque–Bera test is a statistical test used to assess the normality of the residuals or errors in a regression model. It tests whether the distribution of the residuals follows a normal (Gaussian) distribution, which is one of the key assumptions of linear regression (Thadewald and Buning, Reference Thadewald and Buning2007). In Table 6, the Jarque–Bera test statistic is 1.847818, and the associated probability (p-value) is 0.396964. There is no strong evidence to conclude that the residuals in the regression model significantly deviate from a normal distribution. This suggests that the normality assumption for the residuals appears to be reasonably met, which is a positive aspect of the model's statistical validity.

Table 4. Augmented Dickey–Fuller test statistics at level and first differences

Source: Isik Akin and Meryem Akin.

Table 5. The results of the least squares regression model using the Gauss–Newton/Marquardt steps method

Source: Isik Akin and Meryem Akin.

Table 6. Normality test

Source: Isik Akin and Meryem Akin.

Table 7. Breusch–Godfrey serial correlation LM test

Source: Isik Akin and Meryem Akin.

Table 8. Heteroskedasticity test – ARCH

Source: Isik Akin and Meryem Akin.

The F-statistic is 0.692, and its associated probability (Prob) is 0.670. There is no significant serial correlation in the residuals of the regression model. Both the F-statistic and the associated p-value provide strong evidence against the presence of serial correlation.

The F-statistic for the ARCH test is 4.579, and its associated probability (Prob) is 0.175. The ARCH Heteroskedasticity Test results indicate no strong evidence of heteroskedasticity in the regression model's residuals. This suggests that the assumption of constant variance of residuals is reasonable for the analysis.