Investigating the determinants of herd behavior: An application of the Hwang-Salmon method to the Turkish banking sector

Ay, Bayram Erkin; Yağcilar, Gamze Göçmen Article Investigating the determinants of herd behavior: An application of the Hwang-Salmon method to the Turkish banking sector Ekonomika Provided in Cooperation with: Vilnius University Press Suggested Citation: Ay, Bayram Erkin; Yağcilar, Gamze Göçmen (2024) : Investigating the determinants of herd behavior: An application of the Hwang-Salmon method to the Turkish banking sector, Ekonomika, ISSN 2424-6166, Vilnius University Press, Vilnius, Vol. 103, Iss. 3, pp. 40-56, https://doi.org/10.15388/Ekon.2024.103.3.3 This Version is available at: https://hdl.handle.net/10419/323155 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ 40 Ekonomika ISSN 1392-1258 eISSN 2424-6166 2024, vol. 103(3), pp. 40–56 DOI: https://doi.org/10.15388/Ekon.2024.103.3.3 Investigating the Determinants of Herd Behavior: an Application of the Hwang–Salmon Method to the Turkish Banking Sector Bayram Erkin Ay Isparta University of Applied Sciences, Türkiye Email: [email protected] ORCID: https://orcid.org/0009-0002-4089-6254 Gamze Göçmen Yağcilar Süleyman Demirel University, Türkiye Email: [email protected] ORCID: https://orcid.org/0000-0002-5009-4696 Abstract. Efficient financial markets are important for pricing assets at fair value. In an efficient market, investors are rational in the face of fast and accurate information flow, evaluate the information correctly, and reflect it in their pricing decisions. However, particularly in times of crisis and uncertainty, it is observed that some market participants hesitate in their decision-making processes, imitate the behavior of other individuals whom they consider reputable because they cannot rely on their own knowledge and experience, and try to follow the trend. This tendency, which is called herd behavior, destroys market efficiency and prevents correct price formation. Therefore, it is important to identify its determinants. The purpose of the study is analyzing the precense and determinants of herding behavior in the Turkish banking sector during the period 17.10.2017–10.11.2023. Herd behavior is identified using the Hwang–Salmon method, and logistic regression analysis and the Kruskal–Wallis test are applied to identify its determinants. The findings reveal that herding behavior is associated with the rise in risks and returns as well as the fall in interest rates and exchange rates. Keywords: Behavioral finance, Herd behavior, Hwang–Salmon Method, Logistic regression, Banking sector. Introduction Financial decisions and market dynamics are important for economic systems and businesses to achieve sustainable success. In particular, financial decisions are highly strategic processes that require individuals and organizations to make the right investments, allocate their resources effectively and manage their risks consciously, and depend on an understanding of market dynamics. Although investors sometimes act behaviorally in Received: 04/04/2024. Revised: 13/06/2024. Accepted: 07/07/2024 Copyright © 2024 Bayram Erkin Ay, Gamze Göçmen Yağcilar. Published by Vilnius University Press This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Contents lists available at Vilnius University Press Bayram Erkin Ay, Gamze Göçmen Yağcilar. Investigating the Determinants of Herd Behavior 41 accordance with these dynamics, sometimes they may change their behavior, decisions and market perceptions. Rational models such as the Expected Utility Theory or the Efficient Markets Hypothesis fail to explain these perceptions. Behavioral models have been developed to compensate for this gap (Karan, 2013). With their Prospect Theory, Kahneman and Tversky (1979) argued that investors can not be rational all the time and sometimes decide unreasonably in risky situations. According to the Behavioral Finance view, which gained strength in the finance and economics perspective following the Expectation Theory, it states that investors may exhibit behaviors different from the rationality defined in traditional finance models, that these irrational behaviors may lead to erroneous formation of prices in the market and that the arbitrage mechanism may not be able to prevent this situation (Karan, 2022). Price anomalies in the markets cause financial asset prices to deviate from their true value and thus call traditional theories into question. Price anomalies also bring to the forefront the main actor of financial markets, the financial investor and financial investor behavior. This is explained by some cognitive biases in behavioral finance. In the study on Investor Psychology and Asset Pricing by David Hirshleifer (2001), four main groupings were identified. These groups are named as Self-Delusion, Shortcut Inference, Emotions and Self-Control, and Social Interaction. Cognitive biases that occur in the form of errors and biases are shown in Hirshleifer’s (2001) grouping and subheadings in Figure 1 (Başarır, 2021). Figure 1. Grouping of cognitive biases. Source: Inspired by Başarır (2021) Prepared. Social interaction means that individuals learn and are influenced by each other through mutual interaction/communication. Before making a decision about their investment, investors discuss these decisions and the opinions they receive from their environment affect their decisions (Nofsinger, 2017). Social interaction is examined under two groups: ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, vol. 103(3) 42 social contagion and herding behavior. There are many studies in the literature that investigate herd behavior with different methods. However, studies on the determinants of herd behavior are relatively limited. Revealing the factors that cause this behavior will contribute to managing the expectations of investors, portfolio managers and policy makers. In this context, the study aims to investigate the presence and determinants of herding behavior for banking stocks, which have an important place in BIST 100, the most frequently followed index of Borsa Istanbul. For this purpose in section 1, the concept of herd behavior is explained. In section 2, related literature is presented. Information about the methodology and data of the research is given in section 3. Findings are presented in section 4. The last section includes concluding remarks and discussions. 1. Conceptual Framework: Herd Behavior While the concept of herding appears in many fields such as neurology, sociology and zoology, in the fields of economics and finance, it is defined as actors generally imitating each other and shaping their decisions by determining the behavior of others as a basis (Spyrou, 2013). According to Raafat et al. (2009), herding behavior is defined as the alignment of ideas or behaviors of individuals within an environment through local interaction without central coordination, while according to Bikhchandani and Sharma (2000), herding behavior in financial markets is defined as a phenomenon in which investors shape their investments with the intention of mimicking the actions of other investors (Demirer and Kutan, 2006). The formation of a “herd” is triggered when an investor takes an action that he/she would not have taken if he/she had not known about the other investors. When the herd is formed and its presence is felt in the market, it is observed that investor behavior does not include new information about market fundamentals and the social learning process is interrupted (Decamps and Lovo, 2002). Measuring herd behavior is important because herding can lead to market-wide mispricing and trend shaping that alters individuals’ perception of the economic fundamentals of assets (Baddeley, 2013). Due to its importance, various measurement methods have been developed. Hachicha et al. (2007) stated that studies on herd behavior are divided into two categories. In their study, the LSV measure developed by Lakonishok, Shleifer and Vishny (1992) and the PCM measure of Wermers (1994) constitute the first category, which requires detailed information about investors’ trading activities and changes in their portfolios. The second category considers the phenomenon of herding behavior as the collective trading behavior of individuals in order to track the market and uses cross-sectional price movements for measurement. Christie and Huang (1995) (CSSD), Chang, Cheng, and Khorana (2000) (CSAD) and Hwang and Salmon (2001, 2004) are the contributors to this category of measurement (Hachicha et al., 2007). The LSV measurement method defines herd behavior as the imitation of simultaneous buying or selling by a group of fund managers. It uses subsets to measure specific characteristics or behaviors (Lakonishok et al., 1992) and therefore requires specialized information (Hwang and Salmon, 2004). The CH herd behavior measurement method proposed by Christie and Huang (1995) examines whether individual returns concentrate around the market in periods Bayram Erkin Ay, Gamze Göçmen Yağcilar. Investigating the Determinants of Herd Behavior 43 of market complexity and stress. This measurement method was later expanded by Chang, Cheng, and Khorana (2000). Using a nonlinear regression specification, they measured the relationship between the level of stock return distribution and the overall market return using the cross-sectional absolute deviation of returns (CSAD). They argue that the tendency of market investors to conform to the general market sentiment during periods of high price movements is sufficient to transform a linear relationship into a nonlinear one. Additionally, the importance of macroeconomic information for emerging markets is emphasized (Chang et al., 2000). Hwang and Salmon (2001) developed a method to measure herd behavior by considering linear factor models and observed conditions in fundamental movements. Similar to the CH method in terms of utilizing information present in the horizontal cross-section movements of the market, it differs in focusing on horizontal cross-sectional changes in factor sensitivities instead of using return values themselves. It utilizes the cross-sectional standard deviation of loadings in the linear factor model of individual assets and is calculated with the help of individual betas. The method automatically takes into account the effects of changes in the time series volatility included in the cross-sectional variance. It is also argued that herd behavior is a matter of degree, inseparable from any market taken into consideration, and therefore, rather than the presence or absence of herd behavior, it is advocated to use expressions like less herd behavior or more herd behavior. Furthermore, this method allows for a distinction between intentional and false herd behavior and focuses on intentional herd behavior (Caparelli et al., 2004). Investors can be driven towards the same point by informative content about the market, economic expectations, and investor sensitivities. This indicates that investors can also act based on their economic rationales. For example, traditional/nontraditional monetary policies can be given (Krokida et al., 2020). When individuals aim to maximize returns and avoid risks in their investments (Kuzu and Çelik, 2020), it is possible for them to follow preceding signals. In this case, even though an investor may perceive it as more rational to exhibit different behavior based on their unique information, the probability of conforming to the behavior of the majority with the support of previous signals is high (Banerjee, 1992). The foregoing discussion demonstrates the importance of identifying herd behavior in understanding investor behavior. Therefore, explaining the determinants of herd behavior as well as identifying herd behavior may help to clarify market dynamics. 2. Literature Review The issue of herd behavior is among the topics that have been widely covered in the literature. It is possible to classify these studies according to their measurement methods. Although LSV, PCM, CH, CCK, Hwang and Salmon (2004) (hereafter HS-2004) measurement methods are encountered (Setyawan and Ramli, 2016; Pochea et al., 2017; Medhioub and Chaffai, 2019; Qasim et al., 2019; Choi and Yoon, 2020; Ferrouhi, 2021; Li et al., 2023; Hong et al., 2024), this study is limited within the scope of the method to be used here and the studies using the HS-2004 measurement method that are included in the literature. The studies using the HS-2004 herd behavior measurement method (relying ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, vol. 103(3) 44 on stock beta coefficients) started with the study conducted by Hwang and Salmon in 2001 resulting that more herd behavior is observed in developing countries (South Korea) than in developed countries (USA, UK). In the next study in 2004, Hwang and Salmon stated that they found herding behavior when the market rises or falls, and that they found significant movements and persistence, independent of market conditions. Caparelli et al. (2004) found the existence of herding behavior in capital markets of Italy. Kallinterakis (2006) tests herding behavior in stock markets of 8 countries. Results on the impact of specific regulatory restrictions on market-wide herding behavior are presented. Kallinterakis et al. (2007) detected herding behavior in MERVAL index during and after the Argentine financial crisis. Wang (2008) observed higher level of herding behavior in developing countries then developed countries. Demirer et al. (2010), another study on emerging economies, observed herding behavior. Amirat and Bouri (2009) and Hachicha et al. (2010) investigated herding behavior in Toronto stock market and in both studies herding behavior is observed. Altay (2008) examined herding behavior in the Istanbul Stock Exchange (ISE). As a result of the study, although herd behavior was not observed in some periods, it was stated that the general tendency was in favor of herd behavior. Another study on ISE by Medetoğlu and Saldanlı (2019) found herding behavior features. Doğukanlı and Ergün (2015) investigated herding behavior on BIST by examining 15 different sectors. While they observed herding behavior in some periods, it was also stated that more significant observations were made at short frequencies. Akçaalan et al. (2019) argued that herding behavior increases as the trading volume of international investors increases and in reaction to increased volatility. Some studies investigated the herding behavior in markets other than equity markets. De Gama Silva et al. (2019) revealed negative herd behavior during extreme periods in cryptocurrency market. Júnior et al. (2020) examined fifteen commodity markets and observed herding behavior. In the literature, there are also studies that HS-2004 model did not find herd behavior in the market. For example; Abd-Alla (2020) did not find herd behavior in the Egyptian Stock Exchange after the COVID-19 pandemic. There are also studies conducted under financial psychology, where investors’ emotions should be taken into account. Filip and Pochea (2023) applied Hwang and Salmon’s (2004) approach by controlling for changes in investor sentiment, and suggested that herding is a permanent feature in the US and European stock markets. When the accessible literature is reviewed it is observed that herding behavior was measured in different countries and markets. However, studies on investigating its determinants are insufficient. This study differs from other studies in the literature in that it focuses on the relating herding behavior to financial variables identifying its determinants. Analizing the variables (Return, CDS, Volatility, USD/TR, Liquidity, Vix) for identifying the determinants of herding behavior is expected to contribute to the literature. Bayram Erkin Ay, Gamze Göçmen Yağcilar. Investigating the Determinants of Herd Behavior 45 3. Methodology and Data 3.1. Measuring Herd Behavior In order to measure herd behavior, the linear factor model developed by Hwang and Salmon (2004) was used in the study. The process steps (1)–(10) of the Hwang and Salmon (2004) model are as follows. In light of this information, firstly, logarithmic return is calculated using equation (1): 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄 ( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎 ) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (1) In equation (1), ri,t: return of stock in time t, Pt: the closing price of the relevant stock in period “t”, Pt–1: the closing price of the relevant stock in period “t”-1. Following the calculation of returns, excess returns are calculated using the “TwoYear Bond Yields” (derived from the Turkish two-year bond yield (TR2YT)). The calculation of HS-2004 for herd behavior is shown in equation (2): 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓 𝒄𝒄 ( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎 ) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (2) In equation (2), H (m,t): hidden herding parameter, βimt: the beta coefficient of stock “i” at time “t”, si 2 : the variance of the stock beta, Sm: the variance of the market beta. H(m,t) (the hidden herding parameter) is used to measure herding behavior. While calculating the beta values of stocks, estimation (3) from the Capital Asset Pricing Model is used (Doğukanlı and Ergün, 2015: 12). 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋 İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢  𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋 İ −𝑋𝑋)2 t = 𝛽𝛽  2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦 𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖) =1 1+exp (−𝑦𝑦 𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝 𝑖𝑖 1−𝑝𝑝𝑖𝑖 )=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (3) ri,t – rf : the excess return in each period “t” of the stock in the period set as the benchmark, rm,t – rf : the excess market return in each period “t” over the benchmark period. However, Caparelli et al. (2004) offer a different perspective on the calculation of the beta value in the mentioned measure. As Doğukanlı and Ergün (2015) reported, Caparelli et al. (2004) stated that in order to reach the H(m,t) value, the t-test statistical values of the beta coefficients should be calculated through the specified regression and these values give the H(m,t) value of the horizontal cross-section variance. ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, vol. 103(3) 46 In order to reach the t-test values, the regression model presentend in equation (4) was used: 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (4) Yi: (ri,t – rf ) is the risk premium of the stock and is the dependent variable, Xi: (rm,t – rf ) independent variable values by expressing the market risk premium, β1: constant of the regression, β2: coefficient of regressors, ui: the error term. In order to reach the specified regression equation, the following steps should be taken. The methods of obtaining the values of 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 , se( 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 ) and t are shown in equations (5) to (10). (In the equations mentioned, “n” denotes the number of stocks). Step 1 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 : Estimated coefficient of the independent variable. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (5) Step 2 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 : Estimated constant term. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (6) Step 3 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 : Estimated error term. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (7) Step 4 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 : Standard deviation of error terms. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (8) Step 5. se( 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 ) Standard error. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se( 𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (9) Step 6 t: t-test value. 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (10) 3.2. Investigating the Determinants of Herd Behavior In this study, first the periods in which herding behavior emerges are identified with the approach of HS-2004 and then the determinants of herding behavior are investigated using the logistic regression method. The variables thought to be likely to trigger herd behavior are equity returns, USD/TL exchange rate, risk-free interest rate, volatility of equity returns, VIX fear index and Turkey 5-year CDS premiums. Bayram Erkin Ay, Gamze Göçmen Yağcilar. Investigating the Determinants of Herd Behavior 47 Logistic regression analysis is used when the dependent variable is a binary variable (0-1). Following Gujarati (1999, as cited in Budak and Erpolat, 2012), the methodology of logistic regression analysis is explained in equations (11) - (13): Linear regression model for k independent variables is shown in equation (11). 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (11) Equation (12) expresses the curvilinear relationship established between the regressors and the response variable. This calculation assures the response variable to take values between 0 and 1 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (12) Equation (12) must be linearized to obtain a logit model as in equation (13): 𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕 𝑷𝑷𝒕𝒕−𝟏𝟏) 𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄( 𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏 √𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎) (𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕 𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊 𝛽𝛽󰆹2, 𝛽𝛽󰆹1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽󰆹2) 𝛽𝛽󰆹2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 ) ∑( 𝑋𝑋İ − 𝑋𝑋 )2 𝛽𝛽󰆹1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋 𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽󰆹1 − 𝛽𝛽󰆹2𝑋𝑋𝑖𝑖 𝜎𝜎 = √∑𝑢𝑢 𝑖𝑖2 𝑛𝑛 −2 se(𝛽𝛽󰆹2)= 𝜎𝜎  √∑(𝑋𝑋İ −𝑋𝑋)2 t = 𝛽𝛽 2 se(𝛽𝛽 2) 𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖) 1+exp (𝑦𝑦𝑖𝑖)=1 1+exp (−𝑦𝑦𝑖𝑖) 𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖 1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀 (13) By solving the model, it is possible to estimate parameters. 3.3. Data and Variables In the study, herd behavior is investigated for the period 17/10/2017–10/11/2023. In order to apply the Hwan–Salmon method, the data set was started from 03/01/2017 and daily data were used. Nontransaction days were excluded from the analysis. The datasets included in the study were bank stocks listed in BIST Liquid Bank Index (BIST_Bank; as of November 2023). Stock Returns, Dollar/TL Exchange Rate, Risk Free Interest Rate, Volatility of Stock Returns, VIX fear index and CDS premiums were determined as variables included in the study to explain the dependent variable. Investors in the index are considered within the scope of the study. The Borsa Istanbul (BIST) Bank Index typically encompasses stocks of entities engaged in the banking sector. These entities often consist of banks and financial institutions. Consequently, the entities indexed under the BIST Bank Index are typically favored and monitored by institutional investors. While individual investors can also trade in the entities encompassed in this index, institutional investors usually allocate larger sums and possess the potential to sway the index. The adjusted stock prices of banks were obtained through Finnet Elektronik Yayıncılık Data İletişim Ltd. Şti (Finnet Analysis Excel Module). The stock listed in the BIST_Bank are shown below. Table 1. BIST_Bank shares Bileşen Kodu Bileşen Adı *XLBNK BIST LIKIT BANKA 1AKBNK.E AKBANK 2YKBNK.E YAPI VE KREDİ BANK. 3ISCTR.E IS BANKASI (C) 4GARAN.E GARANTI BANKASI Bileşen Kodu Bileşen Adı 5VAKBN.E VAKIFLAR BANKASI 6HALKB.E T. HALK BANKASI 7TSKB.E T.S.K.B. 8SKBNK.E SEKERBANK 9ALBRK.E ALBARAKA TURK ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, vol. 103(3) 54 Akçaalan, E., Dindaroğlu, B., & Binatlı, A. O. (2019). International Investors, Volatility, and Herd Behavior. Uluslararası Ekonomi ve Yenilik Dergisi, 6(2), 247-259. Altay, E. (2008). 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