Global Review of Accounting and Finance Vol. 6. No. 2. September 2015 Issue. Pp. 56 – 81
Culture, Investment Behaviour and Stock Market Volatility A Markov Regime-Switching GJR-GARCH Approach Xin Zheng*1 This paper investigates culture’s impacts upon investment behavior and stock market volatility. The aim is to identify how cultural dimensions influence investment behavior and affect stock market volatility. A Markov regime-switching GJR-GARCH model is estimated using Maximum Likelihood algorithm based on fifteen financial market indices ranging from July 5th 2006 to May 16th 2014 with daily frequencies; the volatility model evolves across two regimes in terms of low volatility state and high volatility state; the volatility dynamics switches between the two regimes according to a Markov transition probability matrix which is estimated using a multinomial regression upon cultural dimensions. The forecasting performances of the models are evaluated using root mean squared errors. Cultural dimensions’ impacts upon the evolution dynamics of the autoregressive parameter, moving average parameter and the leverage effect parameter of the model are compared between high volatility state and low volatility state. This paper contributes to the literature by analysing triangular relationship between cultural dimensions, individual decision making and aggregate stock market volatilities. This paper not only gives portfolio managers insights into balancing risk and return in financial markets with different cultural characteristics, but also sheds light on policy makers’ decision making in designing financial market rules which suit market participants from different cultural backgrounds. This paper concludes that cultural dimensions influence the transition probabilities between the low volatility state and the high volatility state, that cultural dimensions affects the sensitivity of stock market index volatility to volume volatility, and that cultural dimensions tend to generate more significant effects upon the GJR-GARCH model’s parameters in the high volatility state than in low volatility state.
1. Introduction Financial time series data occasionally exhibits structural breaks in their volatility behaviour due to changes in market participants‟ preference and expectation or changes in authorities‟ fiscal and monetary policies. Modelling dynamic volatility of financial markets has been the theoretical and empirical objects of risk diversification, derivative pricing and portfolio management. Hofstede's (2010) cultural dimensions theory provides the fundamental basis to explain cross-cultural differences in decision making. The theory elucidates the influence mechanism of a society‟s culture upon its members‟ beliefs, norms, values and behaviours using the factor analysis structure. He categorizes cultural differences into five dimensions in terms of power distance index, individualism, masculinity, uncertainty avoidance index and pragmatism. Cultural dimensions‟ impacts upon economic agents‟ investment behaviour and financial markets‟ dynamic volatility have been debated heatedly among scholars. Previous literature indicates that culture influences economic agents‟ financial decision making and that the stock markets with different cultural characteristics exhibit different volatility patterns. However, is there a connection between culture‟s impacts upon individual agent‟s financial decision making and culture‟s impacts upon the aggregate economy‟s financial volatility dynamics? Can the investors‟ herding behaviour accumulated 1
Xin Zheng, School of Economics, the University of Sydney, Email:
[email protected]
Zheng by individual financial decisions explain the heterogeneous volatility patterns of financial markets with different cultural background? This paper tests the hypothesis of whether cultural dimensions influence stock market volatilities via the channels of individual agent‟s decision making and aggregate investors‟ herding behaviour. The target is to investigate culture‟s impacts upon investment behaviour and stock market volatility in fifteen North American, European, Asian-Pacific and South American countries. The challenge is to identify how cultural dimensions influence investment behaviour and affect stock market volatility dynamics. The paper is organized as the following. The first section provides the literature review and the main contributions from previous researchers in modelling cultural dimensions‟ influence mechanism upon investors‟ behaviour and stock market volatility. The second section elucidates the theoretical specification of the Markov regime-switching GJR-GARCH model and the transition regime process. The third section summarises statistics from stock market panel data, estimates the transition probabilities in a multinomial logistic regression model, investigates the investors‟ herding behaviour based on dynamic dependence among stock indices‟ volume volatilities, estimates the Markov regime-switching GJR-GARCH model via maximum likelihood method and analyses cultural dimensions‟ impacts upon the behaviour of the GJR-GARCH model‟s parameters. The final section summarises the findings and indicates the limitations of the study which can be further researched. The paper concludes that cultural dimensions influence the transition probabilities between the low volatility state and the high volatility state, that cultural dimensions affects the sensitivity of stock market index volatility to volume volatility, and that cultural dimensions tend to generate more significant effects upon the GJR-GARCH model‟s parameters in the high volatility state than in low volatility state.
2. Literature Review Griblatt and Keloharjut (2001) document that investors simultaneously exhibit a preference for nearby firms and for same-language and same-culture firms, they present a substantial amount of evidence that seems to support the hypothesis that the degree of these effects is inversely related to investor sophistication. Beckmann, Menkhoff and Suto (2007) find that cultural differences are most helpful in understanding country differences which cannot be explained by pure economic reasoning based on Hofstede's four cultural dimensions, they summarize that controlling for various determinants, the dimension of more Individualism predicts less herding behaviour, more Power Distance leads to older and comparatively less experienced managers in the upper hierarchy, Masculinity brings men into top positions and to higher volumes of assets under personal responsibility, and Uncertainty Avoidance is related to higher safety margins against the tracking error allowed and relatively more research effort. Levinson and Peng (2007) conduct an empirical study to examine how cultural background informs economic decision-making and to test whether framing, morality, and out-group information affects judgments of financial value and property ownership across cultures, their results demonstrate that there are dramatic cultural differences in financial value estimations, as well as on the influence of variables such as framing, morality and group membership. Andersona, Fedeniab, Hirscheya and Hilla Skiba (2011) indicate that survey-based country-specific variables on cross-cultural behaviours help to explain both home bias and diversification among foreign equities; they find that investment funds from countries characterized by higher uncertainty avoidance behaviour display greater home bias and are less diversified in their foreign holdings, that portfolios from countries with higher levels of masculinity and long-term orientation display lower levels of home bias, that portfolios from countries with higher levels of masculinity are more 57
Zheng diversified abroad, and that portfolios from culturally distant countries invest less abroad and underweight culturally distant target markets; they conclude that culture impacts investor behaviour directly and not merely though indirect channels such as legal and regulatory framework. Jong and Semenov (2002) relate the factors determining cross-country differences in stock market activity to deeply rooted norms and values in the society which are represented by the position of countries on cultural dimensions, they find that stock markets are relatively more important in countries where inhabitants accept more uncertainty (low score of Uncertainty Avoidance) and regard competition as a good way of interacting (high score of Masculinity). Statman (2008) indicates that the collective set of common experiences that people of the same culture share will influence their cognitive and emotional approach to investing, he finds that people in low-income countries have high aspirations relative to their current income because they pay with risk for a chance to move up in life, that people in collectivistic countries can afford to take more risk because their in-groups provide downside protection and that trusting people are willing to take more risk. Pirouz and Graham (2010) examine the impact of culture on stock price volatility under the assumption of the existing of a focal causal chain linking from dimensions of culture (linguistic structure and values) through globalization to the volatility of stock prices, their find that stock price volatility is influenced by both linguistic structure and values, they also suggest that the influence of cultural values is mediated by the extent of globalization of the countries. Zhan (2012) examines the impacts of national culture on herding behaviour across international financial markets, the relation between national culture and investor behaviour and overall market volatility; he finds that nations with lower value of individualistic culture are more likely to have a higher number of synchronized stock price movements, that correlations between stock price movements increase stock market volatility, that nations with high individualistic culture have a lower number of synchronized stock price movements and smaller stock market volatility, and that the positive relationship between synchronized stock price movements and stock market volatility is stronger for emerging markets during the financial crisis. Time-variation in the conditional variance of financial time-series is essential when pricing derivatives, calculating measures of risk and hedging against portfolio risk. Therefore, there has been an enormous interest amongst researchers and practitioners to model the conditional variance using a variety of volatility models. GARCH models emerge as one of the most popular volatility models to capture the dynamic patterns of financial time series, because GARCH models not only accommodate a variety of flexible structures such as volatility clustering, heavy tailed distributions and correlated residuals but also capture the long term time-varying volatility structure to generate good in-sample estimates. GARCH (1,1) models are popular since they can effectively remove the excess kurtosis in financial time series data, however, scholars holding different opinions about the forecasting performance of GARCH (1,1) model. Bauwens, Preminger and Rombouts (2007) indicate that when GARCH (1,1) is estimated using daily or higher frequency data, the sum of autoregressive parameter and moving average parameter tends to one resulting in high persistent volatility process and non-existence of the second moment of the return process, they highlight that this high persistence may artificially result from regime shifts in the GARCH parameters over time. Diebold (1986) elucidates that while the use of GARCH models is motivated by the fact that appropriate variance „forcing‟ variables are rarely known in the time series context, this motivation is less convincing when the variance series is integrated, he explains that integration implies persistent movements in variances which makes it harder to search for economic explanation of movements, because the existence of 58
Zheng integrated variance disturbance may correspond to the exclusion of dummies for the conditional variance intercept and the stationary GARCH movements within regimes with an unconditional „jump‟ occurring between regimes. Marcucci (2005) compares different GARCH models in terms of their ability to forecast financial time series‟ volatility, he analyses Markov Regime-Switching GARCH models where the parameters are allowed to switch between a low and a high volatility regime to take into account the excessive persistence embedded in GARCH models which implies too smooth and too high volatility forecasts, he assumes both Gaussian and fat-tailed conditional distributions and uses state-dependent degrees of freedom to model possible time-varying kurtosis, he also demonstrates that Markov Regime-Switching GARCH models do outperform all standard GARCH models in forecasting volatility at shorter horizons according to a broad set of statistical loss functions. These motivate researchers to model volatilities using a model that permits regime switching in the intercept and slope parameters the Markov Regime-Switching GARCH (1,1) model, which is a generalization of GARCH models and allows for different persistence in the conditional variance of each regime and accommodates volatility clustering, nesting the GARCH (1,1) model as the special case which excludes regime switches. Some researchers also point out GARCH (1,1)‟s disadvantages in modelling the leverage effects embedded in volatility dynamics compared with symmetric GARCH models and prefer asymmetric GARCH models. Hansen and Lunde (2005) compare a number of volatility models in terms of their ability to describe the behaviour of conditional variance using the test for superior predictive ability and out-of-sample IBM equity data, they conclude that GARCH (1,1) is outperformed by models that can accommodate leverage effects. Awartani and Corradi (2005) examine the relative out-of-sample predictive ability of a variety of GARCH models with particular emphasis on the predictive content of the asymmetric components and perform comparisons of various models against the GARCH (1,1) model, they summarize that for both pairwise and multiple comparisons, the GARCH (1,1) is beaten by the asymmetric GARCH models in both one-step forecasting and long horizon forecasting. Forte and Manera (2006) first investigates the forecasting performance of asymmetric GARCH models with the symmetric GARCH (1,1) models as the benchmark based on Asian and European stock price indexes, next evaluates forecasts produced by all GARCH models using a common set of classical criteria as well as forecast combination techniques with constant and non-constant weights, then concludes that the asymmetric GARCH models generally lead to better forecasts in terms of both smaller forecast errors and lower biases. Liu and Hung (2010) investigate the daily volatility forecasting performance for S&P 100 index and identify the essential sources of performances between distributional assumption and volatility specification using distribution-type and asymmetry-type volatility models through the superior predictive ability test, they suggest that GJR-GARCH models achieve the most accurate volatility forecasts and that GARCH models with normal distribution is preferable to those models with sophisticated error distributions if asymmetries are neglected, and they demonstrate that modelling asymmetric components is more important than specifying error distribution in order to improve volatility forecasting performance in the presence pf fat-tails, leptokurtosis, skewness and leverage effects. Hence, it is essential to incorporate both asymmetric nonlinearities and Markov regime-switching characteristics into modelling the volatility dynamics of the stock market. However, previous researchers usually analyse either the relationship between cultural dimensions and individual agent‟s economic decision making or the relationship between cultural dimensions and stock market volatilities, rarely do they discuss the triangular relationship between cultural dimensions, individual decision making and aggregate stock 59
Zheng market volatilities. Besides, previous literature seldom analyses how do cultural dimensions affect the behavioural dynamics of the GARCH models‟ parameters explicitly. Hence, this paper intends to fill in this research gap and generates new ideas from the study of culture, investment behaviour and stock market volatility.
3. Theoretical Model This paper contributes to the literature by estimating the transition probabilities in a multinomial logistic regression model, investigating the investors‟ herding behaviour based on dynamic dependence among stock indices‟ volume volatilities, estimating the Markov regime-switching GJR-GARCH (1,1) model via maximum likelihood method, and analysing cultural dimensions‟ impacts upon the behavioural dynamics of the autoregressive parameter, moving average parameter and leverage parameter of the GJR-GARCH (1,1) model‟s parameters. 3.1 Measurement of Stock Returns and Stock Volatility Define successive stock market index observations at time t and t+1 as Pt and Pt:1 , and transform a stock market index series *Pt + to a stock market return series *yt + using the P following continuous compounding principle: yt = ln ( Pt+1) = ln(Pt:1 ) ln(Pt ) . Define the t
30-day stock market volatility series *σt
2+
2
as σt =
∑30 ̅)2 t=1(yt ;y 29
.
3.2 Measurement of Culture This paper uses power distance index, individualism, uncertainty avoidance index and masculinity to characterize national cultures based on Hofstede‟s (2010) cultural dimensions theory, the following definitions of cultural dimensions are drawn from Hofstede‟s research work. 3.2.1 Power Distance Index Power distance is defined as the extent to which the less powerful members of organizations and institutions accept and expect that power is distributed unequally, lower power distance means more consultative or democratic culture. 3.2.2 Individualism vs. Collectivism Individualism is defined as the degree to which individuals are integrated into groups, specifically, people highlight personal achievements and individual rights in individualistic societies, whereas people act predominantly as members of a lifelong and cohesive group or organization in collectivist societies. 3.2.3 Masculinity vs. Femininity Masculinity is elucidated as the distribution of emotional roles between the genders. Masculine culture is characterized by competitiveness, assertiveness, materialism, ambition and power, whereas feminine culture values relationships and quality of life.
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Zheng 3.2.4 Uncertainty Avoidance Uncertainty avoidance is explained as a society's tolerance for uncertainty and ambiguity since uncertainty avoidance reflects the extent to which members of a society attempt to cope with anxiety by minimizing uncertainty, specifically, people in cultures with high uncertainty avoidance try to minimize the occurrence of unknown and unusual circumstances and to proceed with careful changes by planning, whereas people in cultures with low uncertainty avoidance accept and feel comfortable in unstructured situations or changeable environments and try to have as few rules as possible. 3.2.5 Pragmatism Pragmatism describes how people in the past as well as today relate to the fact that so much that happens around us cannot be explained. In societies with a normative orientation most people have a strong desire to explain as much as possible. In societies with a pragmatic orientation most people don‟t have a need to explain everything, as they believe that it is impossible to understand fully the complexity of life. The challenge is not to know the truth but to live a virtuous life. 3.2.6 Indulgence One challenge that confronts humanity, now and in the past, is the degree to which little children are socialized. Without socialization we do not become “human”. This dimension is defined as the extent to which people try to control their desires and impulses, based on the way they were raised. Relatively weak control is called “indulgence” and relatively strong control is called “restraint”. Cultures can, therefore, be described as indulgent or restrained. 3.3 Markov Regime-Switching Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroskedasticity (MRS-GJR-GARCH) Models Hamilton (2005) first elucidates that the evolutions and behaviours of financial series data tend to experience structural changes whenever encounter economic crisis or government intervention, next indicates that many economic variables behaviour very differently during economic downturns when underutilization of production factors rather than long term growth trend governs economic dynamics, then suggests that abrupt changes in the behaviours of economic variables should stem from some imperfectly predictable forces with a probability law governing the structural changes, finally concludes that a state variable St should be incorporated into the model to reflect institutional changes and that the simplest specification of St is the realization of a two-state Markov chain with a transition matrix. Hence, this paper formulates a two-state Markov Regime-Switching GARCH model which consists of four elements in terms of the mean equation, the error distribution, the variance equation and the transition regime process. All the models are constituted of two states in terms the low volatility state S1 and the high volatility state S2 . 3.3.1 Mean Equation of Markov Regime-Switching Glosten-Jagannathan-Runkle GARCH (1,1) (MRS-GJR-GARCH (1,1)) Vosvrda and Žikes (2004) elucidated that the empirical distribution function of European stock returns used to exhibit leptokurtosis induced by heteroskedasticity and non-normality so that models with student-t innovations should be applied to simulate the behaviour of
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Zheng volatility of returns over time. Extend Geweke‟s (1993) data augmentation and Ardia and Hoogerheide‟s (2010) model specification to obtain the following return equation structure. yt = μst + εt = μst + σst,t ∙ ξt for t=1,2,3,⋯,T, ξt ~I. I. D. f(ξt |St )
where N denotes standard normal distribution, I.I.D.N. means identically independently normally distributed, *ξt + is a real-valued discrete time stochastic process that represents the innovations or the single-period-ahead forecast error, *yt + is an observed stock market return process. 2
f(ξt |St = 1) = f(ξt |St ) =
ξt 1 ∙ e; 2 √2π
τ(
v+1
)
2 f(ξt |St = 2) = v ∙ (1 + vπ∙τ( ) √ { 2
St = 1, Gaussian Distribution, Low Volatility v+1 ; 2 ξt 2
v
)
St = 2, Student t Distribution, High Volatility
3.3.2 Variance Equation of Markov Regime-Switching Glosten-Jagannathan-Runkle GARCH (1,1) (MRS-GJR-GARCH (1,1)) GJR-GARCH (1,1) captures leptokurtic returns and volatility clustering, and its specification captures the characteristics that negative shocks induce larger volatilities than positive shocks. Balaban (2004) indicated that GJR-GARCH(1,1) models were asymmetric in terms of allowing for different impacts on volatility by positive and negative εt of equal magnitude. Forte and Manera (2006) investigated the forecasting performance of asymmetric GARCH models which included GJR-GARCH model based on Asian and European stock price indices, and they concluded that the asymmetric GARCH models led to better forecasts in terms of both smaller forecast errors and lower biases compared with normal GARCH specification. Emenike (2010) revealed that the distribution of stock returns might exhibit leverage effects in terms of high probabilities for extreme values and that GJR-GARCH (1,1) could be used to capture the leverage effects. Ali (2013) concluded that GJR-GARCH models included the skewed generalized error distribution. σSt,t 2 = β0,st + β1,st ∙ εt;1 2 + β2,st ∙ εt;1 2 ∙ I*εt−1 0, β1,st ≥ 0, β2,st ≥ 0, β3,st ≥ 0 ensure positive volatilities, β1,st + β2,st + β3,st < 1 satisfies stationary condition, N denotes standard normal distribution. σSt,t 2 is current variance, σSt−1,t;1 2 is past variance, εt;1 2 is squared past innovation and εt;1 2 I*εt−1
