The impact of the Brexit referendum on Volatility and Volatility
Spillovers effects of European stock indexes
Thesis for Master Finance University of Groningen Faculty of Economics & Business
January 2017
Author: Lennart Speller Student number: S2087030 Supervisor: Jochen Mierau
Abstract:
The goal of this paper is to assess the impact on volatility and volatility spillover effects of five European stock market indexes (FTSE, AEX, DAX, CAC, and ISEQ) as a result of the exit of the United Kingdom out of the European Union. To be able to compare any differences in volatility or spillover effects the dataset is divided into three time periods. The results show that after the official Brexit referendum announcement the level of volatility of the individual European Stock Indexes increased significantly. In addition, it is found that there are some significant volatility spillover effects between several indexes caused by the Brexit announcement and by the actual Brexit referendum. Finally, a DCC-MGARCH model is used to capture volatility spillover effects between the five indexes as a whole system. This resulted however in no significant volatility spillover effects in any of the periods. These findings offer interesting insights into the impact of an EU membership’s termination on the volatility (co-)movements of the close-related European stock market indexes. Additionally, it offers applicable insights with respect to investment and diversification strategies for investors.
Introduction
The objective of this paper is to provide a deeper insight into the links between European stock market indexes and the exit of the United Kingdom out of the European Union as of the 23th of June 2016. The target is to study the short-term volatility responses of the European stock indexes FTSE (United Kingdom), DAX (Germany), CAC (France), AEX (The Netherlands), and ISEQ (Ireland) to; (1) the first official announcement of the Brexit referendum and (2) the actual outcome of the referendum. In addition, this study elaborates on the volatility spillover effects between these five European indexes to see to what extent these indices are interlinked. Doing so, I want to measure the total impact of the Brexit referendum on the European stock markets. Stock indexes are used since they function as a powerful proxy for a country’s equity market performance. Therefore, this paper will focus on the impact of the referendum announcement and the corresponding outcome on volatility and volatility spillover effects between these European stock indexes. This leads to the following main research question: Has Brexit influenced the volatility of European stock indexes? This research is relevant since not only current research hasn’t touched upon this subject, but mostly because the Brexit referendum is such topical subject with a global footprint on the economy. Therefore, the aim of this research is to shed new light on the vulnerability of the European stock market indexes caused by the abandoning of a current EU member. Additionally, this paper provides investment and diversification insights for investors in case a high-impact macroeconomic event like Brexit occurs.
periods: the ‘pre-Brexit announcement’ period, the ‘in between Brexit announcement and actual Brexit referendum’ period, and the ‘post Brexit referendum’ period. In addition, this chapter provides the data description, the reasoning behind the chosen stock indexes, and the sample collection. Chapter 2 ends with an extensive clarification of the econometric models used in this paper, like the EGARCH model of Nelson (1991) and the DCC-MGARCH model of Engle and Sheppard (2001). In chapter 3 the results with respect to volatility movement and volatility spillover effects are presented, which are evaluated for robustness in chapter 4. Finally, chapter 5 answers the research question, discloses on the practical implications, gives recommendations for further research, and ends with the summary.
1. Literature review
1.1 IntroductionIn section 1.2 of this first chapter I start with a comprehensive description of the concept of volatility. Next, in section 1.3 I use existing academic literature to touch upon volatility spillovers effects. Following, the essence of the Brexit referendum is discussed in section 1.4. This includes the perspectives of both competing parties campaigning the Brexit referendum and the immediate impact of Brexit on the European stock markets. Last, section 1.5 explains to what extend Brexit could have influenced volatility movements and volatility spillover effects of European stock indexes. This leads to the research question of this paper.
1.2 Volatility
For this paper, I will mainly focus on volatility movements caused by the arrival of new information in the market or by the announcement of macroeconomic unexpected events, such as the Brexit referendum. Security price movement as a result of novel information was first introduced by Fama (1971). He argued that, in case of efficient markets, when new information is made publicly available stock prices should react immediately and unbiased. Another perspective was given by Pasquariello (2007) as he mentioned that, markets are imperfect and, therefore, the arrival of new information results to the emerging of disagreement and uncertainty among investors. As a consequence, this should result in increasing heterogeneous trading and thus increasing volatility. The paper of Ross (1989) also linked volatility to the amount of information flow. However, he argues that the degree volatility is related to the degree of information arrival, this implies that when the market receives new information flows the volatility movement should be the highest. Last, Foster and Viswanathan (1993) found that the amount of increase in price volatility and trading volume can be linked to the difference between the actual and the expected information flow. So, if the received information is considerable different than the expectations of the investor, subsequently there will be a larger increase in trading volume and price volatility.
volatility is mentioned by Barber, Odean, and Zhu (2009). They refer to the concept of noise traders, which are investors who make decisions based on herding behaviour. This indicates that investors trade predominantly speculative and that these investors are triggered by the behaviours of other (institutional) investors. As a consequence, investors tend to underexpose their liquidity demands, optimal portfolio strategy, or tax-losses. This herding behaviour of noise traders leads to buying or selling large quantities of the same securities at about the same time which results to a wider variation in the stock price over time. This is also confirmed by the findings of Karpoff (1987) as he argues that an increase in the trade volume of a certain security increases the volatility of that security and vice versa. He found that this relation is presence since trade volume and volatility are both related to new information flows. Additionally, Barber and Odean (2008) conclude that investors have a tendency to buy high abnormal trading stock, such as the ones covered in the news, which they refer to as attention-grabbing stock.
To end this section, I want to reflect on the relevance of studying volatility movements caused by unexpected events. As volatility impacts the value range of a security over time, the price of that security can change considerably after a certain event in either direction. For investors, this holds several implications. For instance, higher volatility of returns results in a wider distribution of possible final portfolio values and thus leads to higher uncertainty. This uncertainty can have a negative impact as higher volatility increases the chance of a shortfall. However, high volatility also offers investors the opportunity to acquire a financial asset cheaply and sell it when overpriced. Risk-averse investors tend to hold a long-term investment strategy and favour low volatile markets as the likelihood of positive returns in the future is higher. However, some amount of volatility in the market can result in higher returns for this kind of investors. Risk seeking investors, meanwhile, have a tendency to invest actively and prefer high volatile markets as this offers greater potential for high excess returns on their investments. So, studying volatility movement caused by an event like Brexit is highly relevant as it greatly influences investment strategies and optimal portfolio compositions for investors taken into account their term and risk preferences.
1.3 Volatility Spillovers
European Union (European Commission, 2016). It enables the free movement of services, capital, and goods within the EU without the intervention of regulatory barriers or international customs duties. According to Baele (2005) the correlation between stock markets of multiple countries can be highly influenced by these strong similarities in financial policies and strong macroeconomic ties. As mentioned by to the European Commission (2016) the Single Trade Market has already increased trade within the EU between approximately 4% and 10% since the introduction of the Euro currency. So, as trade has increased across the EU and regulations and custom barriers have decreased, the European stock markets are likely to have demonstrated stronger spillover effects over time. The well-known paper of Forbes and Rigobon (2002) also touch upon the subject of market co-movement. However, instead of the expression volatility spillover effects they are using the term market contagion, which is defined as, pp 2223: “a significant increase in cross-market linkages after a shock to one country”. This differs from the concept volatility spillover effects as it is only considered contagion in case the market co-movement strengthened significantly after a certain shock in comparison to stable periods. Although this discrepancy, their findings are highly relevant for this paper as they found that an increase in market volatility in one country is able to increase the co-movement coefficient of that market with another country. The risks of correlated markets were highlighted by Diebold and Yilmaz (2009) as they found that the correlation between stock markets increases significantly during turmoil periods. Additionally, it was argued by Antonakakis and Badinger (2016) that in highly correlated markets, economic growth and volatility spillovers from foreign countries are important indicators of a country's own economic perspectives. Therefore, investigating volatility spillovers among the European stock indices does not only reveal the overall vulnerability of the European stock markets to the announcement of the Brexit referendum and to the actual Brexit referendum outcome, in addition it discloses on the overall risk of European stock markets in case an EU member’s terminates its membership.
1.4 Brexit
UK should remain EU member. This commitment formed the legal foundation for a referendum which was accomplished through the European Union Referendum Act (2015). The first announcement of the to be planned referendum was during the Queen's Speech on 27 May 2015. The Brexit referendum resulted in a 51,9% overall vote to leave the EU.
During the run-up to the Brexit referendum there was a ferocious competition between the “leave” and the “remain” campaigners. On the one hand, there was Britain Stronger in Europe which was the official party striving for the UK to remain in the EU. In their referendum manifesto (Britain Stronger in Europe, 2016) they argued that leaving the EU would increase, amongst others, economic uncertainty and risk by; limiting UK's full access to the EU’s single trade market, decreasing the attractiveness of incoming foreign investments, and increasing trade barriers between businesses in the UK and the EU. As a consequence, their concern is that leaving the EU would lead to a declining labour market, increasing risks to business, and delays in investment into the UK. Vote Leave, on the other hand, was the official campaign party pushing for the UK to abandon the EU. Vote Leave argued in their manifesto (Vote Leave, 2016) that the EU undermines UK’s political control and its national sovereignty. According to Vote Leave, leaving the EU would allow the UK to control again for their economy and trade policies. In addition, abandoning the EU should result in cost savings on EU membership fees and the UK would no longer be forced to bail out other EU members.
1.5 Research questions
The official announcement of the Brexit referendum on 27th of May 2015 is expected to have caused an increase in the volatility of the European stock indices (see graph 1). As both campaigning parties mention that the exit of the UK out of the EU will have a significant impact on, among others; foreign investments, the trade market, and the labour market. It therefore would be no surprise that the Brexit announcement has led to an increased level of uncertainty among investors. Some investors might have reacted rational and adjusted their trade portfolio’s accordingly to their risk preferences (Barberis and Thaler, 2003) however, I expect that limited investor attention (Peng and Xiong, 2006) and the herding behaviour of noise traders (Barber, Odean, and Zhu (2009) has led to a substantial increase in volatility of European stock market indexes after the first official announcement. In addition, I expect that after the actual Brexit vote investors perceive less uncertainty, although the outcome might be undesirable, and therefore there can be found a decrease in volatility. This leads to the first and second research questions.
First, did the official Brexit referendum announcement resulted in an increase in volatility of the individual European Stock Indexes?
Second, were the individual European indexes more volatile before the actual Brexit referendum and less volatile afterward?
Based on the findings with respect to volatility spillovers of section 1.3, I expect that the announcement of the Brexit referendum has resulted in increased uncertainty among investors. Additionally, it is highly likely that the European stock indexes are strongly correlated as already was found in literature (Baele, 2005; Diebold and Yilmaz, 2009). Additionally, it was mentioned by Forbes and Rigobon (2002) that in case volatility increases in one market it is likely that there is also an increase in spillover effects with another market. Therefore, I expect an increase in volatility spillovers after the Brexit referendum announcement. After the actual Brexit vote, I anticipate investors to perceive less uncertainty and therefore I suggest less strong volatility spillover effects. This leads to the third and fourth research questions:
Fourth, was there a higher degree of spillover effects between European stock index volatilities before the actual Brexit referendum and less spillover effects afterwards?
2. Data and Methodology
2.1 IntroductionFor this paper, I study the volatility movements and volatility spillover effects between five major stock market indexes across Europe as a result of the Brexit referendum announcement and the actual referendum. The indexes used are FTSE (United Kingdom), DAX (Germany), CAC (France), AEX (The Netherlands), and ISEQ (Ireland). In section 2.2 of this chapter I outline the data sample and the time periods selected. Section 2.3 covers the summary statistics of the distinctive time periods. In section 2.4 the most predominant econometric models with respect to volatility and volatility spillovers effects are explained. Last in section 2.5 a description is provided with regard to the specific methods used to model volatility and spillovers.
2.2 Data & Sample collection
Daily logarithmic closing index returns of five European stock indexes are collected over a period of three years, starting in 2013. The data is collected from Yahoo Finance and Investing.com. Stock indexes are chosen since they function as a good proxy for a countries equity market performance as a whole. In addition, indexes provide a rough reflection of the sentiment of investors on the state of a countries economy. The specific indexes FTSE (United Kingdom), DAX (Germany), CAC (France), AEX (The Netherlands), and ISEQ (Ireland) are selected as these countries perceived high levels of trade (export and import) as a percentage of gross domestic product (GDP) with the UK in 2015 in relation to other large European economies (see table 1). Therefore, I expect that the markers of these countries perceive the highest impact to their stock markets as a result of Brexit.
first official announcement of the Brexit referendum, the period after this announcement, and the period after the actual outcome of the referendum, the data set is divided into three parts: the ‘pre Brexit announcement’ period from 21-01-2013 till 27-05-2015 (578 observations), the ‘in between Brexit announcement and actual Brexit referendum’ period from 28-05-2015 till 22-06-2016 (268 observations), and the ‘post Brexit referendum’ period from 23-06-2016 till 01-11-2016 (91 observations).
Table 1: Amount of Trade in GBP with the UK in 2015 per country
Country Stock Index
Export of all products to UK in 2015 (GBP Thousand) * Export as % of GDP** Imports of all products from UK in 2015 (GBP Thousand) * Import as % of GDP** Germany DAX 61.731.000 2,26% 30.652.000 1,12% France CAC 24.401.000 1,24% 17.959.000 0,91%
The Netherlands AEX 31.729.000 5,20% 16.968.000 2,78%
Ireland ISEQ 12.796.000 5,55% 16.792.000 7,28%
Belgium & Luxembourg BEL & LuxX 21.373.000 5,13% 11.785.000 2,83%
Switzerland SMI 8.462.000 1,55% 9.971.000 1,83%
Spain IBEX 1.4067.000 1,44% 8.937.000 0,92%
Italy FTSE MIB 16.013.000 1,08% 8.509.000 0,57%
*Source: Office for National Statistics: UK’s top 50 export markets and import sources in 2015 **Source: The World Bank
2.3 Log returns and volatility
The raw pricing series data from Yahoo Finance and Investing.com are first converted into time series of returns. To be more precise, I used daily continuously compounded index returns calculated based on the differences between the closing values of each day (see equation 1).
ri,t = ln(pricei,t / pricei,t−1) * 100% (1)
With r being the return of indexes i on time t and pricei,t presents the closing price of index i
Graph 1: Total-period daily log-returns of FTSE, AEX, DAX, CAC, and ISEQ
2.4 Descriptive statistics
The descriptive statistics of the close-to-close daily logarithmic returns for the five stock indexes can be found in Table 2. Based on the summary statistics we can see that the mean return of the FTSE, AEX, DAX, and CAC went from positive in the pre-Brexit period, to negative in the period between the announcement and referendum, to positive again after the actual referendum. The mean returns of the ISEQ however remained negative in the period after the Brexit referendum. Table 2 also shows that the standard deviations for all indexes, except ISEQ, increased significantly during the period between the Brexit announcement and the referendum. After this period the standard deviations decreased slightly, however they all stayed above the values of the pre-Brexit period. This points out that the announcement of the Brexit referendum and the actual referendum resulted in an increase in uncertainty and consequently an increase in volatility of the five indexes. With respect to normal distributions and the symmetric nature of the data, the negative values for Skewness and the positive values for Kurtosis in all periods for all the indexes display that the index returns are not normally distributed and that the data exhibits asymmetry. In the section 2.5 Skewness and Kurtosis will be explained more extensively.
2.5 Econometric models for Volatility
One of the characteristics of financial data is that the relationship between stock return observations tends to be non-linear (Campbell, Lo and MacKinlay, 1997). Therefore, linear models like OLS are unable to explain a number of important features common to much financial data (Brooks, 2008) among which: Leptokurtosis, return distributions on financial assets tend to include excess peakedness at the mean and the presence of fat tails; Volatility
-5 -4 -3 -2 -1 0 1 2 3 4 5
clustering, volatility in financial markets has the tendency to appear in bunches. So, small returns, of either sign, are expected to be followed by small returns and large returns are likely to be followed by large returns, and; Leverage effects, volatility in financial markets has the tendency to rise more as a consequence of a large price fall than as of a large price increase.
Table 2: Summary statistics for all used indexes
Index Period Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
FTSE Total 0.013 0.045 3.515 -4.779 0.948 -0.160 5.036 Pre 0.023 0.066 3.032 -3.027 0.775 -0.254 4.481 Between -0.043 -0.020 3.498 -4.779 1.233 -0.111 3.879 Post 0.109 0.058 3.515 -3.197 0.985 0.317 5.468 AEX Total 0.026 0.048 3.971 -5.873 1.121 -0.329 5.226 Pre 0.063 0.081 3.167 -3.522 0.902 -0.141 4.357 Between -0.049 -0.049 3.971 -5.378 1.474 -0.106 3.553 Post 0.021 -0.009 2.966 -5.873 1.170 -1.391 9.178 DAX Total 0.033 0.101 4.852 -7.067 1.246 -0.377 4.771 Pre 0.073 0.112 3.301 -3.498 1.061 -0.208 3.685 Between -0.058 0.040 4.852 -4.816 1.563 -0.089 3.230 Post 0.049 0.087 2.467 -7.067 1.283 -1.870 12.052 CAC Total 0.019 0.053 4.055 -8.384 1.244 -0.471 6.080 Pre 0.056 0.085 3.523 -3.726 1.055 -0.141 4.101 Between -0.063 -0.048 4.055 -5.493 1.553 -0.106 3.480 Post 0.022 -0.022 2.571 -8.384 1.332 -2.657 18.794 ISEQ Total 0.056 0.041 4.447 -10.416 1.175 -1.281 12.597 Pre 0.105 0.067 3.167 -3.331 0.988 -0.133 3.312 Between -0.005 -0.014 4.447 -5.511 1.306 -0.334 5.041 Post -0.077 -0.009 2.787 -10.416 1.734 -3.352 19.681 Notes: Total stands for the total data sample, Pre for the period before the Brexit announcement (21-01-2013 till 27-05-2015), Between for the period between the Brexit announcement and actual Brexit referendum (28-05-2015 till 22-06-2016), and Post for the period after the actual Brexit referendum (23-06-2016 till 01-11-2016).
To generate non-linear data, the current value of the series is related non-linearly to the current and previous value of the error terms (Campbell, Lo and MacKinlay, 1997). Non-linear models that have been proven useful for modelling volatility and volatility spill overs include, among others, the ARCH(q), GARCH(1,1), EGARCH, and MGARCH models. These models will be elaborated on respectively in order to choose the right models to answer my research questions.
2.5.1 Autoregressive Conditional Heteroscedastic Models
describes how the variance of the error terms evolves over time and thus does not assume the variance to be constant (heteroscedasticity). To do this, Engle (1982) developed the Autoregressive Conditional Heteroscedastic (ARCH) model. An important feature of the ARCH model is that it’s able to explain autocorrelation between values at different times (volatility clustering). There are however some limitations on the ARCH models according to Brooks (2008). For instance, there is no single best approach to determine the appropriate number of previous periods (lags) of the squared residuals. Another limitation of the model refers to its non-negativity constraint. The more lags there are implemented in the conditional variance equation, the more likely it becomes that one of them will exhibit negative estimated values. To overcome some of the limitations of the ARCH model Bollerslev, (1986) and Taylor (1986) developed the GARCH(1,1) model which allows the conditional variance to be dependent upon its previous own lags. However, there are also some important drawbacks on the GARCH(1,1) model. The first restriction of the model is the assumption of symmetry. This means that the model enforces a symmetric response of volatility to negative and positive shocks and is therefore not able to capture any leverage effects. Second, the GARCH(1,1) models experience the same limitations as the ARCH models with respect to non-negativity constraints. These limitations have resulted in a large number of extensions and variants based on the GARCH(1,1) model.
2.5.2 EGARCH model
Taking the constraints of the GARCH(1,1) model into consideration, a more realistic approach to model volatility would be the inclusion of negative parameters and an asymmetry term. This leads to the mean EGARCH model suggested by Nelson (1991) which can be found in equation 2 where ri,t equals the daily return of stock index i on time t and with ut−I
being the error term at time t-1.
rt = a0 + i ri,t-1 + ut−I (2) 𝑙𝑛(ℎ𝑖,𝑡) = 𝜔 + 𝛽 𝑙𝑛(ℎ𝑖,𝑡−1) + 𝛾 𝑢𝑖,𝑡−1 √ℎ𝑖,𝑡−1+ 𝛼 ( |𝑢𝑖,𝑡−1| √ℎ𝑖,𝑡−1 − √ 2 𝜋) (3)
parameters in the equation, since the logistic conditional variances ln(hi,t) for index i on time t
is modeled. So, even if negative parameters are included positive conditional variance is ensured. Further, the constant term ω equals the long-term average value of the variance, α is a coefficient for the ARCH term, and β measures the impact of the GARCH term.
Since this EGARCH model overcomes shortcomings of the GARCH models, I propose to extend this model and apply it to measure for separate volatility spillover effects between the respective European stock indexes and the FTSE. Doing so will give a better understanding if there is any volatility co-movement between, for instance, the AEX and the FTSE. In section 2.6 of this chapter an in-debt description is provided with regard to volatility and the volatility spillover effects, based on the EGARCH model.
2.5.3 MGARCH models
A key shortcoming of the previous mentioned ARCH, GARCH(1,1), and EGARCH models is that they are univariate in nature (Brooks, 2008). This implies that these models construct the volatility of each series entirely independently of all other series. To analyze the volatility of the five stock indexes as a whole system a multivariate model is more appropriate. This is because multivariate models are able to estimates the conditional variances as well as the conditional covariances. The multivariate GARCH (MGARCH) models are therefore capable to capture the dynamic relationship between the respective markets as a whole. The first type of MGARCH model is the Constant Conditional Correlation (CCC) MGARCH model introduced by Bollerslev (1990). In this model, the conditional correlation is assumed to be constant over time, and only the conditional standard deviation is time-varying. However, the assumption that the conditional correlation is constant over time does not always seem reasonable according to Engle and Sheppard (2001).
in relation to the volatility spillover effects between the European stock indexes as a whole system.
2.6 Volatility and Volatility spillover effects using (E)GARCH Models
To answer the first and second hypothesis (did the official Brexit referendum announcement resulted in an increase in volatility of the individual European Stock Indexes? & were the individual European indexes more volatile before the actual Brexit referendum and less volatile afterward?), I first check the five indexes for volatility clustering in the residuals using a standard OLS regression on the entire data sample. Next, an ARCH test is used to check for heteroscedasticity (ARCH effects). When volatility clustering in the residuals and the ARCH effects are present it is appropriate, according to Brooks (2008), to use the previous described EGARCH model of Nelson (1991). The results of the ARCH tests in Appendix B show that there is heteroscedasticity (ARCH effects) present in the residuals of all stock indexes. Therefore, the EGARCH model of equation 3 will be used to compare the logistic conditional variances ln(hi,t) for each of the five indexes between the three selected
periods to see if the Brexit referendum has impacted the level of volatility. The results can be found in section 2 of chapter 3.
It is also relevant to study if volatility caused by a shock like Brexit in one market is transmitted to another market. Therefore, I want to check if there are any volatility spillover effects between one of the five stock indexes and the FTSE and vice versa. Doing so will give a better understanding if there is any volatility spillover effect between, for instance, the AEX and the FTSE. Once the structure of interdependence between two specific indexes is established, I will study the volatility spillover effects on the stock markets as a whole system, which will be explained in section 2.7.
𝑙𝑛(ℎ𝐹𝑇𝑆𝐸,𝑡) = 𝜔 + 𝛽1𝑙𝑛(ℎ𝐹𝑇𝑆𝐸,𝑡−1) + 𝛾 𝑢𝑖,𝑡−1 √ℎ𝐹𝑇𝑆𝐸,𝑡−1+ 𝛼 ( |𝑢𝑖,𝑡−1| √ℎ𝐹𝑇𝑆𝐸,𝑡−1 − √ 2 𝜋) + 𝛽2𝑙𝑛(ℎ𝑖,𝑡−1) (4) 𝑙𝑛(ℎ𝑖,𝑡) = 𝜔 + 𝛽1𝑙𝑛(ℎ𝑖,𝑡−1) + 𝛾 𝑢𝑖,𝑡−1 √ℎ𝑖,𝑡−1+ 𝛼 ( |𝑢𝑖,𝑡−1| √ℎ𝑖,𝑡−1 − √ 2 𝜋) + 𝛽2𝑙𝑛(ℎ𝐹𝑇𝑆𝐸,𝑡−1) (5)
In equation 4 and 5 the presence of volatility spillovers is captured by the statistical significance value of β2. In case of equation 5, a significant negative γ term together with a
significant β2 implies that negative event on the UK’s stock market has a higher impact on the
volatility of stock market i than a positive event (asymmetric spillover effects). Section 3 of chapter 3 provides the results of the extended EGARCH models.
2.7 Volatility Spillover effects using DCC-MGARCH
To answer the third and fourth hypothesis (did the official Brexit referendum announcement affected the existing degree of spillover between European Stock Index volatilities? & was there a higher degree of spillover effects between European stock index volatilities before the actual Brexit referendum and less spillover effects afterwards?), the DCC-GARCH (1,1) model of Engle and Sheppard (2001) is used. Using this model, I estimate the volatility spillover effects between the five indexes as a whole system and afterwards I compare the outcomes with respect to the different time periods.
The preliminary assumptions of the DCC-MGARCH model is that stock index returns from the k series are multivariate, are distributed normally with an expected value of zero, and are based on conditional variance-covariance matrix Ht. In the conditional variance-covariance
matrix of equation 6, term Dt represents a (k*k) diagonal matrix of standard deviations, i.e. Dt
= diag(σ1t , σ2t , , σN t), and Rt is the (k*k) correlation matrix at time t. The correlation matrix Rt
is calculated using equation 7, with Qt as defined in equation 8. diag[Qt]-1/2 being a diagonal
matrix with the square root of the elements of Qt at time t. Term S is the unconditional
covariance matrix of standardized errors, as shown in equation 9.
Ht = DtRtDt (6)
Qt = (1- - ) S + ut-1 u’t-1 + Qt-1 (8)
S = E(u’t u t) (9)
𝑟𝑖,𝑡 = 𝛾0 + 𝛾1𝑟𝑡−1𝐹𝑇𝑆𝐸+ 𝛾2𝑟𝑡−1𝐴𝐸𝑋+ 𝛾3𝑟𝑡−1𝐷𝐴𝑋+ 𝛾4𝑟𝑡−1𝐶𝐴𝐶 + 𝛾7𝑟𝑡−1𝐼𝑆𝐸𝑄+ 𝑢𝑡 (10)
The application of this DCC-MGARCH model involves two steps. In the first step, the model estimates the mean equation for each index in the given sample using the univariate GARCH(1,1) model with the conditional variances Dt. See equation 10 for the specific mean
equation used. In step two, the dynamic conditional correlations are estimated. The correlations create the correlation matrix Rt for which the diagonal elements are coherent. In
order to estimate the correlation coefficient ij,t it is assumed that Qt follows an autoregressive
process. To estimate the DCC-MGARCH model the maximum likelihood estimation technique should be used (Brooks, 2008). In section 4 of chapter 3 the results of the DCC-MGARCH models are given.
3. Results
3.1 Introduction
3.2 Volatility
Table 3 summarizes the estimation results of the EGARCH models for each of the five European stock indexes between the three selected time periods. This table provides the variables which impact the logistic conditional variances ln(hi,t) of each index in the regarding
time period. The constant term is given by ω, which equals the long-term average value of the variance. Term α is the coefficient for the ARCH term and the value of the γ term indicates the presence of the leverage effect. So, when γ is smaller than zero, a negative shock has a larger impact on the volatility of the daily returns than a positive shock of the same magnitude. The beta term β presents the impact of the GARCH term which measures to what extend the conditional variance is dependent upon its previous own lags. The value of the GARCH term indicates the level of volatility for the respective index.
Table 3: Conditional Variance of stock indexes
Index Period 𝝎 𝜶 𝜸 1 FTSE Pre -0.211*** 0.196*** -0.157*** 0.901*** (0.039) (0.048) (0.026) (0.021) Between 0.029 -0.011 -0.232*** 0.965*** (0.027) (0.032) (0.039) (0.014) Post 0.207*** -0.280*** -0.279*** 0.973*** (0.022) (0.005) (0.077) (0.000) AEX Pre -0.134*** 0.146*** -0.201*** 0.913*** (0.031) (0.039) (0.027) (0.019) Between 0.112*** -0.116*** -0.186*** 0.973*** (0.027) (0.029) (0.029) (0.000) Post 0.266** -0.370*** -0.230* 0.935*** (0.000) (0.204) (0.000) (0.000) DAX Pre -0.102*** 0.143*** -0.142*** 0.913*** (0.033) (0.045) (0.031) (0.025) Between 0.177*** -0.161*** -0.139*** 0.948*** (0.022) (0.027) (0.031) (0.000) Post 0.305*** -0.407*** -0.184 0.930*** (0.000) (0.000) (0.131) (0.000) CAC Pre -0.069*** 0.095*** -0.210*** 0.916*** (0.026) (0.033) (0.029) (0.018) Between 0.110*** -0.089** -0.242*** 0.942*** (0.035) (0.037) (0.043) (0.014) Post -0.218 0.628*** 0.135 -0.355*** (0.273) (0.204) (0.183) (0.119) ISEQ Pre -0.095* 0.110* -0.102** 0.825*** (0.054) (0.063) (0.042) (0.080) Between 0.023 0.034 -0.276*** 0.863*** (0.068) (0.087) (0.062) (0.049) Post 0.229*** -0.333*** -0.008 0.940*** (0.022) (0.020) (0.076) (0.000)
The result of table 3 show that all beta’s test significant at a 1% level and almost all indexes in all time periods test a significant negative γ, which indicates the presence of leverage effects. Comparing the pre-Brexit period to the between Brexit period, it is presented that for all five indexes the presence of volatility increased significantly. This confirms the first research question (did the official Brexit referendum announcement resulted in an increase in volatility of the individual European Stock Indexes?) and, therefore, it can be stated that in the period after the official Brexit referendum announcement the level of volatility of the individual European Stock indexes increased. After the actual referendum, the beta values of the AEX and DAX decreased but remain higher than their initial value in the first period. The volatility of the FTSE and ISEQ increases even further in the last period. This partially confirms the second research question (were the individual European indexes more volatile before the actual Brexit referendum and less volatile afterward?) as some of the individual European indexes are more volatile before the actual Brexit referendum and less volatile afterward.
Table 4: Volatility spillover effects with FTSE as independent variable
Index Period 𝝎 𝜶 𝜸 𝜷𝟏𝒊 𝜷 𝟐 𝑭𝑻𝑺𝑬 AEX Pre -0.138*** 0.153*** -0.119*** 0.937*** -0.149*** (0.033) (0.042) (0.031) (0.015) (0.040) Between 0.088*** -0.099*** -0.123*** 0.985*** -0.050* (0.017) (0.025) (0.040) (0.000) (0.033) Post 0.241*** -0.309*** -0.176* 0.957*** -0.173*** (0.003) (0.001) (0.109) (0.000) (0.046) DAX Pre -0.098*** 0.135*** -0.056* 0.953*** -0.158*** (0.032) (0.042) (0.032) (0.016) (0.039) Between 0.148*** -0.142*** -0.128*** 0.962*** 0.003 (0.017) (0.024) (0.035) (0.000) (0.026) Post 0.246*** -0.315*** -0.162* 0.947*** -0.146*** (0.060) (0.091) (0.121) (0.000) (0.051) CAC Pre -0.084*** 0.112*** -0.136*** 0.937*** -0.123*** (0.028) (0.036) (0.034) (0.015) (0.039) Between 0.111*** -0.116*** -0.164*** 0.972*** -0.026 (0.038) (0.045) (0.033) (0.000) (0.039) Post -0.166 0.546** 0.180 -0.272** -0.141 (0.270) (0.255) (0.195) (0.137) (0.132) ISEQ Pre -0.053 0.065 -0.003 0.922*** -0.166*** (0.039) (0.048) (0.027) (0.030) (0.040) Between 0.085*** -0.098** -0.136*** 0.980*** -0.076** (0.034) (0.041) (0.044) (0.001) (0.033) Post 0.249*** -0.337*** -0.054 0.946*** -0.126** (0.019) (0.008) (0.075) (0.000) (0.054)
3.3 Volatility spillover effects using (E)GARCH Models
Table 4 provides the results with respect to the spillover effects between the FTSE and index i, with i being the DAX, CAC, AEX, or ISEQ. Table 5, meanwhile, offers the spillover effects between index i and the FTSE. The result of both table 4 and 5 are composed with the use of the extended EGARCH models of equation 4 and equation 5 respectively. Additional to the variables of the previous discussed EGARCH variables of table 3, the extended EGARCH models contain a second beta term β2. This metric β2 measures the impact of conditional
variance of the independent variable to the conditional variance of the dependent variable, which equals the amount of volatility spillover between two indexes.
Table 4 shows that during the pre-Brexit period all values measuring the volatility spillover effect have negative values and test significant on significance level of 1%. This indicates that for the pre-Brexit period, past shocks in the FTSE’s volatility had substantial impact on the volatility of the AEX, DAX, CAC, and ISEQ. In the between Brexit period there are only found significant negative spillover effects between the AEX and FTSE (-0.050) at a 10% significance level and between the ISEQ and FTSE (-0.076) at a 5% level. Post-Brexit, displays again highly significant negative values for volatility spill over effects between the indexes AEX, DAX, and ISEQ and the FTSE. Table 5 shows that for the pre-Brexit period similarly all values measuring the volatility spillover effect have negative values and test significant at with a minimum of 10%. In the in between period all spillover effects between the FTSE and the other indexes test significant and exhibit negative values. Post-Brexit, there are only low significant negative values for volatility spillover effects between the indexes the FTSE and DAX, and between the FTSE and ISEQ.
The results of table 4 and table 5 reveal that there are bidirectional spillover effects between the FTSE and the other indexes in the pre-Brexit period. In addition, the values of the spillover effects in this period have roughly the same value in both directions. However, the between Brexit period indicates single direction volatility spillover effects as there are almost no spillover effects from the FTSE towards the other indexes, only significant effects the other way around. For the post-Brexit period, there are again predominately singe direction spillover effects, however this time in the opposite direction. So, spillover effects for the indexes AEX, DAX, and ISEQ caused by previous values of the FTSE. In addition, both tables reveal that all beta’s 1 test significant at a 1% level and almost all indexes in all
Table 5: Volatility spillover effects with FTSE as dependent variable Index Period 𝝎 𝜶 𝜸 𝜷𝟏𝒊 𝜷𝟐𝑨𝑬𝑿 FTSE Pre -0.207*** 0.207*** -0.076*** 0.915*** -0.163*** (0.040) (0.049) (0.028) (0.016) (0.035) Between 0.065* -0.082** -0.086* 0.996*** -0.102*** (0.035) (0.038) (0.051) (0.000) (0.040) Post 0.207*** -0.284*** -0.266*** 0.968*** -0.037 (0.037) (0.010) (0.087) (0.000) (0.088) 𝜷𝟐𝑫𝑨𝑿 FTSE Pre -0.228*** 0.216*** -0.097*** 0.894*** -0.145*** (0.044) (0.052) (0.029) (0.019) (0.034) Between 0.018 -0.020 -0.093* 0.964*** -0.119*** (0.046) (0.057) (0.057) (0.013) (0.038) Post 0.236*** -0.338*** -0.234** 0.951*** -0.091* (0.030) (0.009) (0.106) (0.000) (0.055) 𝜷𝟐𝑪𝑨𝑪 Pre -0.203*** 0.200*** -0.080*** 0.918*** -0.152*** FTSE (0.041) (0.049) (0.028) (0.017) (0.033) Between 0.069* -0.093* -0.070* 0.993*** -0.114*** (0.043) (0.056) (0.040) (0.013) (0.041) Post 0.219*** -0.296*** -0.268*** 0.972*** -0.013 (0.000) (0.000) (0.103) (0.000) (0.035) 𝜷𝟐𝑰𝑺𝑬𝑸 FTSE Pre -0.219*** 0.209*** -0.142*** 0.899*** -0.053* (0.040) (0.049) (0.029) (0.020) (0.036) Between 0.087*** -0.095*** -0.168*** 0.989*** -0.050* (0.001) (0.003) (0.037) (0.009) (0.033) Post 0.231*** -0.323*** -0.267*** 0.957*** -0.026* (0.001) (0.000) (0.107) (0.000) (0.014)
Notes: Pre stands for the pre Brexit announcement period (21-01-2013 till 27-05-2015), Between for the period between the Brexit announcement and actual Brexit referendum (28-05-2015 till 22-06-2016), and Post for the period after the Brexit referendum (23-06-2016 till 01-11-2016). ω Being the intercept, γ the leverage effect, the ARCH term, and being the GARCH(1,1) term. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
These results confirm some volatility spillover effects between the AEX, DAX, CAC, and ISEQ and the FTSE. So, there is some first evidence that volatility spillover caused by a shock like Brexit in one market is transmitted to another market. In section 3.4 of this chapter the volatility spillover effects on the European stock markets as a whole system are studied.
3.4 Volatility spillover effects using DCC-MGARCH models
Table 6: DCC-MGARCH volatility spillover effects
Index Period 𝝎 ARCHi GARCHi FTSE AEX DAX CAC ISEQ
FTSE Pre 0.031*** 0.055*** 0.890*** -0.064*** -0.101** 0.053* -0.041 0.049** (0.010) (0.022) (0.032) (0.025) (0.046) (0.033) (0.039) (0.022) Between 0.042** 0.020 0.944*** 0.001 -0.158 -0.034 0.028 -0.051 (0.019) (0.023) (0.026) (0.068) (0.152) (0.078) (0.139) (0.065) Post 0.197* 0.261 0.519** 0.165 0.278* -0.181* 0.075 -0.359** (0.108) (0.277) (0.257) (0.119) (0.157) (0.098) (0.081) (0.140) AEX Pre 0.038*** 0.067*** 0.889*** -0.077** -0.108* -0.019 0.007 0.049** (0.013) (0.024) (0.027) (0.035) (0.060) (0.047) (0.061) (0.026) Between 0.092*** -0.019 0.971*** 0.098 -0.301* -0.276 0.217 0.085 (0.027) (0.019) (0.022) (0.105) (0.177) (0.116) (0.185) (0.073) Post 0.139 0.026 0.802*** 0.315 -0.338 -0.213* 0.187 -0.035 (0.105) (0.074) (0.156) (0.293) (0.347) (0.137) (0.405) (0.172) DAX Pre 0.027** 0.057*** 0.922*** -0.070** -0.110* 0.017 -0.097 0.104*** (0.014) (0.022) (0.025) (0.030) (0.069) (0.051) (0.069) (0.030) Between 0.124*** -0.030* 0.974*** 0.110 -0.070 -0.468*** 0.166 0.193 (0.004) (0.020) (0.021) (0.166) (0.218) (0.119) (0.171) (0.087) Post 0.070*** -0.001 0.938*** 0.319*** -0.489* -0.097 -0.216 0.195*** (0.018) (0.014) (0.016) (0.014) (0.266) (0.100) (0.330) (0.074) CAC Pre 0.047*** 0.040*** 0.922*** -0.106*** -0.037 -0.030 -0.126* 0.087*** (0.013) (0.017) (0.019) (0.044) (0.086) (0.054) (0.073) (0.026) Between 0.061* -0.038*** 1.007*** 0.140 -0.055 -0.299** 0.012 0.085 (0.033) (0.012) (0.000) (0.126) (0.208) (0.152) (0.195) (0.080) Post 0.257* 0.106 0.636*** 0.686*** -0.405 0.042 -0.010 -0.098 (0.147) (0.171) (0.229) (0.254) (0.465) (0.172) (0.415) (0.278) ISEQ Pre 0.023 0.027 0.953*** -0.121*** -0.051 0.000 0.024 0.016 (0.018) (0.019) (0.030) (0.046) (0.062) (0.044) (0.062) (0.024) Between 0.112 0.022 0.901*** -0.028 -0.088 -0.084 0.124 -0.144 (0.082) (0.029) (0.071) (0.152) (0.252) (0.130) (0.201) (0.104) Post 0.492 0.408 0.408 0.492 0.132 0.254 0.048 -0.537 (0.490) (0.370) (0.285) (0.842) (0.760) (0.771) (0.483) (0.486)
Notes: Pre stands for the pre-Brexit announcement period (21-01-2013 till 27-05-2015), Between for the period between the Brexit announcement and actual Brexit referendum (28-05-2015 till 22-06-2016), and Post for the period after the Brexit referendum (23-06-2016 till 01-11-2016). ω Being the intercept, Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
volatilities?) there are some spillover effects between two indexes depending on the period, based on the findings of table 4 and table 5. However, table 6 finds almost no spillover effects taken into account all the indexes and all the time periods. Therefore, the third research question cannot be confirmed which implicates that the official Brexit referendum announcement does not significantly affect the existing degree of spillover effects between European stock index volatilities. The fourth research question (was there a higher degree of spillover effects between European stock index volatilities before the actual Brexit referendum and less spillover effects afterwards?) is also rejected as results show that there is not a higher degree of spillover effects between European stock index volatilities before the actual Brexit referendum and a lower degree of spillover effects afterwards.
4. Robustness checks
To assess the robustness of the results of chapter 3 all the used EGARCH models were checked for autocorrelation in the residuals and remaining ARCH effects. The test for autocorrelation (or serial correlation) checks whether there is only a relationship between an error term and its immediately previous value. A significant Durbin-Watson statistic indicates the presence of serial correlation between the constant and the dependent variable, which is undesirable according to Brooks (2008). It’s also important to check the outcomes for heteroscedasticity, indicated by remaining ARCH effects. A significant R-squared value indicates the presence of remaining ARCH-effects which is also undesirable (Brooks, 2008). Appendix B provides all robustness checks for table 3, 4, and 5. In all cases, serial correlation and the presence of remaining ARCH effects can be rejected since all p values were above the ten percent level.
5. Discussion and Conclusion
5.1 IntroductionThis final chapter of my paper summarizes the results. Section 5.1 elaborates thoroughly on the results of chapter 3 and additionally discusses the limitations, the recommendations for future research, and the practicalities of the findings. Section 5.2 ends this research with a brief summary.
5.2 Discussion
The results of section 3.2 clearly point out the difference in the level of volatility for the FTSE, AEX, DAX, CAC, and ISEQ between the three time periods. In addition, for the FTSE, AEX, and DAX the second hypothesis holds as well. This means that the level of volatility increased after the Brexit announcement and decreased slightly after the actual referendum. These findings indicate that the Brexit announcement and the actual referendum have resulted into an increased level of uncertainty among investors. This is also in line with what was found in the literature; Volatility increase can be caused by investors who reacted rational to certain events and correct their trade portfolios to their risk preference accordingly (Barberis and Thaler, 2003). Or, the irrational behavioural traits of investors (Hirshleifer and Teoh, 2003; Peng and Xiong, 2006; Barber, Odean, and Zhu, 2009) explain the increased volatility movements over the time periods caused by new information and uncertainty.
Additionally, the results of the DCC-MGARCH model of table 6 do not suggest any spillover effects in the European stock market as a whole system.
There could be several reasons why there were found little spillover effects using the EGARCH models and almost no market wide effects using the multivariate DCC-MGARCH model. First, since the European economy is so interlinked due to its Single Trade Market, the shock caused by the announcement of the referendum and the actual referendum had an immediate impact on each of the used indexes. Therefore, the increase in volatility might not be the direct result of the past volatility movement of one of the other used indexes. It is likely that in this specific case; it would have been more appropriate to account the independent European indexes as a single European market. It is therefore recommended for further research to asses for volatility spillover effects between the European indexes and other global indexes like the S&P500 (United States), Nikkei225 (Japan), or SSE (China). Second, the data sample size for the second (268 observations) and third time period (91 observations) was significant smaller than the first period (578 observations). According to Brooks (2008) lager sample sizes leads to smaller coefficient standard errors and the more significant outcomes. For the last period, it was unfortunately not possible to gather more observations since the Brexit referendum is such a recent event. Overtime more observations will become available and it is recommended to for further research to check weather this has impact on the results. Third, the multivariate DCC-MGARCH regressions were performed using Eviews 9.5. This most recent version of Eviews does not provide the DCC model in their standard software package and therefore an add-in package was used. Before using this add-in, extensive research was performed with regard to its reliability and no peculiarities were found. However, since the complexity of the DCC-MGARCH model (Syriopoulos et al. 2015) there is a possibility for some inconsistencies. In addition, this extension only allowed for implementing five variables into the equation. Among other reasons it was therefore not possible to compare all major European stock indexes for volatility spillover effects in the entire European market.
increased amounts of volatility movement in each of the tested indexes. This is relevant since after Brexit the quiescence among EU members has not yet returned. There are other political parties in some of the EU countries which claim leaving is considered as an option. For investors, it thus is important to understand what the impact of such an event could have on the expected returns of their trading portfolio. Knowing the potential degree of volatility movement and spillover effects allows investor to make upfront adjustments accordingly to their risk and term preferences.
5.3 Summary
The goal of this paper is to gain deeper insights into the links between European stock market indexes FTSE, AEX, DAX, CAC, and ISEQ and the exit of the United Kingdom out of the European Union as of the 23th of June 2016. This paper studies the short-term impact on volatility and volatility spillovers effects on the European indexes with respect to the ‘pre-Brexit announcement’ period from 21-01-2013 till 27-05-2015 the ‘between ‘pre-Brexit announcement and actual Brexit referendum’ period from 28-05-2015 till 22-06-2016, and the ‘post Brexit referendum’ period from 23-06-2016 till 01-11-2016. Using the EGARCH model of Nelson (1991) I first performed analysis to assess whether there is any difference in the level of volatility for each of the five indexes between the three time periods. This resulted in the first research question to be confirmed as it was found that in the period after the official Brexit referendum announcement the level of volatility of the individual European Stock Indexes increased significantly. After the actual referendum, the volatility of the AEX and DAX decreased slightly and the FTSE and ISEQ increases even further in the last period. This partially confirmed the second research question as only the AEX and DAX were more volatile before the actual Brexit referendum and less volatile afterward.
volatility spillover effects between the five indexes as a whole system, which rejects the third research question. The fourth research question was also rejected as there was no indication for a higher degree of spillover effects between European stock index volatilities before the actual Brexit referendum and a lower degree of spillover effects afterwards.
It is likely that insignificant volatility spillover effects where a result of the strong interlinkage of the European economy due to its Single Trade Market. The shock caused by the announcement of the referendum and the actual referendum probably had an immediate impact on each of the used indexes. Further research should be performed to find this out.
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Appendix B: Diagnostic statistics
Diagnostics for Table 2
Index Period Observed R-Squared Probability
FTSE Total 74.98334 0.000 AEX Total 59.20139 0.000 DAX Total 29.11279 0.000 CAC Total 13.5397 0.000 SMI Total 131.6174 0.000 IBEX Total 1.83077 0.176 ISEQ Total 155.8858 0.000
Notes: Total stands for the total data sample (21-01-2013 till 01-11-2016). Probability < 0.05 indicates there are ARCH effects in residuals, thus heteroscedasticity is present.
Diagnostics for Table 3
Index Period Value’s Serial Correlation Value Remaining ARCH Effects FTSE pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 AEX pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 DAX pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 CAC pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 ISEQ pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100
Diagnostics for Table 4.
Index Period Value’s Serial Correlation Value Remaining ARCH Effects AEX-FTSE pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 DAX-FTSE pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 CAC-FTSE pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 ISEQ-FTSE pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100
Notes: Pre stands for the period before the Brexit announcement (21-01-2013 till 27-05-2015), Between for the period between the Brexit announcement and actual Brexit referendum (28-05-2015 till 22-06-2016), and Post for the period after the actual Brexit referendum (23-06-2016 till 01-11-2016). For serial correlation, a high p value indicates no serial correlation, for remaining arch effects in residuals (heteroscedasticity) a high p value indicates no remaining ARCH effects.
Diagnostics for Table 5.
Index Period Value’s Serial Correlation Value Remaining ARCH Effects FTSE- AEX pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 FTSE- DAX pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 FTSE-CAC pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100 FTSE- ISEQ pre p > 0.100 p > 0.100 between p > 0.100 p > 0.100 post p > 0.100 p > 0.100
