Measuring equity movement synchronicity

Heterogeneous Contagion:

Measuring equity movement synchronicity

University of Groningen Faculty of Economics & Business

JEL code: G01, G15, F30, F36

Key words: financial contagion, synchronicity, financial crises ABSTRACT

This paper examines contagion effects within a sample of 14 European OECD countries for 13 crisis periods from 1990 until 2012. I use a relatively new type of co-movement metric named synchronicity to test for contagion within 3 subsamples. Within region results show contagion effects in 3 out of the 13 predefined crisis periods. Country results are mixed with only a full 14 country wide contagion effect for the Russian LTCM crisis. The industry sample shows heterogeneous contagion results among industries. Furthermore, this research provides the first steps in creating a better understanding of the synchronicity measure. It puts a doubt on any straight forward relationship between contagion and synchronicity.

* Martinus van der Wal (s1693670) is a Master of Science in Business Administration specialization Finance

Asset price co-movements across equity markets tend to increase during financial crises in comparison with more tranquil periods. These co-movements can be explained by the effect of economic and other fundamental linkages between markets, which can simultaneously affect equity markets to move in a similar direction: I call this interdependence. When this increase in co-movement cannot be explained by existing fundamentals, the literature speaks of contagion. More specifically, I define contagion as a significant increase in cross-market/stock linkages during a crisis caused by a shock to one country or group of countries.

These possible contagion effects are especially important to policy makers and investors. Contagion effects can destabilize financial markets when, for example, a crisis in one region rapidly expands to other regions due to increased equity co-movements. Chang and Majnoni (1999) point out that the effect of policy makers’ rescue packages strongly depends on the existence of contagion effects. Therefore a large extent of the recent research on contagion is fuelled by policy makers such as the DNB (Netherlands Central Bank) and ECB (European Central Bank), which focus on maintaining the stability within the international financial markets.

Co-movements between equity markets and stocks are also an important input for modern portfolio theory models. The optimal portfolio compositions during crisis periods are different from the compositions during tranquil periods as a result of contagion. Information about contagion can thus play a large role in the portfolio rebalancing or hedging efforts of portfolio investors.

The contagion literature has been rapidly expanding since the work of King and Wadhwani (1990), with the recent subprime crises acting as an extra catalyst for this growth. Nevertheless there is still no clear consensus about the definitions, causes and measurement methods for contagion. This paper tries to establish when and where contagion exists on a regional, national and industry basis using a new type of co-movement metric. It does not, however, focus on the causes of contagion.

movements or: volatility. This measure is originally developed by Morck Yeung and Yu (2000) and first applied to measure contagion effects by Mink and Mierau (2009). As this is a fairly new contagion measure, this paper tries to create a better understanding of the advantages but also possible disadvantages of this metric.

Secondly, this paper is the first to test for contagion effects using synchronicity on disaggregated samples of stock returns within national indices. Most of the existing literature on contagion analyses aggregated stock market indices. Studies on non-aggregated stock data are rare (Baur (2012)). Next to the disaggregated sample, I test for contagion within an aggregated sample of national equity indices. The use of both samples provides a more in depth view and robust approach to find contagion effects.

Third, this paper contributes to the still relatively small base of literature on industry contagion. I do this by testing for contagion effects within industry subsamples from the disaggregated stock data. Industry contagion is relevant for investors as some industries may prove to be less sensitive to contagion than others. The financial sector is seen as an important driver behind the subprime crisis. Knowing which industries are prone to contagion effects can help policy makers in assessing the contagion transmission mechanisms.

I use daily equity return data for 14 developed European countries over a period from 1990 until 2012 to measure for contagion effects. Within this timeframe I focus on 13 predefined crisis periods, including the recent subprime crisis, to test for contagion effects during these crises in comparison to tranquil periods.

This paper is organized as follows. The next section will present the literature review, elaborating on the definitions, causes and methodologies for measuring contagion. Section 2 and 3 focus on the methodology and the data. Due to the relatively new application of the synchronicity measure to measure contagion, section 4 will elaborate on some of the mathematical and statistical properties of the metric. Section 5 contains the results and the analysis of those results. The final section will summarize the findings and conclude.

I. Literature review

and Szeto (2009) and Mollah and Hartman (2012). These reviews show that the contagion literature is dictated by the development of methodology. Many papers explain their methodology to be their main contribution. They often apply their method on the data as a case study to test for different results from their newly developed methodology. The definition of contagion is at the core of every paper, combined with the methodology it explains to a large extent the difference in contagion results. Therefore subsection A will first give an overview of the main contagion definitions. Subsection B will follow with a description of the possible contagion causes. Subsection C will discuss the relevance of contagion for investors and policy makers and in the final section the main contagion models are discussed.

A. Contagion definitions

The contagion literature uses a broad range of definitions of contagion, as can be seen from the reviews from Forbes and Rigobon (2001), Rigobon (2002), Pericoli and Sbracia (2003). First a distinction needs to be made. Fundamental contagion refers to a cross market transmission of a shock (Calvo and Reinhart (1996)). Under this definition existing real and financial linkages cause co-movement between markets. In contrast Forbes and Rigobon (2002) classify fundamental contagion as regular interdependence and not as contagion. For the remainder of this paper I refer to interdependence as co-movement caused by fundamental and real linkages. Even though the range of contagion definitions is very broad, most definitions are based on only a few influential papers.

Forbes and Rigobon (2002) define contagion as an increase in cross-market linkages after a shock to one country or group of countries. This definition can be placed under the umbrella of shift contagion definitions. Shift contagion is defined as a shift in the strength of the transmission of shocks from one stock or market to another (Claessens and Forbes (2001)). Tests for shift contagion typically boil down to some sort of statistical test for the significance of any observed change in cross linkages between a stable period and a crisis period (Pappas, Ingham and Izzeldin (2012)).

shock, but defined as a set of trading days in which returns exceed a specific predefined threshold value.

The two previous definitions speak of contagion when it is apparent in a certain predefined period. Beaker, Harvey and Ng (2005) in contrast define contagion as a correlation over and above what one would expect form economic fundamentals. As a result contagion can be found along the full sample period. Dungey, Fry, González-Hermosillo and Martin (2004) find the differences between the definitions to be minor and under some conditions often equivalent. They argue that most papers work from the same definition with differences emerging due to the information and method used to detect contagion.

I define contagion as a significant increase in cross-market/stock linkages during a crisis caused by a shock to one country or group of countries. This definition is most similar to the definition of Forbes and Rigobon (2002) but differs on two points. First, including stocks as well as markets gives the opportunity to test for contagion within a more disaggregate sample in comparison to the often used aggregated market samples such as Forbes and Rigobon (2002), Corsetti, Pericoli and Sbracia (2005), Bekaert, Harvey and Ng (2005), Mink (2012) use. Second, I only speak of contagion when there is a significant increase purely during a crisis period. This is because of the possible effect of globalization on the cross-linkages between markets and stocks. Due to globalization interdependence between stocks and markets has increased over time (Berben and Jansen (2005), Briere, Chapelle and Szafarz (2012)). Basing the contagion only on the crisis period keeps it from measuring a globalization effect. However it could be reasoned that crises on itself are a catalyst of a globalizing and more interdependent international market.

There exists a great amount of literature on the possible contagion transmission mechanisms but Claessens and Forbes (2001) shows it is difficult to measure these mechanisms directly. I use this contagion definition because it avoids having to define and measure the precise transmission mechanisms behind a possible increase in cross market linkages. However to get a view of the possible causes of contagion, the following section will elaborate on these possible mechanisms. This paper will focus on finding evidence for the theories which predict an increase in cross market linkages versus those theories which state there is merely an effect of existing cross linkages.

B. Interdependence and contagion mechanisms

these fundamentals is one of the main topics under discussion within the contagion literature. Therefore I first discuss the fundamental linkages. In the second part I discuss the investor behaviour linkages and some of the main hypothesis for the existence of contagion are discussed. B.1. Fundamental causes of co-movement in financial markets

A sudden shift in commodity prices or a change in the EU interest rate can trigger large capital flows (Chuhan, Claessens and Mamingi (1998)). These shifts are referred to as common shocks and can lead to an increased co-movement in equity prices across markets. One of the most straightforward co-movement causes are trade links across markets. Glick and Rose (1999) show that trade linkages help explain cross-country correlation. In addition and especially relevant for our European sample Kaminsky and Reinhart (1998) find that countries sharing a common trade block are particularly susceptible to effects from member economies. Competitive devaluations can also be a channel of transmission. A sudden devaluation of one country can reduce the competitiveness of other countries. A game of competitive devaluation can cause a greater devaluation that required by any initial deterioration according to Corsetti, Pesenti and Roubini (1998).

Financial links can also play an important role in the co-movements between markets. Kaminsky and Reinhart (2000) identify that a common creditor might pull lending in a market when a real shock in another market has weakened its capital position. Gai, Haldane and Kapadia (2011) show by using a network model, that shocks can easily spread through the interbank network due to the large concentration and great complexity of these networks. These possible causes for increased co-movement have in common that these movements are transferred through existing fundamental linkages between markets.

B.2. Contagion causes emerging from investor behaviour

collateral value of leveraged investors; this leads them to sell part of their investment to meet margin calls. Adrian and Shin (2008) find evidence of a leverage cycle, where financial intermediaries have a high leverage during booms and low leverage during busts; as a result this would make them even more sensitive to equity price adjustments.

Incentive schemes of investors can be another way to explain possible contagion within this first type of investor behaviour. Suppose we have an investor who needs to equally divide her investments among two regions A and B and there is a sudden decline in region A which creates an unbalance. As a result the investors needs to rebalance by selling of stocks in region B and buying extra in region A. A decline in overall wealth may also alter the investors risk aversion leading to a different risk profile according to which the investor will rebalance her investments. Briere, Chapelle and Szafarz (2012) find a flight to quality during crises as investors move their capital to more save asset classes. Calvo and Mendoza (1998) and Kodes and Pritsker (1998) find that countries which are more open to the international financial market are more vulnerable to contagion as a result of these incentive and liquidity problems.

Information asymmetries may also be an important channel of contagion. For example, when region A is in distress and no clear information about possible distresses in region B is available, investors may falsely expect region B also to be in distress due to the lack of information. In case of an information constraint it may be optimal to follow other investors causing herding behaviour. Similar Goldstein (1998) was the first to develop the “wake-up call hypothesis”. It hypothesizes that once investors wake up due to a crisis in a specific region, they will avoid regions which hold the same characteristics as that region. Bekaert, Ehrmann, Fratzscher and Mehl (2011) find evidence for this hypothesis during the 2007 subprime crisis. Calvo and Mendoza (2000) show that when the costs to gather and process specific information becomes too high for an individual investor, the most rational decision for the investor is to follow other investors as this is the best information source at hand. This herding behaviour can even have a reputational cause as Kim and Wei (2002) show that the reputational risk for institutional investors is fairly high. As a result these investors may not dare to be the first mover and rather act according to other investors as their performance is reviewed in comparison to a market benchmark.

last to withdraw from a country in distress you may be left with a limited pool of foreign exchange reserves.

The last type of investor behaviour is caused by expected changes in “the rules of the game” within the financial markets. The Cyprian crisis of 2013 is an example of this. Confusion about the deposit guarantee scheme on bank savings during the bail-out of Cyprus caused for a simultaneous turbulence along the international financial markets. Furthermore, Dornbusch (1997) and Calvo (1998) and find evidence that the discussion about the international financial architecture following the Asia 1997 crisis triggered the turbulence in Brazil during 1998.

Overall investor behaviour and financial linkages are the most prominent in the explanations of contagion (Dungey and Tambakis (2005)). Nevertheless a thin line exists between the fundamental causes of co-movement and behavioural causes of contagion. When, for example, region A contaminates region B we would speak of contagion. If following up to this region B affects region C through its fundamental linkages we speak of interdependence. However, the total effect from region A to region C is marked as contagion because somewhere along the transmission channel cross linkages are strengthened.

C. Investors’ and Policy makers’ viewpoint

The two most important “contagion stakeholders” are investors and policy makers. The distinction between the two can be mainly made on their objectives. Investors are generally more concerned whether there are contagion effects and where they emerge in order to hedge their portfolios against the risks. Co-movements between stocks plays an important role in the portfolio balancing of an investor concerned with diversifying his portfolio, thus not only contagion but also the general interdependencies is of interest to them. Phylaktis and Xia (2009) and Baur (2012) focus on this investor viewpoint and find that contagion can have a serious effect on the optimal portfolio composition during crisis periods.

contagion in order to keep a crisis from destabilizing economies and markets. Chang and Majnoni (1999) study a wide spread of contagion types and policy tools and conclude that the effectiveness of international rescue packages strongly depends on the type of contagion to which a country is exposed.

D. Contagion models

I will give a brief overview of main models used within the contagion literature. From this I will give a more in depth view of the correlation and synchronicity models.

First, in case of a non-observable exogenous shock, like a change in beliefs of investors, latent factor models are used to test for contagion. A specific type of these models is the unanticipated shock model. Dungey, Fry, González-Hermosillo and Martin (2002, 2003) adopt this approach and find a significant effect for both the crisis caused by the fall of Long-Term Capital Management (LTCM) and the Russian crisis in 1998. Another type of these latent factor models are the multiple equilibrium models. Jeanne and Masson (2000) and Fratzscher (2003) use this approach applying a Markov switching model. They find contagion effects in a large number of the currency crises from 1986 to 1998.

A second broad type of models are the asymmetries and non-linearity models. These models test for non-linearity or asymmetries in transmission mechanisms between assets returns. Favero and Giavazzi (2002) apply such a model by filtering asset returns from interdependence using a vector autoregression (VAR) model and testing its residuals for non-normality and heteroskendasticity. They find non-linearity in the propagation of devaluation expectations among seven European countries over the period from 1988 to 1992. Bae, Karolyi and Stulz (2003) focus on the excess returns above certain threshold values which they call exceedence events. In their sample ranging from 1992 to 2000 they find various contagion effects within the US, Asia and Latin America regions.

The last broad category of contagion models are the so called co-movement models. These models test for a strengthening in co-movements among markets and/or stocks during crisis periods. I will give a more detailed view of these models as the synchronicity model used in this paper belongs to this type of models.

“leverage effect”, meaning that markets tend to be more volatile during negative shocks. Forbes and Rigobon (2002) show that this effect is of large impact and biases correlations. They define two subsets; one during high volatility (h) and one during low volatility (l). Defining a model of two asset markets they show that, even if the fundamental relationship between two markets does not change correlations are affected. The prove that an increase of volatility of return in the first asset market causes the correlation between both markets to become higher . To

correct for this they model a correlation conditional to the amount of volatility during the crisis and tranquil period. After applying this conditional correlation metric Forbes and Rigobon (2002) do not find any evidence of contagion during the 1994 Mexico and 1997 Asia crisis.

Building on this framework Corsetti Pericoli and Sbracia (2005) show that also the composition of variance has to be taken into account. They show that a relative increase of idiosyncratic variance in proportion to systemic variance during crisis periods biases the test of Forbes and Rigobon (2002) towards the null hypothesis of non-contagion. In contrast to Forbes and Rigobon (2002) they find some evidence of contagion during the 1997 Asia crisis.

Bekaert, Harvey and Ng (2005) take another approach and define an asset pricing factor model to control for the effects of fundamentals and volatility and test for increased correlations within the residuals of the model. They find contagion within the 1997 Asia crisis and no contagion during the 1994 Mexican crisis. Even though these methodologies commonly use market data, some papers test for contagion within industry subsamples. Phylaktis and Xia (2009) and Baur (2012) both apply the model of Bekaert, Harvey and Ng (2005) on industry subsamples and find contagion effects to be heterogeneous among industries.

A measure which directly incorporates the volatility characteristics in its estimation is the dynamic conditional correlation (DCC) model originally developed by Engle (2002). The DCC is estimated by the standardized residuals of a GARCH model. Also other explanatory variables can be included to control for exogenous changes. Since its introduction it has become a popular model and a common basis for contagion models, the IMF uses the measure as an indicator of cross market return correlation in their surveillance reports (IMF, 2008)1_.

A more unfamiliar type of co-movement measurement tools are the synchronicity measures. Originally Morck, Yeung and Yu (2000) developed two types of synchronicity measures. The first type is the of a regression in the following form:

(1)

Where i is the firm index, j a country market index, t time period, the domestic market index and the U.S. market return in local currency. The US stock market return is included to incorporate the co-movement caused by foreign fundaments. The of this regression tells how much of the variation in the firms’ stock can be explained by variation of local and US market. By calculating a weighted average, , given by equation (2), they create a measure that indicates the frequency in which stocks in a market move together with the domestic index and US market.

∑ ∑

(2)

Where is the sum of squared total variations between the predicted values of the regressions and the actual values. The is closely related to the correlation as it can also be defined as the coefficient of multiple correlation. This is the square of correlation coefficient between the predicted and the actual values of the dependent variable in a linear regression model that includes an intercept. Forbes and Rigobon (2002) show that pure correlations are biased by the characteristics of the volatility during crisis periods. The correlation related measure is therefore also exposed to this bias, because the measure incorporates the direction as well as the strength of the returns movements.

The second type of co-movement measure developed by Morck, Yeung and Yu (2000) only incorporates the direction of the stock price movement and is thus not exposed to this bias. It is calculated by estimating the percentage of stocks which move in a similar direction in a specific time period. The methodology section will elaborate on the exact estimation. Mink and Mierau (2009) and Mink (2012) are the first to apply this metric to test for contagion. And as Mink (2012) points out, the advantage of this metric is that it does not need to correct for the possible biases related to the strength of stock return movements.

II. Methodology

A. Synchronicity metric and hypotheses

Most methods for testing contagion, such as correlations, test for the strength as well as the direction of stock price movements. During crisis periods the volatility characteristics and thus the strength of the stock price movements often changes. As a result these correlation type metrics need to control for these changes in volatility characteristics during crisis periods. The model in equation (3) of Morck, Yeung and Yu (2000) only incorporates the direction of the movement and is not exposed to these volatility characteristics.

∑ [ ] ∑ (3)

In which T is the number of trading days in each period and and _{are the number of}

stocks or indices moving up and down. is the average value of and denotes the fraction of stocks or markets moving together over a specific period T in a specific universe j. The measure is bounded between 0.5 and 1, as at minimum 50% of the stocks or indices move in the same direction and at maximum all move in the same direction. The measure in equation (3) is the proxy I use to measure co-movement and is called synchronicity for the remainder of this paper.

To test for an increase in co-movement I compare the crisis period to its corresponding tranquil period synchronicity using a standard two sample t-test with equal variances assumed:

√ ₍₄₎ in which:

Here and are the crisis and tranquil period synchronicity, and their standard

deviations and and their corresponding period lengths in days. When the t-statistic exceeds

assumed. I apply this synchronicity metric to test for three alternative types of contagion. All three are based on a different universe j.

Test 1 Within region contagion:

Increased co-movement among national stock indices in a crisis period compared to a tranquil period.

The first within region synchronicity is based on universe j of national stock indices of European OECD countries. I test for contagion effects within the European region by comparing synchronicity between the national stock indices. Using aggregated stock index data is the most common approach in contagion literature, research on disaggregate stock data is very limited as Baur (2012) points out.

Test 2 Within country contagion:

Increased co–movement among stocks of a country in a crisis period compared to a tranquil period. The second approach is a within country synchronicity measure. It is based on a universe j of stocks within a national stock index of European OECD countries. This disaggregate measure has not yet been applied in the literature, nevertheless it has some attractive characteristics when testing for contagion effects in comparison to its counterpart based on aggregated data. National indices differ in composition, market size and stock selection criteria thus their underlying fundaments are different which makes cross comparison on an aggregated index basis restrictive. Also, valuable information is lost as stock index movement is an aggregation of separate stock movements. This is especially relevant for the synchronicity measure as it is only based in the direction of the movement. For example, an index can move up if all stocks in an index moving up, or if a large number of the stock slightly move down and some move up. Nevertheless both options would result in different conclusions towards contagion effects.

The within country synchronicity measure is not biased by the index or country characteristics, as it is constantly exposed to the same national index characteristics. Although this within country metric is based on national data, it measures international contagion. Because the source of a crisis is not often the country itself, any effect on synchronicity in this country can be seen as international “contamination” from the crisis source.

concerned with their international and local diversification needs, the within country measure has extra relevance. Policy makers can use it as well in order to get a better grasp on the local exposure and possible transmission mechanisms of contagion.

Test 3 Within industry contagion:

Increased co-movement among stocks within an industry in a crisis period compared to a tranquil period.

The third approach is the within industry synchronicity measure, based on the co-movement among stocks in ten Europe wide industries. I construct the measure by pooling the stocks from the individual national stock indices by their corresponding 1 digit ICB industries codes. This could put a country bias on this measure as some countries with a higher number of stocks may be more predominant than others in certain industry categories. However, as it is purely used to measure contagion within an industry this is no problem as this is partially inherent to the metric. For example the oil and gas industry sample may be dominated by Norwegian companies as many of these companies are placed in Norway.

The null hypothesis ( ) and alternative hypothesis ( ) for test 1-3 are given by:

Under the null hypothesis, the synchronicity during the crisis period is lower or equal to that of the tranquil period. This concludes that there is no contagion. Under the alternative hypothesis there is an increased synchronicity during the crisis period in comparison to the tranquil period. This indicates to the existence of increased co-movements or contagion. Based on the country bias I do not construct a disaggregate synchronicity measure for the whole European stock universe. Combining all stocks from the national indices would create an unbalanced sample biased towards countries with larger indices. As the metric would be used to measure within Europe contagion this bias makes it unsuitable for testing European contagion effects.

B. Tranquil and crisis period definitions

definitions can change the outcomes towards contagion. In the example of the Asian crisis Forbes and Rigobon (2002), Bekaert, Harvey and Ng (2005) and Essaadi, Jouini and Khallouli (2009) all use different time periods and come to different results. In defining the crisis period Essaadi, Jouini and Khallouli (2009) use a method from Bai and Perron (1998), identifying structural breaks in correlations. Bekaert, Harvey and Ng (2005) define the crisis periods by identifying a period of abnormal unexpected market returns. Forbes and Rigobon (2002) and Corsetti, Pericoli and Sbracia (2005) base their definition on specific ad-hoc crisis events. Nevertheless both end up with different period definitions as shown in Table II due to the varying perspectives on which events triggered and ended the Asian crisis.

Boyer and Loretan (1999) find an ex post selection bias as crisis periods are generally identified by high return volatility. Therefore, I use the predefined crisis periods of Briere, Chapelle and Szafarz (2012) as it has one of the most well developed crisis period definitions to my knowledge, based on a wide array literature on the fundamental determinants of crises.

Instead of limiting to one specific crisis period, the analysis is based on multiple crisis periods over the past twenty years. Conclusions towards contagion are often found to be strongly linked to the methodology used. Incorporating multiple crisis periods gives more power towards conclusions about the existence of contagion, as well as the usability of synchronicity for measuring contagion effects. Briere, Chapelle and Szafarz (2012) are one of the few who incorporate a large number of crisis periods in their analysis. In total they define 13 crisis periods from 1990 to 2012. Table I presents the precise definitions.

Table I Crisis definitions

Crisis* Code Type From Thru Days

EMS crisis 1992 EMS Currency 16/09/1992 01/08/1993 228

Bond crash 1994 BND Market crash 04/02/1994 03/11/1994 195

Mexico 1994 MEX Currency 20/12/1994 10/03/1995 59

Asia 1997 ASI Currency 02/07/1997 13/01/1998 140

Russia and LTCM

1998** RUS Sovereign debt + Corporate bankruptcy 17/08/1998 15/10/1998 44

Brazil 1999 BRA Currency 13/01/1999 31/01/1999 13

E-crash 2000 E20 Market crash 28/03/2000 14/04/2000 14

Argentina 2001 ARG Sovereign debt 01/10/2001 23/12/2001 60

11 September 2001 911 Confidence 11/09/2001 28/09/2001 14

Enron 2001 ENR Corporate bankruptcy 28/11/2001 31/12/2001 24

WorldCom 2002 WCO Corporate bankruptcy 25/06/2002 31/07/2002 27

Subprime 2007 S07 Housing market +

Corporate bankruptcy 08/02/2007 13/03/2007 24

Subprime 2008 S08 Housing market +

Corporate bankruptcy 07/09/2008 03/10/2009 280

Even though the crisis period definition is touched upon in virtually every contagion paper, there rarely exists any explicit discussion about the tranquil period definition. I develop three approaches based on the literature. Table II shows the tranquil periods used in research on the Asian crisis, and although the tranquil periods are very different, none of the papers gives a clear line of reasoning or approach for their tranquil period definition. The first tranquil period definition is based on Forbes and Rigobon(2002) and Corsetti, Pericoli and Sbracia (2005). They define a specific tranquil period before the crisis as tranquil period. Forbes and Rigobon(2002) are the only who control for longer tranquil periods, the results prove to be robust for different period lengths. The only clear reasoning for taking a pre-crisis tranquil period is when one sees crises as a catalyst for globalization. Possibly investors wake up during a crisis and see the interdependence between markets and act accordingly. This results in an increase in synchronicity during the crisis, but also afterwards as investors still keep an eye for this interdependence. In this case taking a pre-crisis period is most optimal as this is a good basis period in which investors have not woken up yet.

Table II

Tranquil and crisis period definitions for the Asia crisis

Literature Tranquil period definition* Control tranquil period** Basis crisis period*** Forbes et al. (2002) 01-01-96 to 16-10-97 01-01-95 to 16-10-97

01-01-93 to 16-10-97 17-10-97 to 16-11-97

Corsetti et al. (2005) 01-01-97 to 17-10-97 None 20-10-97 to 30-11-97

Bekaert et al. (2005) 01-01-86 to 31-12-98 None 01-04-97 to 01-10-98

Mink et al. (2012) 01-01-96 to 31-12-98 None 17-10-97 to 16-11-97

* The tranquil period definition used in the paper **The tranquil period definitions used to control for different periods specifications ***The main crisis period used in the paper

The second definition is based on Bekaert, Harvey and Ng (2005) and Mink (2012). They use their full sample period, including the predefined crisis period, as their tranquil period. Including the crisis period seems counterintuitive and no clear reasoning behind this approach is given in both papers. However, as long as the weight of the crisis period is not too high within the full tranquil sample the possible bias may be limited. For Bekaert, Harvey and Ng (2005) and Mink (2012) the crisis periods compose about 12% and 3% of the full sample tranquil periods. As I research multiple crises with different lengths the bias would be more pronounced for longer crises and therefore I will exclude crisis periods itself from any tranquil period.

treaties lowering trade barriers within Europe over the past 20 years. Therefore, I take a tranquil period consisting out of an equal period before and after the crisis period. This corrects for a possible overall increase in interdependence over time due to globalization. Table III gives the three dummies constructed for the different tranquil period definitions. The stable periods are selected using a period before crisis which is long enough to be robust but short enough not to incorporate too many globalization effects over time. Therefore, a period of one year or 261 trading days is chosen.

Table III

Tranquil period definitions

Dummy name Description tranquil period

DA (Full sample) Full sample period before and after the crisis period* DF (Before) 261 trading days before the crisis period*

DN (Before and after) 261 trading days before and 261 trading days after the crisis period*

* The dummy loads 0 during the defined tranquil period and 1 during the predefined crisis period. When the tranquil period overlaps with other predefined crisis periods these are excluded from the DA dummy. For the DF and DN dummy these periods are not included in the 261 trading days.

C. Filtering fundamental co-movements

Economic fundamentals can influence stocks and indices to simultaneously move in a similar direction and thus affect the synchronicity, while there are no real contagion effects. To correct for this I will use the approach of Mink (2012) using a VAR model to filter the returns from these fundamental movements.

The earlier research of King and Wadhwani (1990) assumes constant economic fundamentals over time, nevertheless Forbes and Rigobon (2002) refine this view and show that these fundamentals can be time-varying. They propose a correction to adjust the correlation metric, they use to measure to contagion, to incorporate these time varying characteristics. Corsetti, Pericoli and Sbracia (2005) build on this and show that the specification of the fundamentals is of large importance to assess what type of correlation adjustment is needed.

(5) (6)

Where is the national index or the MSCI Europe, included as an exogenous variable for the within country or within Europe sample. is the corresponding stock or index return. The residuals from the stock or index return, , are filtered from fundamental movement and are taken as the input for the synchronicity measure. Based on the approach of Mink (2012), I use a VAR containing 5 lags. This is to control for any trading patterns over the preceding 5 day week as I use daily return data.

III. Data

The research focuses on developed European countries. Less developed equity markets exhibit more synchronicity, as a result of lower information transparency according to Morck, Yeung and Yu (2000). Due to a lack of firm specific information, stock prices are more strongly based on fundamental and country specific information, resulting in a more synchronous movement between stocks. This information availability effect on synchronicity can be avoided by using countries which are marked as developed from the beginning of our sample period. I include European countries which are member of the OECD before the beginning of the sample period in 1990. Austria and Turkey are excluded due to a lack of data availability. The indices of Ireland and Luxemburg are excluded, because they consist of too few stocks which makes them unsuitable for the synchronicity metric as the synchronicity characteristics section will show. This leaves a total of 14 developed European countries in the sample.

Most of the indices use the market capitalization of the stock as the main criteria for index inclusion and exclusion. Nevertheless, there are significant differences in company size and index turnover rates. For example, the German DAX has a market capitalization of 598 billion2 _{and Greece} ASE has a market capitalization of only 32 billion3_{. This shows that the average market} capitalization of stock included in the DAX is about 37 times as high as that of a stock included in the ASE. The last column in Table IV shows the average yearly stock replacement within the index. It shows that also on the basis of rebalancing the indices differ. In Norway on average 21% of the OSE index is replaced each year, in contrast this is only 4% for the German DAX. These differences make cross country integration of this disaggregate data hard to interpret as a country index specifications bias will exhibit. Using the within country synchronicity measure keeps the research free from this possible bias.

Table IV

Descriptive statistics of countries and equity indices

Country Ticker Compustat TIC Index From Thru Stocks in index⁰ Stocks listed⁰⁰ Stock replacement⁰⁰⁰ Belgium BEL I3BEL001 BEL 20 31/12/90 31/10/12 20 50 6.8% Denmark DEN I3DNK002 OMX

Copenhagen 31/10/89 31/10/12 20 90 15.2% Germany GER I3DEU001 DAX 31/07/88 31/10/12 30 59 4.0% France FRA I3FRA001 CAC 31/12/87 31/10/12 40 91 5.1% Finland FIN I3FIN020 OMX Helsinki 29/04/88 31/10/12 25 103 13.0% Greece GRE I3GRC020 ASE 60 31/07/88 31/10/12 60 199 9.7% Italy ITA I3ITA027 MIB 30 31/12/92 29/05/09 30 107 15.1% Netherlands NLD I3NLD014 AEX 01/02/94 31/10/12 25 65 8.9% Norway NOR I3NOR004 OSE 30/10/00 31/10/12 25 88 21.0% Portugal POR I3PRT002 PSI 20 02/01/96 31/10/12 20 58 11.9% Spain SPA I3ESP005 IBEX 31/12/88 31/10/12 35 110 8.9% Sweden* SWE I3SWE004 OMX Stockholm 01/06/04 31/10/12 30 42 5.0% Switzerland SWI I3CHE018 SMI 30/06/88 31/10/12 25 52 4.5% United

Kingdom*

ENG I3GBR049 FTSE 100 01/01/96 31/10/12 100 327 14.2% Total 385 1114

*The index constituent data is retrieved from Thomson Reuters Datastream on a monthly exclusion and inclusion basis. ⁰The number of stocks listed in the index at any given date. ⁰⁰The total number of unique stocks ever listed within the sample period. ⁰⁰⁰The average yearly stock inclusion and exclusion rate as a percentage of the stocks listed in the index ((stocks in index / stocks listed) – 1)/ number of years of data.

All stock price data is retrieved in local currencies as proposed by Mink (2012). This is done to control for exchange rate fluctuations. If in contrast the prices would be denominated in one common currency, a sudden depreciation of this common currency against the local currency could falsely create the impression of increased stock price co-movement. All price data is converted to daily logarithmic returns data using the end of day prices. In case of a non-trading day, the return is calculated using the last known end price. Using daily returns is appropriate as all countries in the sample are exposed to the same time zone except the UK for which the one hour closing time difference is not assumed to have a strong effect on the data.

The resulting database of daily stock returns within the specific indices is used to construct the within country synchronicity measure. To control for national non-trading days, the days in which none of the stocks move are marked as non-trading day and excluded from the synchronicity. In total this results in the creation of 68,926 synchronicity data points of which the descriptive statistics are shown in Table V.

Table V

Descriptive statistics within country synchronicity

BEL Fjt DEN Fjt ENG Fjt FIN Fjt FRA Fjt GER Fjt GRE Fjt ITA Fjt NLD Fjt NOR Fjt POR Fjt SPA Fjt SWE Fjt SWI Fjt

N 5558 5850 4255 6187 6283 6176 4005 4167 4794 3065 4249 6111 2123 6103 Mean .715 .715 .700 .722 .739 .746 .729 .743 .727 .737 .708 .739 .767 .745 Med .700 .692 .685 .708 .735 .741 .714 .733 .714 .722 .684 .733 .767 .739 Std. .140 .143 .131 .143 .145 .146 .144 .145 .142 .147 .139 .142 .148 .146 Min .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Fjt is the synchronicity measure is shows the fraction of stocks within a national index moving together on a specific trading day. The variable is bounded within the minimum of 0.5 where 50% of the stocks move in the same direction and 1 where 100% of the stocks move in the same direction. The country codes can be found in Table IV.

To build the 14 country wide industry database, the companies are categorized by industry, ICB codes retrieved from Thomson Reuters Database service on basis of company tickers or by converting the company industry SIC codes retrieved from Compustat Global. The SIC codes are rearranged to their corresponding ICB codes using Thomson Reuters industry code conversion table. Using ICB industry categories makes the approach comparable to that of Baur (2012). The descriptive statistics for the 10 industries can be found in Table VI. The daily index price data is retrieved for the indices of the corresponding 14 countries used in de disaggregate sample. Based on these 14 index returns a within Europe synchronicity measure is build. Table A2 in the appendix gives the descriptive statistics.

Table VI

Descriptive statistics within industry synchronicity

Fjt BM Fjt CG Fjt CS Fjt FI Fjt HC Fjt IN Fjt OG Fjt TC Fjt TE Fjt UT N 6386 6423 6424 6409 6383 6411 6365 6231 6345 6381 Mean .711 .687 .693 .710 .700 .685 .762 .755 .756 .717 Median .692 .667 .673 .696 .667 .667 .750 .750 .739 .700 St. Dev. .140 .129 .131 .135 .139 .127 .164 .170 .172 .143 Minimum .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 Maximum 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Fjt is the synchronicity measure is shows the fraction of stocks moving together in an industry on a specific trading day. The industry codes can be found in Table A1 of the appendix.

IV. Synchronicity characteristics

using a simple 4 stock model I want to create some intuition behind the drivers of the synchronicity measure, and its ability to measure contagion effects.

A. Statistical properties of synchronicity

The underlying number of stocks has a predominant effect on synchronicity in two ways. First by the possible values the synchronicity measure can take. For example, a synchronicity measure made from three stocks can return two synchronicity values, 1 when all stocks move up or down and 2/3 when one stock moves in an opposite direction of the other two stocks. When the total number of stocks increase, the number of possible synchronicity values increase. The relation between the number of stocks and the possible synchronicity values is given by equation (7):

( ) (7)

In which is the number of stocks on which the synchronicity measure is based. The number of stocks also affects the minimum value the synchronicity can take when it is based on an odd number of stocks. From the previous example we could see that a synchronicity based on 3 stocks is truncated between 2/3 and 1. This is caused by the odd number of stocks. Equation (8) shows how the minimum synchronicity value depends on the number of stocks it is based on. For every even number of stocks the synchronicity is truncated between 1/2 and 1. For higher odd numbers of stocks the minimum synchronicity value also approaches 1/2 see equation (9).

⌈ ⌉ (8)

(

⌈ _⌉

) (9)

A second effect of the number of stocks is given by Morck Yeung and Yu (2000) in equation (10). The Law of large numbers dictates that, when the sign of the stock returns is randomly distributed, the synchronicity pushes to 1/2 when the numbers of stocks ( _{) increase:}

( ) ( ∑

) (10)

Markets containing fewer stocks may have higher synchronicity as each individual security is of higher importance to the market index, in contrast to markets with larger numbers of traded stocks. Morck, Yeung and Yu (2000) regress the log (number of stocks) against the synchronicity to correct for this market size effect. However, as this number of stocks is highly index related and thus country specific, controlling for this may lead to endogeneity problems. Regressing the synchronicity on the number of stocks may result in the number of stocks explaining country specific characteristics of synchronicity. This makes an extra case for the use of the within country synchronicity measure as it is constantly exposed to a similar number of stocks, nevertheless comparing within country synchronicity across different countries is not suitable without filtering for these market size effects.

B. Modelling synchronicity and its determinants

Building on these result, I further developed a simplistic model to show how stock return characteristics can influence the synchronicity. As crises are even often defined by strong negative returns and/or increasing volatility, it is relevant to know how this influences the synchronicity measure.

The model is based on a universe of 4 stocks. When making the assumption that a stock can either move up or down, a stock movement is binomial with a chance p of going down and 1-p of going up. I make a second assumption, that all stocks are exposed to the same probabilities, this makes it possible to create the following overview. Table VII shows an example in which there is an equal probability of 0.5 for up and downward movements.

Table VII

Four stock synchronicity model with p=0.5

Stocks

Combined

probability combinations Possible State of

movement SYNCH A B C D probability Total

100% down/up p p p p 1 _{0.5 0.5 0.5 0.5 0.0625 1} (1-p) (1-p) (1-p) (1-p) 0.125 0.5 0.5 0.5 0.5 0.0625 1 75% down/up p p p (1-p) 0.75 _{0.5 0.5 0.5 0.5 0.0625 4} (1-p) (1-p) (1-p) p 0.5 0.5 0.5 0.5 0.5 0.0625 4 50% down/up p p (1-p) (1-p) 0.5 _{0.5 0.5 0.5 0.5 0.0625 6} 0.375 E(SYNCH) 0.6875

The downward probability is p, SYNCH is the synchronicity. The table shows that in a universe of 4 stocks. There are 3 possible synchronicity values. Calculating the total probability for each value and multiplying it by its synchronicity value gives the expected synchronicity value given by E(SYNCH).

Multiplying the SYNCH values with their corresponding probabilities gives the total expected SYNCH. It shows that for a 4 stock universe with an equal probability of moving up or down the expected SYNCH is 0.6875.

By conducting a sensitivity analysis Table VIII shows that the expected synchronicity is sensitive to the underlying probability of the stocks moving downward.

Table VIII

Expected Synchronicity for different stock downward probabilities

Downward probabilities SYNCH value p = 0.5 p = 0.6 p = 0.7 1 P(SYNCH=1) 0.1250 0.1552 0.2482 0.75 P(SYNCH=0.75) 0.5000 0.4992 0.4872 0.5 P(SYNCH=0.5) 0.3750 0.3466 0.2646 E(SYNCH) 0.6875 0.7024 0.7459

The downward probability is p, SYNCH is the synchronicity. The table shows the expected synchronicity for three different downward probabilities. For every synchronicity value the corresponding cumulative probabilities are given.

synchronicity can also be affected by the possibly extra high probability of the stocks moving up in this period before the crisis. Many studies such as Forbes and Rigobon (2002) use a period before the crisis as a proxy for their tranquil period. The synchronicity value is indifferent between an up or downward stock movements. A downward probability of 0.6 results in an equal expected synchronicity value as with a downward probability of 0.4 as the upward probability is 1-0.4=0.6 and thus equal to the first downward probability.

Assuming that stock returns follow a lognormal distribution figure 1 displays several cumulative distributions functions. A value below 1 is a downward movement, thus the cumulative probability where a distribution line crosses the 1 line can be viewed as the downward probability of a stock with that distribution. First, very intuitively, the probability of downward movement increases when the mean return decreases, see lines 1 and 3. This is because the cumulative probability of a negative return becomes higher. The effect of the volatility on the probability dependents on the mean value. When the mean is equal to zero a change in volatility does not have any effect on the probability, see lines 1 and 2.

Figure 1. The graph displays multiple cumulative lognormal distribution functions against a 1 line. Any value

below 1 can be seen as a downward movement. Therefore the probability points at which the distribution lines and the 1 line intersect can be seen as the downward probability for that distribution.

However, when the mean return is negative a higher volatility lowers the downward probability, see line 3 and 4. In crisis periods the mean return is generally lower increasing the downward probability but the increased volatility you often find during crisis periods counteracts by lowering the downward probability.

The question remains, what could cause such a probability shift? Again let us look at it from the definition of contagion as a strengthening in cross linkages. Say we first add a fundamental

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pro ba bil it y 1

Cumulative lognormal distibutions

variable Y with an equal probability of being -1 or 1 on each trading day. Let us further assume that this fundamental variable influences the four stocks in the same way and the conditional probability is influenced in an equally strong but opposite way for both states of Y, see equation (11). { { | | | (11) where { | }

The average downward probability over time is equal to the original unconditional probability of going down:

This shows that taking daily versus weekly returns as an input for the synchronicity can make a large difference. The downward probabilities of the weekly returns may lay closer to P(D) as daily fundamental movements filter out over time.

What happens to the average synchronicity value depends on the original downward probability. The least synchronous state is with a down and upward probability of 0.5. And for every case in which up or downward probability moves further away from 0.5, the total synchronicity will increase.

Suppose P(D) = 0.5 at the beginning, than synchronicity will increase as in both states of Y because the downward probability will move further away from 0.5. However, suppose originally P(D) = 0.7 than synchronicity will increase when Y is 1 as the up and downward probabilities moves further away from 0.5. When Y is -1 the probabilities moves closer towards 0.5 resulting in a decreasing synchronicity, see equation (12). Overall the effect on the average synchronicity over time is more ambiguous in this case.

{ {

| | { _| |

(12)

previous example the effect on synchronicity depends on the original probabilities. Only departing from an original “steady state” in which P(D)=0.5, we can say that a rise in X causes an increase in synchronicity.

The assumptions that all stocks are exposed to equal probabilities and that a fundamental has a binomial and proportional effect are stringent and somewhat simplified. Nevertheless, these simplified models cast some serious doubt on any straightforward or linear relationship between contagion and synchronicity. Applying this probability framework on the data is beyond the scope of this paper, but it gives insight in the application of synchronicity as a contagion metric for further research.

V. Empirical findings and analysis

The results of the 3 different contagion tests are displayed in subsections A, B and C. In subsection D the effect of the tranquil period definition is analyzed. The fundamental filtering procedure is not applied as it did not prove to impact the results. Subsection E present robustness checks and elaborates on this fundamental filtering procedure. The final subsection explores the connection between contagion, synchronicity and crisis periods.

A. Within country synchronicity

Table IX shows the within country differences between the predefined tranquil and crisis periods synchronicity means. A significant increase of mean synchronicity during a crisis period is an indication of contagion and rejects . On the crisis axis is rejected at the 1% level for the Russian LTCM crisis as we see a significant synchronicity increase within all countries in Table IX. The only other two crises which also exhibit contagion effects within more than 50 percent of the countries are the Asia and WorldCom crises. is accepted for the Brazilian, E2000 and the first Subprime crisis in 2007 as in none of the countries a significant increase of synchronicity is found.

increase is marginal or negative for most countries in these short crisis periods. Shorter crises may not have the magnitude to affect other equity markets internationally. This is in line with the wakeup call hypothesis of Goldstein (1998) and flight to quality results of Briere, Chapelle and Szafarz (2012). As investors will not flight to quality or wake up on the first days / weeks of a crisis, but only when a crisis increases in magnitude. This could explain absence of contagion for these smaller crisis periods.

When comparing the results along the country axis, the results have to be interpreted with care, since not all countries have data along the full crisis periods sample. Therefore I base this analysis on the 8 countries for which data is available over the full 13 crisis periods. Denmark and Finland prove to be the most affected by contagion with 5 out of 13 contagion effects. Both Spain and Sweden are the least affected with 2 out of 13 contagion effects. Overall results are heterogonous on the country axis.

B. Within industry synchronicity

Table IX

Within country mean synchronicity difference and significance

Country 911 ARG ASI BND BRA E20 EMS ENR MEX RUS S07 S08 WCO

BEL 0.131 0.007 0.041 -0.012 -0.029 -0.008 -0.026 -0.005 0.003 0.052 -0.001 -0.024 0.110 3.749* 0.420 2.899* -0.958 -0.749 -0.205 -2.330 -0.159 0.171 2.420** -0.02 -2.223 4.190* DEN 0.086 -0.016 0.031 0.053 0.024 0.022 0.019 0.017 0.023 0.093 0.052 0.007 0.092 2.403** -0.930 2.290** 4.243* 0.597 0.641 1.602 0.588 1.188 4.115* 1.642 0.633 3.370* ENG 0.085 0.018 0.037 NA 0.026 -0.022 NA 0.014 NA 0.064 0.026 -0.017 0.109 2.563** 1.074 3.348* NA 0.822 -0.778 NA 0.537 NA 3.554* 0.891 -1.592 4.127* FIN 0.030 0.039 0.029 0.001 0.012 -0.045 0.038 0.059 -0.003 0.089 0.029 0.017 0.040 0.873 2.204** 2.116** 0.114 0.333 -1.397 3.251* 1.979** -0.174 4.195* 0.976 1.529 1.596 FRA 0.017 0.019 0.044 0.016 0.018 -0.052 -0.007 -0.009 0.040 0.059 -0.001 -0.012 0.068 0.468 1.036 3.307* 1.332 0.487 -1.661 -0.634 -0.309 2.120** 2.792* -0.046 -1.009 2.370** GER 0.039 0.023 0.044 0.005 -0.045 -0.055 -0.003 0.081 0.006 0.055 -0.029 0.008 0.039 1.037 1.230 3.326* 0.381 -1.224 -1.628 -0.226 2.668* 0.296 2.674* -0.943 0.764 1.423 GRE 0.061 0.011 0.024 NA -0.015 -0.048 NA -0.031 NA 0.114 0.011 -0.008 0.024 1.459 0.530 1.651*** NA -0.365 -1.125 NA -0.894 NA 4.918* 0.411 -0.743 0.808 ITA 0.083 0.048 0.004 0.026 0.031 -0.020 -0.000 0.045 0.039 0.090 0.032 -0.002 0.032 2.166** 2.446** 0.272 1.975** 0.754 -0.556 -0.023 1.376 1.918*** 3.940* 1.028 -0.149 1.146 NLD 0.055 0.036 0.048 0.025 0.001 -0.051 NA -0.017 0.015 0.067 0.006 0.001 0.085 1.547 2.054** 3.603* 1.882*** 0.016 -1.732 NA -0.588 0.785 3.278* 0.213 0.064 3.145* NOR 0.021 -0.031 NA NA -0.031 NA NA 0.027 NA NA 0.031 0.023 0.029 0.524 -1.602 NA NA -0.799 NA NA 0.88 NA NA 1.043 2.012** 0.983 POR 0.027 0.005 0.019 NA 0.015 -0.007 NA -0.050 NA 0.072 -0.003 -0.027 0.067 0.787 0.254 1.331 NA 0.380 -0.204 NA - 1.688 NA 3.154* -0.115 -2.445 2.681* SPA 0.053 0.031 0.020 0.014 0.015 -0.038 -0.017 0.064 0.031 0.065 0.004 -0.002 0.039 1.472 1.733*** 1.393 1.121 0.395 -1.120 -1.484 2.162** 1.610 2.838* 0.144 -0.227 1.468 SWE NA NA NA NA NA NA NA NA NA NA 0.020 0.013 NA NA NA NA NA NA NA NA NA NA NA 0.675 1.143 NA SWI 0.051 0.007 0.018 0.025 0.015 0.032 -0.011 -0.022 -0.004 0.085 -0.011 -0.016 0.084 1.333 0.361 1.275 1.954*** 0.395 0.906 -0.973 -0.665 -0.185 3.904* -0.358 -1.429 2.929* Total 13 13 12 9 13 12 8 13 9 12 14 14 13 5% 4 3 7 2 0 0 1 3 1 12 0 1 7

Every first row represents the mean synchronicity difference _{where is the crisis period synchronicity and is the tranquil period synchronicity. Every}

second row gives the corresponding t-statistic for this difference and the rejection of _{at the * 1%, * 5% and ***10% level. The last two rows}

Table X

Within industry mean synchronicity difference and significance

Sector 911 ARG ASI BND BRA E20 EMS ENR MEX RUS S07 S08 WCO 5%

BM 0.098 0.031 0.029 0.021 -0.026 -0.025 -0.038 -0.007 0.028 0.087 0.011 0.024 0.085 6 2.985* 1.856*** 2.419** 1.844*** -0.799 -0.887 -3.515 -0.249 1.565 4.512* 0.389 2.223** 3.377* CG 0.040 -0.004 0.027 0.018 0.024 -0.005 -0.041 0.008 0.023 0.095 0.041 -0.002 0.071 4 1.304 -0.241 2.447** 1.679*** 0.762 -0.203 -4.032 0.322 1.382 5.469* 1.535 -0.24 3.052* CS 0.041 0.022 0.036 0.005 0.030 0.015 -0.018 0.015 0.013 0.071 -0.011 -0.017 0.090 3 1.254 1.375 3.309* 0.428 1.023 0.551 -1.714 0.585 0.780 4.059* -0.421 -1.675 3.669* FI 0.097 0.043 0.026 0.000 0.023 -0.030 -0.026 0.011 0.022 0.113 0.012 -0.020 0.090 6 2.696* 2.372** 2.149** 0.005 0.666 -1.017 -2.676 0.399 1.355 5.797* 0.402 -1.834 3.317* HC 0.120 -0.005 0.042 0.004 0.045 -0.036 -0.040 0.004 0.002 0.052 -0.004 -0.003 0.088 5 3.77* -0.332 3.238* 0.309 1.191 -1.138 -3.332 0.160 0.113 2.472** -0.151 -0.270 3.604* IN 0.061 0.012 0.031 0.025 0.018 0.001 -0.030 0.008 0.022 0.093 0.010 0.012 0.086 6 2.105** 0.847 2.870* 2.430** 0.595 0.042 -3.324 0.352 1.478 5.384* 0.339 1.105 3.890* OG 0.068 0.058 0.044 0.013 0.024 0.046 -0.023 0.014 0.036 0.060 0.021 0.015 0.103 4 1.835*** 3.109* 3.105* 0.854 0.572 1.207 -1.673 0.458 1.450 2.554** 0.702 1.415 3.797* TC -0.021 0.008 0.017 -0.001 0.054 0.065 -0.020 -0.022 -0.039 0.084 -0.022 -0.010 0.088 2 -0.522 0.388 1.321 -0.063 1.383 1.677*** -1.195 -0.700 -1.69 3.884* -0.758 -0.863 3.163* TE 0.002 0.007 0.043 0.014 0.032 0.067 -0.018 -0.021 0.022 0.079 -0.002 -0.002 0.024 2 0.044 0.352 3.136* 0.840 0.866 1.791*** -1.080 -0.686 0.868 3.719* -0.077 -0.193 0.875 UT 0.058 -0.007 0.020 0.008 -0.007 -0.019 -0.012 -0.006 0.006 0.035 0.007 0.004 0.094 1 1.896*** -0.487 1.568 0.666 -0.199 -0.627 -1.064 -0.259 0.307 1.789*** 0.235 0.351 4.118* Sig 5% 4 2 8 1 0 0 0 0 0 9 0 1 9

Every first row represents the mean synchronicity difference _{where is the crisis period synchronicity and is the tranquil period synchronicity. Every}

second row gives the corresponding t-statistic for this difference and the rejection of _{at the * 1%, * 5% and ***10% level. The crisis period}

The result suggests a case of industry specific contagion originally defined by Kaufman (1994), where information about one or more firms in an industry adversely affects all other firms in that industry.

C. Within Europe synchronicity

As noted earlier, using the t-test for the aggregated national indices synchronicity may not be suitable due to the lower number of components underlying the synchronicity measure in combination with the short crisis samples. This shows in both short crisis samples of the 9/11 and WorldCom crisis. The t-test displayed in Table C1 in the appendix is not robust in comparison to the non-parametric Mann Whitney U test in Table XI for both crises.

Table XI

Within developed European countries indices synchronicity

Crisis ticker 911 ARG ASI BND BRA E20 EMS

Mean difference 0.055 0.032 0.017 0.037 -0.012 -0.036 -0.035

z-statistic (MW U) -1.197 -1.443 -1.454 -2.884* -0.223 -0.874 -2.271

Crisis ticker ENR MEX RUS S07 S08 WCO

Mean difference 0.036 0.039 0.096 0.015 0.003 0.047

z-statistic (Mann Whitney U) -1.101 1.929*** -4.23* -0.475 -0.469 -2.04**

Every first row represents the mean synchronicity difference _{where is the crisis period synchronicity and is the tranquil period synchronicity. Every second row gives the corresponding Mann Whitney U z-statistic for this}

difference and the rejection of _{at the * 1%, * 5% and ***10% level. The crisis period}

definitions are based on the DN coding, made up from 261 non crisis trading days before and after the predefined crisis period. The crisis symbols can be found in Table I.

Therefore I use the non-parametric test results for my analysis. The Russian LTCM crisis is rejected at a 1% level, combined with the within country results, this gives a strong evidence that the Russian LTCM crisis is affected by contagion. For the WorldCom, and 1994 bond crash, is rejected, even though the 1994 Bond crash crisis did not raise any strong contagion flags in the earlier within country sample. The EMS crisis exhibits a significant but negative effect on synchronicity and therefore cannot be rejected. Interesting to see is that even though both the within region and within country samples are based on different samples, both approaches complement each other. Basing the conclusions towards contagion on both approaches creates a more robust method in testing for contagion effects.

D. Tranquil period definitions and globalization effects

every crisis in comparison to the DF definition used by Forbes and Rigobon (2002). Using the DN approach in comparison to the DA approach, results in a lower number of contagion effects for 9 out of the 13 crisis samples. Thus both the DA and DF approach mainly overstate the number of contagion effects when comparing it to the DN approach.

Table XII

Significant within country synchronicity differences for different tranquil period definitions

Crisis ticker 911 ARG ASI BND BRA E20 EMS ENR MEX RUS S07 S08 WCO

Total countries 13 13 12 10 13 12 8 13 9 12 14 14 13 DA Significant difference at 5% 2 4 8 5 1 6 4 1 5 10 2 9 6 DN Significant difference at 5% 4 3 7 2 0 0 2 2 1 12 0 3 7 DF Significant difference at 5% 7 7 6 2 0 1 2 4 2 12 1 4 9

The first row represents the total number of countries for which data is available for every crisis period. The other rows give the number of significant rejections of _{at a 5% level for a specific tranquil}

period definition using a t-test. The tranquil period definitions and crisis definitions are given in Table III and Table I.

The support I gave earlier for using the DN definition instead of the DA or DF is that there might be an increased interdependence over time. Figure 2 supports this. The graph shows the yearly rolling average of the within Europe national indices sample. It shows that the synchronicity is not stationary but is increasing over time. This is in line with Berben and Jansen (2005) and Briere, Chapelle and Szafarz (2012) who find a significant globalization effect in the equity markets. The globalization effect creates extra interdependence and thus extra synchronicity between markets over time, as can be seen in Figure 2. The synchronicity measure is bounded to the upper value of 1. Therefore we can see a diminishing increase in the trend line. Resulting in less inference from this globalization bias on the contagion results as interdependence tends to become more stationary.

Figure 2. The horizontal axis represents the start date of every one year rolling average synchronicity. The thin

line is a polynomial trend line of the order 2. 0.65 0.7 0.75 0.8 0.85 0.9 s yncrh onicit y

Within Europe 1 year rolling average synchronocity