SYSTEMIC RISK & CONTAGIONIN A

GLOBAL CONTEXT

Candidate No. 1607760

MSc FinanceBridgett Goebel

Supervisor: Prof. Alessio Sancetta

AbstractThe purpose of this paper observes the concept of systemic risk during periods of financial crisis. It will focus on analyzing connectedness between international markets by observing indexes from each. The paper uses econometric measurements of principal components analysis, and Granger-causality. By applying these measures to sets of weekly and daily returns of the indices of multiple national markets it is possible to measure market fragility and analyze contagion. The paper will demonstrate to observe the importance of financial crisis origin and how contagion and global market fragility impact the system as a whole. It also looks at individual global indices systemic importance and the causal relationships of each index between 1993 to 2010.

1

2

Introduction and motivationThe global financial crisis of 2007-2008 has presented a need to understand what systemic risk really is, how contagion applies, and how it may be measured and observed. It is also important to understand the elements that led to the crisis. Lack of oversight and regulation needed to prevent the crisis caused a systemic failure of the global financial system. Due to the crisis there is renewed interest in the stability of financial systems, both national and international. Although the global financial crisis is the worst in recent history triggered by systemic risk that originated from an established economy, similar crises have also been observed during the 1994 Mexican Peso crisis, the 1998 Russian financial crisis, and the 1997 Asian Financial Crisis. There is a problem understanding how shocks that originate in one financial system can propagate through one market to another on the international level. Systemic risk is more than just the downfall of a single institution or market. It is the susceptibility of financial instability spreading not only between institutions but also to different markets. It is the transmission of financial disorder between institutions, markets, or systems. The global crisis has many major policy implications. Institutions, policymakers and organizations, such as the SEC and PRA, are responsible for maintaining stability within the financial system without inhibiting the useful connectedness of the global markets. One factor resulting from the lack of oversight is the Dodd-Frank Wall Street Reform of 2010 that changed supervisory regulations of the Federal Reserve and SEC. This paper will demonstrate two econometric methods, previously

proposed1 to monitor the fragility, and connectedness of 18 equity indices from different country markets from 1993 to 2010. The data spans several crisis periods from different nations and economic development levels. The analysis will apply the principal components, and the Granger causality test to weekly and daily returns. This paper will include a literature review of systemic risk and contagion. Subsequent the review there will be an explanation of economic models and an overview of data used in the analysis. This data will include a summary statistics of the indices used in each econometric model, which precedes an analysis of the research finding. The analysis explores the question of measuring and monitoring global systemic risk, the transmission of risk from one market to another, and the systemic significance of each market upon another. In conclusion of the paper there is a summary and outline of the findings.

Literature review

1 The authors Billio, Getmansky, Lo, and Pelizzon (2010, and

Kritzman, Li, Page, and Rigobon (2010).

3

There are many definitions of systemic risk, but this paper will use the definition from Smaga (2014) “Systemic risk is the risk that a shock will result in such a significant materialization of imbalances that it will spread on a scale that impairs the functioning of the financial system and to the extent that it adversely affects the real economy”. Smaga (2014) analyzed the concept of systemic risk by review of prior articles that define this concept. He builds a “blue print” that classifies systemic risk process into accumulation, materialization and contagion. In Smaga’s paper he addresses the questions: How is systemic risk defined by central banks, what is the idea of systemic risk, what are the contributing factors, and what is contagion? Smaga’s study does not try to quantify and measure systemic risk, but Billio, Getmansky, Lo, and Pelizzon (2010) suggested two econometric measures, which will be used in this paper. These authors proposed principal components analysis (PCA) and Granger-causality to determine the interconnectedness of hedge funds, insurance companies, banks and broker’s monthly returns. They propose that statistical interactions of returns can bring forth information on the accumulation of systemic risk. In their paper the authors find that the four have become closely interconnected, associated with the insurance and financial sectors. Billio, Getmansky, Lo, and Pelizzon use these concepts to distinguish periods of financial crisis. Their evidence found that the majority of variation in returns is gathered in first and second principle components, with the first PC increasing thru periods of strain. Furthermore, the authors investigate contagion and the relationship direction in the monthly returns of hedge funds, insurance

companies, banks, and brokers. This study is accomplished through the use of Granger causality, which examines the relationships between time yt-1 and yt. The authors use Granger causality to analyze returns at two different levels, 1: Studied at a given period to find the causal relationships or 2: Relationship is studied in rolling windows of time periods to calculate the (DGC) dynamic Granger causality. Billio, Getmansky, Lo, and Pelizzon suggest that an increase in the DGC signals greater system interconnectedness. Using the methodology the authors continue their study by applying it to individual institutions to determine the “directional network”, finding nine different risk measures. Further study of Granger-causality extends to a nonlinear test suggested by Billio and Di Sanzo (2006), which observe relationships centered on the mean and volatility of the institutions. Kritzman, Li, Page, and Rigobon (2010) introduce another tool to measure systemic risk called the Absorption Ratio (AR) by means of principle components analysis. The authors define the AR ratio as “the fraction of the total variance of a set of assets explained or absorbed by a fixed number of eigenvectors”. With this ratio they can measure how tightly coupled the markets are by assessing the fragility. They imply that negative shock will promulgate quicker and more greatly with a more unified market than those that are more disparate. The authors use the AR ratio as a target to quantify the extent to which areas of risk are becoming more closely linked, it is not meant to be a determinant of financial turbulence, but an indicator of market fragility. Kritzman, Li, Page, and Rigobon accomplish this by applying the absorption ratio to markets, measuring changes in the AR. They monitor how

4

these changes correspond to price fluxuation in the asset, and the turbulence during that period. By studying the AR, evidence is found that the measures of systemic risk successfully computes the fragility in the market. Adrian and Brunnermeier (2010) propose another measure of “linkage” of financial crisis with conditional value-at-risk (CoVaR) of financial systems. The measure is conditional on the institution experiencing financial distress. Although this theory is not tested in this paper, it lies within the ideas of determining a measure of systemic risk. The CoVaR measurement identifies risk of a specific systemically important institution. This institution is inter-related and big enough to cause contagion and negative impact to other institutions. This is the thought behind “too big to fail.

Economic theory and econometric model

This section will break down the economic models and theories used to analyze the correlation, causality, and quantify the contribution to the systemic risk of different international indexes. The Absorption Ratio, derived from principle components analysis, is used to isolate periods of time when an index of foreign markets exhibited higher levels of correlation in returns. The Granger causality test examines the direction of correlations, looking at directional relationships and each index’s statistical significance to one another.Market Fragility

The goal of principal components analysis is to highlight variation and exposes patterns in the data. It does this by breaking down data into smaller uncorrelated linear variables (components). The number of components is equal to the number of original variables. Each component accounts for a percentage of the variability of the variable. The first component will account for the largest variability possible followed by the remaining components in descending order. To formally explain, let A be the covariance matrix of m index variables with n dimensions (returns). So the covariance matrix is defined as:

Anxn=(ai,j=cov(Idxi,Idxj)) (1)

In order to calculate principal component the eigenvectors and eigenvalues of the covariance matrix of A must be fround. Eigenvalues and eigenvectors for Anxn are the scalars λ and vectors xnx1≠0 that satisfy Ax=λx respectively. The distinct eigenvalues are denoted by σ(A)(1)2. Therefore:

is singular (2)

is the set of all eigenvectors associated with λ.

In eigenvector x, the eigenvalues λ represent the variation when the eigenvector is transformed by A from the eigenvalues calculated from the covariance matrix. The Absorption ratio (AR)(2) is calculated:

2Formulas interpreted from

http://www.ime.unicamp.br/~andreani/matrizes/capitulo7.pdf

5

AR (3)3

=Number of eigenvectors used to calculate AR

= Variance of eigenvector

= Variance of asset

The absorption ratio represents market fragility, if the AR is high then that the markets are more unified. Propagation In economics, testing variable causality is a vital issue, but also difficult due to the nature of social science. It is impossible to perform an experiment where the main factor under examination is isolated from other possible causes. The most challenging issues that arise are: 1. Correlation dose not implicitly mean causality. 2. The possibility of common factors that have been ignored. When these attributes are taken into account the causal relationship may not exist. As of yet there is no absolute answer to these issues, but through the use of Granger causality time series analysis, we can look at the unidirectional relationship of the cause, then effect. To understand Granger cause, is also important to know that “Cause” is not taken literally but a description of a statistically possible relationship of correlation. The word cause is meant as a linear prediction and only carries merit if one event occurs before another, i.e. finding an unidirectional Granger-causality. The test seeks to answer the question, “Are changes in Xt, a cause for changes in Yt”, by testing the null hypothesis: “Xt does not cause Yt, if for all h>0”

F (Y t+h|Ωt )=F ( y t+h|Ωt−X t ) (4)

3 Kritzman, Li, Page, and Rigobon (2010)

To specify, let F be the conditional distribution and Ωt-Xt contain all the data excluding Xt up to time t. To take a look at this theory assume a data set Ft=(y1t, y2t,., ynt)’ denoted by a (nx1) vector of time series variables. Showing this in the basic (VAR(p)) model form with estimated lag of (p) 4.

(5)F t=c+Π1 Ft−1+Π 2 F t−2+…+Π p Ft− p+εt ,t=1 , …, T

Πi is a (nxn) matrix of coefficients and εt

is a (nx1) matrix of white noise with zero mean that is unobservable or seen bellow as:

( y1 t

y2 t)=(c1

c2)+(π111 π12

1

π211 π22

1 )( y1 t−1

y2 t−1)+… (6)+(π11p π12

p

π21p π22

p )( y1 t−p

y2t−p)+(ε 1t

ε 2t)The VAR model informs us of a variable(s) forecasting ability to another variable(s) due to Granger Causality. If the variables y1 is useful in the prediction of the y2 variables then y1 is a causes of y2, if not, it then fails to Grange cause. When this is the case y1 fails for y2 when for all n > 0 the (MSE) Mean Square Error of y2,t+n forecast from (y2,t,y2,t-1,…) is identical in to the MSE of y2,t+n forecast from (y2,t,y2,t-1,…) and (y1,t,y1,t-1,…). For example, in (6) y2t would fail to Granger cause y1t when every coefficient Π1 to Πp

has a 0 for π12, giving a lower triangle for all Π coefficients. This means that all the lagged values of y2 are 0 for the y1t

equation. In reverse y1t fails when y1t

lagged values are 0 for the y2t equation. When testing multivariate models the same process can be used. This is suggested in the data analysis while using the linear restrictions of the Wald statistical Granger test. When Xt causes Yt, this is called a causal unidirectional

4 Lag length may be estimated by (AIC) Akaike information Criterion, which measures the quality one statistical model against other models in the data set to provide model selection

6

relationship and Xt is strongly exogenous, but if Yt causes Xt there is bidirectional feedback. These relationships can be used to break down information into certain measures such as the Degree of Granger causality, number of connections and closeness. These measures are also outlined in Billio, Getmansky, Lo, and Pelizzon (2010).

Degree of Granger causalityDegree of Granger causality is a measurement of the percentage of statistical significant causal relationships that one index j carries against all other indexes, N(N-1). This formula considers the relationship that j Granger causes i, but not i Granger causes j.

DGC=∑j ≠i

N

( j→ i)

N (N−1)

(7)5

This measure, signifies that an event of a systemic event is more likely to occur when DGC is higher than the computed K threshold.6

Number of connections This measure calculates the level of systemic significance of a single index in a system denoted by S. The measure calculates three fractions 1. (# of Out), this is a fraction of the number of indexes granger caused by the observed index in the system. 2. (# of In), calculates the amount of financial systems that Granger cause the observed index. 3. (# of In+Out) is the sum of # of In + # of out relationships to a specific index.

5 Formulas for Degree of Granger causality, # of In, # of

Out, # of In + Out, and Closeness found in Billio, Getmansky, Lo, and Pelizzon (2010).6

K threshold is estimated at the 95th percentile of .055, 5.5% of the significant relationships in data observed

¿of Out= ( j→ S )|.DGC≥ K =∑i ≠ j

j →i ¿¿¿

(8)

¿of ∈¿ ( S→ j )|.DGC ≥ K=∑i ≠ j

i → j¿¿¿

(9)

¿of ∈+Out= ( j↔ S )|.DGC≥ K =∑i ≠ j

i→ j ¿¿¿

(10) ClosenessThis measure calculates the shortest path for a single index to reach all other accessible indexes in the system, which is averaged across all other indexes. There are several steps to this measure, the first is to isolate a weakly causally connected index of ji. This would be a path that includes k relationships to get C# relationships between j and i, to illustrate:j → k →i, Where j → k=1 ,∧k →i=1

C ji=∑ j→ k , k →iTherefore:

C js|.DGC ≥ K=∑i≠ j

C ji ( j c→

i)|.DGC≥ K

N−1

7

DataPrinciple Components Analysis DataIn researching this topic, the paper uses several different sets of data. The data is broken down into data sets for each period, and each period is assessed as its’ own analysis. Principal components uses daily returns from 18 market indexes starting the year 1993 ending in 2010. The data excludes secular and non-secular holidays and weekends observed by at least 50 percent of the markets to reduce error in correlation. During the assessed periods the data covers several periods of financial struggle, such as the Mexican Peso, Russian Financial, and the Global Financial Crisis. For the periods of Mexican Peso and Russian Ruble Financial Crisis, not all 18 indexes were used in the PCA to calculate the absorption ratio due to lack of information for some indexes. To eliminate error each period is treated as a separate analysis to look for similarities and changes. Analysis of the Mexican Peso crisis uses daily log returns of the S&P 500, CAC 40, All Ordinaries, TA-100, DAX, IPC MXX, SSE Composite Index, Hang Seng, S&P TSX/Composite, FTSE 250, Swiss Market, KLSE Composite from December 1993 to February 1996. Data for the Russian Crisis includes all the former indexes listed and the RTS.RS. For the final period of December 1999 to December 2010 all the proceeding indexes are used with the addition of Merval, KOSPI, JKSE, TWII, and S&P BSE SENSEX. Table 1 exhibits the period summary statistics of each index. The data in the table highlights the largest mean and standard deviation in green, with the smallest in yellow. All data for this test has been found in Finance.Yahoo database. .

8

Table 1 Principle Components Analysis

12/7/93 - 2/29/96 Mexican Peso Crisis

STATS S&P500 CAC40 AORD TA100 DAX MXX SSE Comp

HSI S&PTSX

FTSE 250

SSMI KLSE

Mean .024 -.007 .008 -.01 .012 .013 -.044 .011 .011 .013 .013 .003

SD .248 .462 .330 .732 .407 .871 1.589 .682 .255 .215 .368 .621

Min -.996 -1.506 -1.322 -3.577 -1.77 -3.276 -7.776 -2.891 -1.219 -.863 -1.387 -2.889

Max .917 1.387 1.075 3.23 1.399 3.664 12.534 2.48 .78 1.442 1.128 4.218

Skewness -.264 .058 -.011 -.23 -.284 .098 1.992 -.166 -.613 .003 -.268 .283

Kurtosis 4.362 3.015 3.65 6.933 3.891 5.397 19.357 4.909 5.287 7.559 3.698 9.045

Autocorr 0.02 -0.033 0.059 0.005 0.014 0.068 -0.042 0.037 0.133 0.218 0.009 0.121

Principle Components Analysis 3/1/96 - 11/30/99 Russian Ruble Crisis

STATS S&P500 CAC40 AORD TA100 DAX MXX SSE Comp

HSI S&PTSX

FTSE 250

SSMI KLSE RTSI

Mean .035 .044 .013 .033 .039 .035 .043 .015 .019 .017 .036 -.018 .02

SD .478 .567 .379 .577 .617 .792 .898 .924 .402 .268 .554 1.069 1.825

Min -3.089 -2.444 -3.235 -4.509 -2.801 -6.217 -4.533 -6.4 -2.768 -2.235 -2.271 -10.49 -13.556

Max 2.167 2.648 2.635 3.341 2.56 5.278 4.073 7.49 2.034 1.32 3.241 9.041 12.913

Skewness -.464 -.202 -.521 -.513 -.48 .009 -.437 .314 -.924 -1.256 -.256 .581 -.214

Kurtosis 7.608 5.268 11.027 10.523 5.405 12.046 7.705 13.2 9.545 11.563 6.17 26.625 15.385

Autocorr -0.035 0.035 -0.027 0.013 0.038 0.044 -0.08 -0.042 0.08 0.133 0.019 -0.104 -0.012

Principle Components Analysis 12/1/99 - 12/31/10 Market Crash of 2002 & Global Financial Crisis of 2007-2008

STATS S&P500 CAC40 AORD TA100 DAX MXX SSE Comp

HSI S&PTSX

FTSE 250

SSMI KLSE RTSI MERV

KOSPI

JKSE

TWII SPBSE

Mean -.002 -.005 .007 .016 .002 .028 .01 .006 .009 .01 -.002 .011 .042 .029 .011 .028 .002 .023SD .591 .678 .437 .573 .705 .643 .721 .711 .545 .487 .552 .465 1.038 .934 .77 .644 .681 .742Min -4.113 -4.113 -3.715 -4.576 -3.228 -3.59 -4.02 -5.899 -4.251 -2.925 -3.521 -6.761 -9.207 -

5.625-5.561 -4.757 -4.315 -5.129

Max 4.759 4.601 2.328 3.005 4.689 4.534 4.083 5.823 4.07 3.241 4.685 6.958 8.774 6.1 4.901 3.311 3.184 6.944Skewness -.112 .058 -.675 -.484 .0633 .045 -.066 -.048 -.638 -.291 .059 -.481 -.27 -.073 -.555 -.644 -.168 -.172Kurtosis 10.769 8.072 10.371 8.363 7.270 7.278 7.346 11.022 11.699 7.232 9.218 55.057 11.827 8.198 8.12 9.215 5.729 9.326Autocorr -0.091 -0.014 -0.002 -0.002 -0.023 0.078 -0.044 -0.038 -0.034 0.097 0.036 -0.054 0.08 0.03 0.003 0.074 0.006 0.006

9

Table 2 Granger Causality Period 1

1/1/98 - 3/31/01

Stats SP500 CAC40

AORD TA100 DAX MXX SSE Comp

HSI SPTSX

FTSE250

SSMI KLSE RTSI MERV JKSE TWII SPBSESEN

BOVESPA

Mean .05 .137 .044 .068 .074 .025 .148 .046 .032 .061 .035 .032 -.214 -.115 -.019 -.089 .0001 .093SD 1.196 1.346 .754 1.461 1.517 2.197 1.316 2.018 1.375 .889 1.255 2.209 4.117 2.233 2.494 1.878 1.864 2.438Min -4.836 -3.715 -1.991 -6.698 -6.115 -7.694 -3.672 -7.947 -5.107 -2.540 -6.358 -6.575 -14.816 -7.459 -7.754 -6.207 -5.799 -7.64Max 3.067 3.985 2.162 2.843 5.188 7.601 4.523 6.044 4.044 2.698 4.899 11.517 12.792 4.741 8.166 4.829 5.246 9.449Skewness -.369 .141 -.128 -.833 -.278 .085 .386 -.301 -.559 -.32 -.568 .98 -.144 -.342 .148 -.094 -.024 -.035Kurtosis 4.153 3.308 3.207 5.012 4.294 4.144 4.308 4.133 4.668 3.5444 7.339 7.414 3.963 3.55 4.723 3.519 3.773 4.742

Granger Causality Period 2 4/1/01 - 6/30/04Stats SP500 CAC4

0AORD TA100 DAX MXX SSE

CompHSI SPTS

XFTSE250

SSMI KLSE RTSI MERV JKSE TWII SPBSE BOVESPA

Mean -.008 -.087 .034 .116 -.096 .148 -.098 -.011 .028 .005 -.063 .064 .308 .199 .171 -.002 .069 .103SD 1.109 1.457 .65 1.244 1.782 1.153 1.169 1.312 .838 1.093 1.39 .978 1.854 2.616 1.382 1.753 1.416 1.992Min -5.085 -5.266 -2.291 -3.141 -6.045 -3.626 -3.538 -3.372 -2.912 -5.572 -5.165 -4.972 -7.02 -8.507 -4.031 -5.681 -5.313 -8.684Max 3.254 4.792 1.799 4.942 5.597 2.869 4.486 4.68 2.456 2.791 7.074 2.864 4.365 9.923 4.115 7.956 5.131 4.842Skewness -.546 -.256 -.371 .454 -.034 -.593 .371 .255 -.421 -.896 .205 -.701 -.571 .261 -.064 .293 -.601 -.754Kurtosis 5.811 3.962 4.05 4.783 3.7 4.145 4.858 3.276 4.119 6.472 8.147 7.574 4.095 4.46 3.259 5.951 5.488 4.7067

Granger Causality Period 3 7/1/04 - 9/30/07Stats SP500 CAC4

0AORD TA100 DAX MXX SSE

CompHSI SPTS

XFTSE250

SSMI KLSE RTSI MERV JKSE TWII SPBSE BOVESPA

Mean .078 .113 .16 .154 .172 .279 .347 .205 .13 .147 .12 .122 .333 .21 .296 .127 .321 .265SD .649 .81 .668 .964 .889 1.09 1.482 .941 .713 .843 .684 .759 1.604 .459 1.271 .9482 1.157 1.426Min -2.181 -2.346 -2.274 -3.875 -2.488 -3.912 -3.275 -2.896 -2.559 -3.182 -2.21 -4.218 -6.429 -4.484 -6.316 -4.295 -5.042 -3.585Max 1.513 1.992 3.081 2.362 2.448 2.751 5.75 5.089 1.539 2.513 2.037 2.889 4.584 3.69 5.032 3.106 2.962 3.799Skewness -.424 -.454 -.609 -.514 -.429 -.902 .382 .374 -.891 -1.075 -.407 -1.346 -.884 -.605 -1.01 -.873 -.832 -.436Kurtosis 3.538 3.405 6.798 4.015 3.483 4.644 4.179 7.108 4.159 5.868 4.465 11.23 5.047 4.001 8.222 6.141 5.259 3.214Granger Causality Period 4 10/1/07- 12/31/10Stats SP500 CAC4

0AORD TA100 DAX MXX SSE

Comp HSI SPTS

XFTSE250

SSMI KLSE RTSI MERV

JKSE

TWII SPBSE BOVESPA

Mean -0.05 -0.104 -0.078 0.028 -0.031 0.062 -0.174 -0.042 -0.012 0.012 -0.082 0.033 -0.04 0.122 0.122 -0.012 0.049 0.035SD 1.579 1.807 1.398 1.398 1.785 1.784 1.972 1.844 1.562 1.609 1.593 0.954 3.036 2.373 1.841 1.521 1.923 2.007Min -8.722 -10.879 -7.692 -5.508 -10.574 -7.786 -6.47 -7.737 -7.618 -7.173 -10.945 -3.684 -10.305 -13.542 -10.439 -4.89 -7.548 -9.695Max 4.932 5.399 3.518 4.572 6.489 8.069 6.056 4.938 5.566 4.517 5.717 2.462 14.848 7.883 4.74 4.087 5.72 7.315Skewness -.822 -1.347 -1.145 -.703 -1.101 -.015 -.066 -.354 -.958 -.668 -1.558 -.818 -.083 -1.458 -1.444 -.484 -.388 -.563Kurtosis 8.289 10.148 7.459 4.933 10.749 7.844 3.858 4.608 8.167 5.304 16.584 4.665 7.356 11.594 9.102 3.455 4.512 7.503Granger Causality All Periods 1/1/98 - 12/31/10Stats SP500 CAC4

0AORD TA100 DAX MXX SSE

CompHSI SPTS

XFTSE250

SSMI KLSE RTSI MERV JKSE TWII SPBSE BOVESPA

Mean 0.018 0.014 0.04 0.091 0.029 0.128 0.0551 0.049 0.044 0.056 0.002 0.063 0.097 0.104 0.141 0.006 .109 .124SD 1.18 1.404 0.923 1.278 1.538 1.621 1.526 1.587 1.175 1.149 1.276 1.35 2.838 2.213 1.811 1.565 1.623 1.996

10

Min -8.722 -10.879 -7.692 -6.698 -10.574 -7.786 -6.47 -7.947 -7.618 -7.173 -10.945 -6.575 -14.816 -13.542 -10.439 -6.207 -7.548 -9.695Max 4.932 5.399 3.518 4.942 6.489 8.069 6.056 6.044 5.566 4.517 7.073 11.517 14.848 9.923 8.166 7.955 5.72 9.449Skewness -0.775 -0.863 -1.266 -0.513 -0.607 -0.163 0.09 -0.291 -0.928 -0.844 -0.923 0.824 -0.383 -0.478 -0.472 -0.153 -0.414 -0.416Kurtosis 9.03 9.156 11.357 11.357 7.682 6.787 4.803 5.406 8.998 7.206 14.829 14.142 7.114 7.121 7.366 5.112 4.983 5.915

11

Granger Causality Test Data To examine granger causality data weekly returns are isolated from January 1998 to December 2010 of 18 indexes: S&P 500, FTSE 250, CAC 40, All Ordinaries, IPC, MXX, TA-100, Hang Seng, SSE Composite, S&P TSX/Composite, SWII, KLSE Composite, RTS.RS, MERVAL, DAX, JKSE, TWII, S&P BSESENSEX, and BOVESPA. When examining weekly data it is key to note the limitations. First, not all years contain 52 weeks, so statistical error can occur when segregating data. Second, floating holidays such as Thanksgiving Chinese New Year and Easter vary each year and effect the calculation of coefficients for the week. With that being said, the data is then broken into four periods of 39 months and a granger causality test is then used to assess the data. The dates used in Granger causality test cover the 2002 market crash and the global financial crisis of 2007-2008. The table highlights the highest and lowest mean and standard deviation in green and yellow, respectively. To find an analysis of each period’s summary statistics see Table 2. All data for this test has been collected from the financial database at Finance.Yahoo.

Analysis of DataData analysis will use the measures explained in Economic Theory and Economic Models to analyze the historical data pertaining to 18 indexes explained in the previous section. The paper will first explain the periods of financial crisis by means of principal components analysis, which is applied to the daily returns for the years of 1993 – 2010. Following this explanation of PCA is a break down of the findings from the Granger causality analysis. Fragility In Global ContextPrincipal components analysis is a study of the correlation between the variables. In this research it is the correlation of the variance of indexes. Systemic risk’s main theme is interconnectedness. This driving force is what leads to the ability of contagion from market to market. In Fig. 1, the PCA is used to gather information about the commonality of the indexes over the period of December 7th 1993 to September 1st 1999. It produces a three-month rolling absorption ratio that is broken in to two segments, using different data to calculate each segment. The second segment uses an additional index, RTS.RS with the

indexes used in the first segment. Each ratio is computed using the eigenvalues of around 15 percent of the indexes represented in the analysis. These absorption ratios are compared to the three-month average close price of indexes from the national market where a systemic crisis originated, the MXX (Mexico) and the RTS.RS (Russia). The data appears to suggest that the occurrence of each systemic event follows an increasing absorption ratio. It also proposes that the increase in AR is the followed by a decrease in both the MXX and the RTS.RS index. It is important to also note that an increase in the AR dose not imply a systemic crisis will occur, but is a tool that signifies increased commonality between markets. Fig 2 is much like Fig. 1, except the absorption ratio is calculated on a continuous six-month basis and is compared to the S&P 500. The S&P 500 is calculated on a six-month average index close price over the period of December 1, 1999 to December 1, 2010. As before in Fig 1, a trend proposes that a decline in S&P 500 close price and periods of systemic crisis begin following an increase in the absorption ratio. In Fig. 2 the graph illustrates an increase in the AR in periods December 2001 to June 2002 and June 2005 to December 2007. The 2002 market crash and the global financial crisis of 2007-2008 follow both increases, presented by the steep decline in index price. Figure 3 illustrates, through the use of an area graph, the proportion of variance explained by groups of components. When fewer components explain more of the variation of the sample it is a sign of interconnectedness in the variables of the sample. Throughout the periods leading up to the 2002 market crash and 2007-2008 global financial crisis build up occurred, so the majority of the variation was explained by the first few principal components. During the period of the 2002 crash the 1st and 2nd component explained 60% of the total variance in the sample. The increase in percentage of variation started in October 2001, climbing until June 2002, and then dropping until November 2005. From 2005 to June 2007 PC1 and PC2 started to accumulate variation percentage, topping out at 75 % of the total variance. Through these periods the first five PC’s explain 81% and 84% of total variance in June of 2002 and December of 2007, respectively. The build up of variation in principal components is

12

also visible for the periods of the Mexican Peso and Russian Ruble crisis in Fig. 3b and 3c. These graphs both demonstrate a pattern of few components explaining the majority of the total return variance, which as said before is linked to a

rise in interrelation of the indexes. Figure 3a displays an accumulation of 73% of total variance linked to PC1 as of June 1, 1994. Figure 3b displays an amassing of 69% of variation PC1 that preceded a steep decline it the RTS.RS.

Figure 1 Absorption ratio broken into two time periods, the second period contains additional index RTS.RS

13

Figure 3

Causal relationships and Granger Cause

14

Once again, the data is broken down into periods of 39-months, starting in January of 1998 ending in December of 2010. Table 4 displays the four-period break down and the explanation of findings of the Granger causal relationships tested at a threshold of 0.055, the 95th percentile. By viewing the chart it is easy to see that the total causal connections (Green Cells) increase from the first to the second period, 11 to 25, then decreasing in the third period to 17 followed by an increase to 58 during the fourth period. The total causal connections represent 3.59%, 8.17%, 5.56%, and 18.95% of the 306 possible connections. It is revealed that the total number of granger causal relationships has grown as time progressed, ending in an increase of more than double the starting period. Observing the measurements suggests that prior and during the times of historical financial crisis the indexes’ interconnectedness raises. This trend appears during January 1998 to March 2001 and October 2007 to December 2010. Systemic events such as the Dot.com, the market crash of 2002 and the global financial crisis of 2007-2008 are covered during these periods.Table 3

15

AUTOCORRELATIONS1/1/98- 3/31/01

4/1/01- 6/30/04

7/1/04- 9/30/07

10/1/07 - 12/31/10

SP500 -0.1654 0.1411 -0.0885 0.108CAC40 0.0056 0.0064 -0.1334 0.0818AORD -0.056 0.0714 -0.0378 0.0969TA100 -0.0319 -0.0093 -0.1814 0.1381DAX 0.0403 0.0519 -0.1052 0.0589MXX 0.0344 0.0967 -0.0294 0.0306SSE Composite 0.0283 0.0691 0.0602 -0.0438HSI 0.0326 -0.0379 -0.0223 0.0439SPTSXComposite -0.1094 0.0997 -0.0711 0.1175FTSE250 0.3009 0.1736 -0.0993 0.1059 SSMI 0.1136 -0.0388 -0.0112 -0.0203KLSE 0.0556 0.0641 -0.0275 0.0749RTSI 0.1499 0.0833 0.1273 0.1082MERV 0.1894 0.1237 -0.0656 0.0722JKSE -0.0391 0.0615 -0.1023 0.0167 TWII -0.0382 -0.0081 -0.0069 0.156 SPBSESEN 0.0394 0.0362 0.0464 -0.0654BOVESPA 0.0537 -0.1112 -0.1566 0.0086

Table 41/1/98- 3/31/01

Relationship DGC# OF OUT # OF IN # OF IN+OUT AVG. Closeness

SP500 1 0.33 1 5.88 1 5.88 2 5.88 5.88CAC 40 1 0.33 1 5.88 1 2.94 5.88TA - 100 2 0.65 2 11.76 2 5.88 7.84DAX 1 0.33 1 5.88 1 2.94 11.76SSE COMP 1 0.33 1 5.88 1 5.88 2 5.88 5.88

H.S.I 2 11.76 2 5.88SSMI 1 0.33 1 5.88 1 5.88 2 5.88 5.88KLSE 1 0.33 1 5.88 1 2.94 13.24

RTSI 0 1 5.88 1 2.94MERV 2 0.65 2 11.76 1 5.88 3 8.82 5.88JKSE 1 0.33 1 5.88 1 5.88 2 5.88 5.88

TWII 1 5.88 1 2.94

SPBSE 1 5.88 1 2.94

IBOVESPA 1 5.88 1 2.94

TOTAL 11 3.59 11 11 22Mean 0.40 7.19 6.47 4.62 18.14

4/1/01- 6/30/04

Relationships DGC# OF OUT # OF IN # OF IN+OUT AVG.Closeness

SP500 10 3.27 10 58.82 2 11.76 12 35.29 8.14CAC 40 4 1.31 4 23.53 1 5.88 5 14.71 9.80AORD 3 0.98 3 17.65 1 5.88 4 11.76 11.76TA - 100 1 5.88 1 2.94DAX 2 0.65 2 11.76 1 5.88 3 8.82 11.76MXX 1 0.33 1 5.88 1 2.94 5.88SSE COMP 1 0.33 1 5.88 1 2.94 5.88H.S.I 1 5.88 1 2.94

SPTSX 3 17.65 3 8.82FTSE 250 1 0.33 1 5.88 3 17.65 4 11.76 8.82SSMI 1 0.33 1 5.88 4 23.53 5 14.71 5.88

RTSI 1 5.88 1 2.94

MERV 3 17.65 3 8.82JKSE 1 0.33 1 5.88 1 2.94 5.88

TWII 2 11.76 2 5.88SPBSE 1 0.33 1 5.88 1 5.88 2 5.88 5.88

IBOVESPA 1 5.88 1 2.94

TOTAL 25 8.17 25 25 50Mean 0.82 14.71 10.50 8.65 7.97

7/1/04- 9/30/07Relationships DGC # OF # OF IN # OF IN+OUT AVG.Closeness

16

OUTSP500 1 0.33 1 5.88 2 11.76 3 8.82 16.18

CAC 40 1 5.88 1 2.94

AORD 1 5.88 1 2.94TA - 100 1 0.33 1 5.88 1 5.88 2 5.88 11.76DAX 2 11.76 2 5.88MXX 6 1.96 6 35.29 1 5.88 7 20.59 7.35SSE COMP 1 0.33 1 5.88 1 2.94 5.88

H.S.I 1 5.88 1 2.94SPTSX 1 0.33 1 5.88 2 11.76 3 8.82 5.88

SSMI 1 5.88 1 2.94

MERV 2 11.76 2 5.88JKSE 6 1.96 6 35.29 6 17.65 11.27TWII 1 0.33 1 5.88 1 5.88 2 5.88 5.88

SPBSE 1 5.88 1 2.94

IBOVESPA 1 5.88 1 2.94

TOTAL 17 5.56 17 17 34Mean 0.79 14.29 7.69 6.67 9.17

10/1/07 - 12/31/10

Relationships DGC# OF OUT # OF IN # OF IN+OUT

SP500 14 4.58 14 82.35 1 5.88 15 44.12CAC 40 1 0.33 1 5.88 5 29.41 6 17.65AORD 2 0.65 2 11.76 3 17.65 5 14.71TA-100 5 1.63 5 29.41 2 11.76 7 20.59DAX 3 17.65 3 8.82MXX 6 35.29 6 17.56SSE Composite 1 0.33 1 5.88 1 2.95H.S.I 4 1.31 4 23.53 3 17.65 7 20.59 S&PTSX 2 11.76 2 5.88FTSE 250 1 0.33 1 5.88 3 17.65 4 11.76SSMI 8 2.61 8 47.06 4 23.53 12 35.29KLSE 1 0.33 1 5.88 2 11.76 3 8.82RTSI 5 1.63 5 29.41 3 17.65 8 23.53

MERV 13 4.25 13 76.47 3 17.65 16 47.06JKSE 2 0.65 2 11.76 6 35.29 8 25.53TWII 3 17.65 3 8.82SPBSESEN 1 0.33 1 5.88 3 17.65 4 11.76

BOVESPA 6 35.29 6 17.65Total (ALL) 58 18.95 58 58 116

Mean 1.24 26.24 20.07 20.20

The indexes are more interconnected in comparison to the third period where the global financial climate was relatively stable. The third period indicates a drop in connections to 17 at 5.56% of all total possible connections. By mid-2007, the number of connections increased dramatically from 17 to 58, at 18.95% of all possible connections for the period of the 2007-2008 financial crisis. Notice another trend in Table 4 by looking at the S&P 500, a U.S. based index, and the country of origin of the 2007-2008 financial crises. The number of In connections jumps from 1 in period 3, with a percentage of all In connections of 5.88, to 14, at 82.35% in period four. What this information means is that the S&P 500 at date t-1 is a cause “possible correlation” to 14 other indexes during time t.

Highlighted in yellow and blue in Table 4 sequentially, are the largest contributors to period total DGC and # of In connections. By using the Granger causality measure, it proposes that during the period of the market crash of 2002 and the global financial crisis the S&P 500 was extremely interconnected with other indexes. Meaning that it had significant impact on other indexes, but it appears that it was not influence by many others. By inspecting the # of In measures provided, it gives us the ability to determine that during the 2007-2008 Financial crisis, the indexes JKSE (Jakarta), BOVESPA (Brazil), and MXX IPC (Mexico) were the most greatly “influenced” (# of in) by other indexes. Figure 4 (a) represents a time line of the system variance determined by a GARCH (1,1) model. By comparing Fig. 4(a) to

17

Fig. 4(b), a time line of the four periods DGC in 39-month blocks, a ruff copy of the variance spikes and lulls appears. The figures insinuate that the variance and connections move together with some slight differences. Notice in Fig 4b, the percent of all possible connections in the third period is higher than the first period, when the variance in the first period is greater than the third period in Fig. 4a. This is due to the Granger test capturing events and of variables that are not defined in the analysis. Fig. 4(a)

Fig. 4(b)

Table 3 lists the index autocorrelations for each time period. Notice for that for periods one, two, and four, the majority of the index autocorrelations are positive. Furthermore, in period 3 during, a tranquil financial time, the autocorrelations are mostly negative. What the

autocorrelation suggests is that as more of the indexes’ autocorrelation is positive the more connected the global index system becomes. In the following Diagrams A: D is a demonstration of the directional Granger causal relationships.

Diagram A

Diagram B

Diagram C

18

Diagram D

When observing the diagrams one can see that from the first period to the last all indexes connectedness increases into the global financial crisis. By observing the measures of granger causality an inference can be made that in times of financial tension interconnectedness will be higher and increase the chance of financial contagion.

ConclusionThe global economy is a dynamic and ever changing system of connections. Over the past 23 years the system has become more interrelated due to globalization, and even more so during times of financial struggle. This paper reviews various risk measurements that attempt to quantify the level of systemic risk and observe contagion. By using the Principle components analysis it allows the observation of systemic risk by observing eigenvalues associated with the index returns variance. We use these eigenvalues to calculate the absorption ratio to analyze market fragility. When that absorption ratio is high it infers that the system is more susceptible to systemic events and shock, when low the system is not as interconnected and more stable. Therefore when the majority of the variance is observed in the first few principal components, it does not mean that there will be a systemic crisis. Through Figures 1 and 2 suggest that following spikes in the absorption ratio after a market shock there was a noticeable decline in index price. The research goes on to use Granger causality

analysis by analyzing 18 different weekly index returns to isolate specific relationships between the indexes. It labels statistic importance of each index by quantifying in measure of degree of Granger causality, number of in, number of out, number of in + out and closeness. These quantifying measures allow for us to monitor the historic trends of interconnectedness. By doing so give evidence that during financial strife the interconnectedness of the index system rises. With Granger causality, it is possible to create a web of relationships to monitor direct and weakly causal relationships, as seen in Diagram A-D. Due to the nature of risk, and that there are always events that are unpredictable (Black Swan), it is impossible to determine for sure through systemic measures that adverse events may occur. Globalization, trade, the freedom of people to make their own decisions, and the unexpected event prevents true measure for social science to isolate the main factor. Due to these limitations it is likely impossible to circumvent and avoid disruptions in the financial system caused by market shocks. Therefore in order to recognize times when a systematic event may occur it is important to monitor the global system closely by measures such as the ones outlined in this paper.

19

BibliographyMeyer, C. D. 2000 Matrix Analysis and Applied Linear Algebra Philadelphia, Pa Society for Industrial and Applied Mathematics, Page 489-498

Billio, M., Getmansky, M., Lo, A.W. and Pelizzon, L., 2012. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), pp.535-559.

Adrian, T. and Brunnermeier, M.K., 2011. CoVaR (No. w17454). National Bureau of Economic Research.

De Bandt, O. and Hartmann, P., 2000. Systemic risk: a survey, European Central Bank.

Jeong, D.H., Ziemkiewicz, C., Ribarsky, W., Chang, R. and Center, C.V., 2009. Understanding principal component analysis using a visual analytics tool. Charlotte visualization center, UNC Charlotte.

Smaga, P., 2014. The concept of systemic risk. Systemic Risk Centre Special Paper, (5).

Danielsson, J., James, K.R., Valenzuela, M. and Zer, I., 2016. Model risk of risk models, Journal of Financial Stability, 23, pp.79-91.

Toda, H.Y. and P.C.B. Phillips (1994) : “Vector Autoregressions and Causality: A Theoretical Overview and Simulation Study”, Econometric Reviews 13, 259-285.

Lütkepohl Helmut (2005) New introduction to multiple time series analysis. Berlin: New York.

Anon (2016) Akaike Information Criterion. Wikipedia. Available at:https://en.wikipedia.org/wiki/akaike_information_criterion (accessed 01/08/16)

Hamilton, J.D., 1994. Time series analysis (Vol. 2). Princeton: Princeton university press.

Anon (2016) Major World Indices - Yahoo! Finance. [Online] Available at: https://uk.finance.yahoo.com/intlindices?e=asia (accessed 15/ 06/ 16).

Danielsson, J., James, K.R., Valenzuela, M. and Zer, I., 2011. Model risk of systemic risk models. Jon Danielsson.

Cuadro-Sáez, L., Fratzscher, M. and Thimann, C., 2009. The transmission of emerging market shocks to global equity markets. Journal of Empirical Finance, 16(1), pp.2-17.

Lin, J., 2008, Notes on Causality, Institute of Economics Academia Sinica, National Chengchi University.

Pukthuanthong, K. and Roll, R., 2009. Global market integration: An alternative measure and its application. Journal of Financial Economics,94(2), pp.214-232.

Jeong, D.H., Ziemkiewicz, C., Ribarsky, W., Chang, R. and Center, C.V., 2009. Understanding principal component analysis using a visual analytics tool. Charlotte visualization center, UNC Charlotte.

Sidaoui, J., Ramos-Francia, M. and Cuadra, G., 2010. The global financial crisis and policy response in Mexico. BIS Papers No, 54, pp.279-298.

Bisias, D., Flood, M.D., Lo, A.W. and Valavanis, S., 2012. A survey of systemic risk analytics. US Department of Treasury, Office of Financial Research.

Toda, H.Y., and Phillips P.C. (1994), Vector Autoregressions and Causality: A theoretical Overview and SimulationStudy, Econometric Reviews 13, 259-285.

Bisias, D., Flood, M.D., Lo, A.W. and Valavanis, S., 2012. A survey of systemic risk analytics. US Department of Treasury, Office of Financial Research, (0001).

Brooks, C., 2008. Introductory Economics for Finance, 2nd , Cambridge University Press

AcknowledgementsAlessio Sancetta Joseph PalinRoyal Holloway Library Staff

20