Stock Market Co-Movements – Contagion or Interdependence?
Raghunath “Newt” Ganugapati
Term Paper-ECON 718
Abstract
This paper examines the stock market co-movements in response to crisis. Contagion is defined as transmission of shocks from one country to other with higher intensity in response to crisis. The crisis could in general be transmitted in two different ways, either through cross country linkages or through a sudden change in these linkages of varying persistence. This nature of transmission mechanisms is important for policy makers to decide economic adjustments.
The goal is to establish the existence of contagion in a shock propagation mechanism between two countries and to distinguish it from interdependence and structural breaks .Standard tests report an increase in the cross market correlation coefficients following the period of crisis. In this paper the objective is to show that the measurement of cross market correlation using standard techniques and analysis is biased. The argument in this paper is that during a period of turmoil the stock market volatility increases causing the standard estimates of correlation coefficients to be biased upwards. After accounting for this heteroskedasticity and correcting the relevant test statistics it is shown that there is no visible change in the intensity of the shock propagation mechanism. The change in the biased correlation coefficients is a feature of interdependence between these countries. The scope of this definition mandates the requirement that the shift in linkages be temporary to distinguish “contagion” from a permanent shift in the transmission channels also referred to as “structural breaks”.
In this paper the focus is on the econometric problems in the estimation of the conditional and unconditional correlation coefficients and subsequently testing them for contagion. Citing the example of the mid October 1997 Hong Kong stock market crash and the events that followed (referred as East Asian crisis) it is observed that tests based on unadjusted correlation coefficients (to heteroskedasticity) show evidence for the possibility of the phenomenon of contagion, while the adjusted coefficients show no evidence supporting contagion, suggesting that high market co-movements are a continuation of strong cross market linkages. Rolling period moving averages are employed on the time series of stock market returns in different countries. An attempt has been made to discuss some econometric problems, explain the nature of assumptions and subsequently use OLS regression to estimate the correlation parameters between the stock market returns of different countries. The statistical significance of the estimated difference in the coefficients before and after the crisis is checked using t-statistics to show that after accounting for increased volatility, there is virtually no contagion.
1. Introduction
To illustrate the arguments that follow, let us start by considering a simple fair coin toss game you and your graduate advisor play over a Friday evening beer at the terrace. In the first game you flip the coin: heads lets you win the coin and tails, you lose it. The game is played either with a penny or a special $100 coin that the graduate school has procured for all such games. In the second game, you always flip a quarter coin but the graduate school promises you a payoff in this game that includes the payoff from the first game (say for simplicity assume it pays 10% of the outcome of the first game). When the first game is played with a penny, your return on the second game is a quarter plus or minus a tenth of penny. Therefore the outcome of the first game is almost negligible compared to the outcome of the second one and hence the two gambles have a correlation close to zero. On the other hand, assume that the first game is played with the $100 coin. The returns in the second game are the quarter plus or minus 10 dollars, enough to get a graduate student very excited. In this case the outcome of the second coin is negligible to the second gamble. The correlation between the two gambles is almost one. Now we have to understand that the propagation of shocks is always 10% from one gamble to the other, yet the correlation coefficient moves from close to zero to close to 1. When the variance of the first coin game is taken into account and is corrected for in the second one by decoupling the propagation relationship and accounting for the variance in the first game the two gambles which look coupled now would start looking more independent. A more econometric and academic formulation of this intuition is done in the following section.
Theories explaining international shock propagation mechanisms are based on multiple equilibrium frameworks. The regime shift is driven by a change in investor expectations. One popular theory is that the investors imperfectly recall past events. A crisis in one country would cause investors to recompute their priors and assign higher probabilities to bad states based on crisis history. The resulting downward co-movement in returns occurs due to the fact that memories are correlated across an event and that this generates volatility due to the movement of investment from one asset class to another. We must also bear in mind that there is hardly any change in the fundamental way in which the countries are related. International shock propagation mechanisms are strengthened during crisis and this shift is not driven by real economic linkages.
Stock market returns in East Asia fluctuated wildly in the later half of year 1997. One difficulty about the nature of this problem is that there is no single event that triggered this crisis to test for the presence of contagion. It started with the Indonesian and Thai markets crashing in around July 1997, however the press paid little attention to these events. There was hardly any panic in the world stock market markets to identify this as a source for contagion. Later the Honk-Kong Hang-Seng index crashed in Mid-October and an avid discussion began on the East Asian “crisis” and the possibility of contagion. Though there is a possibility that contagion occurred during other periods of time, or from the combined impact of turmoil in a group of East-Asian markets [1], for purposes of this paper I will focus on tests for contagion from Hong Kong across the rest of the world during the tumultuous period after the crash.
2. Econometric Framework and Methodology
For the econometric treatment in this paper, I make the assumption that the stock market returns are influenced by three factors
a) Aggregate shocks which affect the economic fundamentals of more than one country.
b) Country specific shocks which affect the economic fundamentals of other countries.
c) Shocks which are not explained by fundamentals and are categorized as pure contagion.
x i,,t = ai + biXt + giat + ei,t
where the term x i,,t on the left hand side of the equation represents stock prices in country ‘i’ at any time ‘t’ and the terms on right hand side represent constant terms, the stock prices in countries other than ‘i’, and the aggregate variable which affects all countries along with the idiosyncratic risk respectively with the relevant coefficients. The procedure outlined in this paper is to identify contagion based on the reduced form variant of the above equation. The idea is that if the cross country linkages do not change with time, the coefficients estimated for the above equation should remain the same for any length of period. In other words for the entire length of interval, the period before turmoil or the period immediately following the turmoil. The coefficients are forced to be equal across time and tests for significant variations in them are conducted. Further not all markets are open at the same time and this needs to be accounted for, for instance the Latin American markets (Mexico in our example) were not even open when the Hong Kong crash took place. They would only be reflected in the returns on the next trading day in Mexico. To account for this I incorporate rolling average two day returns. The aggregate variable in the above equation is taken as the US short term interest rate, considering that any aggregate crisis is usually reflected on the safe heaven and an adjustment to monetary policy by the Federal Reserve. Further there is also some evidence of auto correlation in the stock markets returns. Here the estimation of parameters is done using a lagged Vector of Auto Regression (VAR) model implemented in MATLAB.
where xtHK and xtj represents the rolling average two day returns in the Honk Kong and country ‘j’ respectively. The variable itUS represents the short term interest rates in US, f(L) and F(L) represents the vector of lags and ht is the vector of disturbances. A lag of five days to account for any within the week variations of trading patterns is assumed. Using these specification estimates for the coefficients, an OLS method for the entire period (period before turmoil and the period immediately following it), was employed. I use the asymptotic distribution of the standard, unadjusted correlation coefficient and as a first calculation this coefficient is not adjusted to account for the bias introduced by changing market volatility. Subsequently the adjustment to the correlation coefficients is derived to account for changing volatility and thereby this calculation is repeated. The test for contagion is done by testing if there is any significant increase in these coefficients during market turmoil. This is done by using a standard t-test with the null hypothesis that the correlation during turmoil is less than or equal to the correlation estimated during the full period. The critical value for a t-test at 5% level is 1.65 which implies any test statistic greater than this value indicates contagion ‘C’ and a value less than this indicates no contagion ‘N’.
2b) Heteroskedasticity Correction to regression coefficients
Assume x and y are two stochastic variables and are trying to fit a linear relationship between them using the model
y,t = a + bxt + ei,t
Using standards OLS the assumptions for residuals would be
E(et)=0, E(et2)< ,and E(xtet )=0
Now divide the sample is such a way that the variance of xt is lower in the first group (l) and higher in the second group (h) since E(xtet)=0. By assumption OLS estimates are both consistent and efficient for both groups leading to bh=bl
Next define
Combining with
leads to,
Therefore,
The adjustment to the correlation coefficient to account for heteroskedasticity when the t-test is used is derived above. As can be seen the adjustment is an increasing function of delta, thus higher the volatility during a particular period the higher the estimates for correlation coefficient. These corrections have to be applied to the correlation coefficient for the full time period while performing the t-test.
3. Data Sample and Partitions
The data sample used is the daily values of aggregate stock market indices reported on “yahoo” (international finance section) from Jan 2nd 1996 to November 20th 1997. The very likely event that started the Asian crisis is identified as the Mid-October (October 17th 1997) Hong Kong market crash. The one month period following this is identified as the period of crisis while the period from Jan 1st 1996 to October 17th 1997 is identified as the period of relative stability(this relatively shorter length of period is used due to the fact that any structural change during this period would invalidate our test for contagion). The choice of parameters here looks capricious but the conclusions in this paper have been demonstrated to be robust in [1]. To account for the fact that all markets are not open at the same time we use the rolling average two day returns for our estimation. Some of the data had missing observations for national holidays in a specific country amongst other deviations, in such cases the previous days index was assumed. In some cases the data dating back to January 2nd 1996 could not be obtained and here the data starting Jan 3rd 1997 or the closest dates once could obtain were taken. The period of data is also summarized along with the results in table [1] and table [2]. The test for contagion is done for several East Asian countries as well as several countries across the globe. The countries included in this analysis are Japan, Indonesia, Korea, Malaysia, Taiwan, Singapore, Belgium, France, Amsterdam, Switzerland and Mexico. Using the MATLAB econometrics toolbox the estimation of coefficients is done for a VAR model with five lags. The t-statistics in MATLAB are normally quoted for the hypothesis that the coefficient for the total period is zero, however in our case this has to be done for the coefficient (obtained from regression) estimated for the total period on a country basis. Hence modification to the code was made. The code is attached at the end for reference.
4. Results and Conclusion
The unadjusted coefficients (biased) of regression for the total length of period, the period of relative stability and the period of turmoil and the corresponding t-statistics are shown in table [1] while the corresponding results after adjustments to correlation coefficients (discussed in previous sections) is shown in table [2]. There are several patterns that are apparent from these results: firstly cross market correlations increase during period of turmoil as expected. Hong Kong is strongly correlated with many of the other East Asian countries The t-tests indicate significant increase in unadjusted correlation coefficients during period of turmoil for all countries. According to interpretation in the literature this is consistent with the fact that contagion occurred to some extent during the East Asian crisis using an unadjusted correlation coefficient framework. In lieu of the central proposition of this paper the correlation coefficient might result from a bias due to increased market volatility and this does not constitute contagion.