No Contagion, Only Interdependence: Measuring Stock Market Comovements

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No Contagion, Only Interdependence Measuring
Stock Market Co-movements

• Kristen J. Forbes and Roberto Rigobon
• Journal of Finance, Vol. 57, 2002
• Presented By
• Saurin Patel
• Desautels Faculty of Management, McGill University

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Presentation Outline

• Motivation
• Literature Review
• Main Contribution
• Base Model and Evidence
• East Asian Crisis
• Mexican Peso Crisis
• Stock Market Crash 1987
• Caveats and Conclusions
• Other Methodologies

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Motivation

• East Asian Crises - 1997

4
Motivation

• Mexican Peso Crises - 1994

5
Motivation

• US Stock Market Crash - 1987

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Motivation

• Last two decades have witnessed series of
  financial and currency crisis
• Mexican peso collapse 1994
• East Asian crises 1997
• Russian and LTCM 1998
• Brazilian devaluation 1999
• IT bubble - 2000-01
• Sub-prime mortgage crisis 2007
• Aftermath of sub-prime mortgage crises Early
  2008 - ?
• Striking feature how an initial country-specific
  shock rapidly transmitted to markets of very
  different sizes and structures around the globe.

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What is Contagion?

• Despite huge literature to understand
  transmission of shocks from one country to
  another, there is little consensus on what
  exactly is Financial Contagion.
• Why?
• Consider, with Russian devaluation Brazilian
  stock market fell over 50 (different
  geographical region). Is this Contagion ?
• Polish currency (same geographical region)
  depreciated by 11 in the same month Or this is
  contagion?
• The point is even though Russia and Brazil are
  located in different geographic regions, have
  very different structures and have virtually no
  direct trade linkages there move together only in
  crises period.

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Definitions of Contagion

• Broad Definition World Bank
• Contagion is the cross-country transmission of
  shocks or the general cross-country spillover
  effects during crises periods.
• Restrictive Definition
• Contagion occurs when cross-country
  correlations increase during "crisis times"
  relative to correlations during "tranquil times.
  
• Forbes and Rigobon Definition
• ..as a significant increase in cross-market
  linkages (correlation coefficient) after a shock
  to one country.

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Definitions of Contagion

• The definition of Forbes and Rigobon (2002) has
  three important features
• It is only contagion, if cross-market co-movement
  increases significantly after the shock.
• It is only interdependence, if there is no
  significant increase in co-movement after the
  shock.
• It is comparison between tranquil and turmoil
  periods.
• Why use this restrictive definition ?
• Straight forward framework to test for
  contagion.
• Simple method of distinguishing between
  alternative explanations of how crises are
  transmitted across markets.
• This paper focuses only on tests for contagion
  based on cross-market correlation coefficients.

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Literature Review

• The empirical literature on testing financial
  contagion can be broadly categorized into four
  parts The test that uses
• Cross-market Correlation Coefficient test.
• King and Wadhwani (1990) Test for Contagion
  Oct 1987 Find evidence of Contagion.
• Lee and Kim (1993) Study 12 major markets,
  average weekly cross-market correlations Find
  evidence of contagion.
• Calvo and Reinhart (1996) Test for contagion
  between stock prices and Brady bonds after 1994
  Mexican crises Find evidence of contagion.
• ARCH and GARCH models
• Hamao, Masulis and Ng (1990) Test for Oct 1987
  and find evidence of price volatility
  spillovers between US-UK- Japan
• Edwards (1998) Mexican peso crises Find
  evidence for spillovers from Mexico to Argentina,
  but not from Mexico to Chile.

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Literature Review

• Co-integration Techniques.
• Longin and Solnik (1995) Test 7 OECD countries
  from 1960 -1990 and report that average
  correlations in stock market returns between US
  and other countries have increased.
• Direct estimation of specific transmission
  mechanisms.
• Eichengreen, Rose and Wyplosz (1996) Use binary
  probit model to predict the probability of crisis
  occurring in industrialized countries between
  1953-1993.
• Forbes (2000) tests for the impact of Russian
  and Mexican crises on stock returns of 10,000
  companies around the world.

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Main Contribution

• This paper shows that tests for contagion based
  on correlation coefficients are biased and
  inaccurate due to heteroskedasticity in market
  returns.
• It also provides a theoretical proof for the
  existence of bias and proposes a simple model to
  specify the magnitude of this bias and how to
  correct for it.
• Provides empirical evidence of this bias on
• East Asian Crises 1997
• Mexican Peso Crises 1994
• US Stock Market Crash 1987

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Bias in Correlation Coefficient Theory

• Assume x and y are stochastic variables.
• where
• Divide the sample in 2 groups L with low
  variance of xt, H with high variance of xt
• OLS estimators are consistent and efficient for
  both groups and

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Bias in Correlation Coefficient - Theory

• Variance of yt is given
• Now since the variance of residual is constant
  over the entire sample, increase in variance of
  yt is less than proportional to increase in
  variance of xt
• Correlation coefficient is

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Bias in Correlation Coefficient - Theory

• Therefore, test of change in cross-market
  correlation coefficient can be misleading. Thus
  are biased and conditional on the variance of x
• The conditional correlation is
• where
• Clearly, conditional correlation is increasing in
  d

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Bias in Correlation Coefficient - Theory

• Unconditional correlation is
• This has important direct implications on test
  for contagion.
• The conditional correlation coefficient will tend
  to increase after a crisis, even if the
  unconditional correlation coefficient is the same
  as during more stable periods.
• Thus, formal test for contagion might find
  significant increase in correlation coefficient
  after a crisis.

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Bias in Correlation Coefficient - Theory

• This proof of biasness is only valid if there are
  no exogenous global shocks and no feedback from
  stock market y to x.
• Graphically, HK-Philippines during 1997.

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Base Model

• VAR framework
• where xCt stock market return in crisis
  country
• xjt stock market return in another
  country j
• iCt short-term interest rate in crisis
  country
• iUSt short-term interest rate in US
• ijt short-term interest rate in another
  country j
• ?t residual terms

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Base Model

• First use VAR model to estimate the variance -
  covariance matrices for each pair of countries
  during
• Stable period
• Turmoil period
• Full sample period
• Then, use this variance-covariance matrices to
  calculate the cross-market correlation
  coefficients for each set of countries and
  periods.
• Use five lags for dependent variables to control
  for autocorrelation.
• Interest rates are included to account for
  aggregate macro economic shocks.

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Evidence

• Data source DataStream.
• Analysis of three main shock events
• East Asian crises
• Mexican peso crises
• 1987 Stock market crash
• For the first two events, sample includes 28
  different markets 24 largest markets plus
  Argentina, Chile, the Philippines and Russia.
• Stock market crash (1987) sample includes 10
  largest markets (due to illiquidity of markets at
  that time).
• Rolling-average two-day stock market returns are
  calculated and utilized to control for different
  operating hours.
• Returns are calculated in US dollars.

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Evidence I - East Asian Crises

• One difficulty with this shock event is that
  there is no single event that can be identified
  as clear catalyst behind this turmoil. For
  example,
• Thai markets sharply declined in June
• Indonesian market fell in August
• Hong Kong market crashed in mid-October
• They take Hong Kong crash (October) as reference
  point and define turmoil period as the month
  starting on October 17, 1997 and stable period as
  January 1, 1996 October 16, 1997.
• They use t-tests to evaluate if there is a
  significant increase in any correlation
  coefficient during the turmoil period.

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Evidence I - East Asian Crises

• Test the hypothesis

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Evidence - I

• Conditional Correlation
• Unconditional Correlation

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Evidence II Mexican Peso Crises

• In December 1994, the Mexican government suffered
  a balance of payment crisis, leading to
  devaluation of the peso and decline in Mexican
  stock market.
• Turmoil Period December 19 31, 1994
• Stable Period January 1, 1993 to December 31,
  1995 excluding the turmoil period.
• Repeat the procedure from the previous slides to
  estimate the variance-covariance matrix using VAR
  framework.

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Evidence II Mexican Peso Crises

• Conditional Correlation
• Unconditional Correlation

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Evidence III- 1987 Stock Market Crash

• They test for contagion for the 1987 Stock market
  crash in U.S.
• Turmoil Period October 17 December 4, 1987.
• Stable Period January , 1986 to October 17,
  1987.
• Focus on 10 largest stock markets.
• Repeat the estimation of variance-covariance
  matrix using VAR framework.

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Evidence III- 1987 Stock Market Crash

• Conditional Correlation
• Unconditional Correlation

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Caveats and Conclusions

• This paper suggests that cross-market correlation
  coefficient are biased if not adjusted for
  heteroskedasticity during crisis.
• The paper presents a method for correcting this
  bias based on the assumption of no omitted
  variables or endogeneity.
• Using three events- this paper shows existence of
  interdependence rather than contagion.
• Thus, the objective of this paper is to show that
  test based on conditional correlation coefficient
  can be misleading if not adjusted for biases.