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Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht
Michael Smurfit Graduate Business School
University College Dub...
Introduction
This paper explores the changing magnitude of synchronised equity
index return correlations within the G7 sto...
Literature Review
Is correlation between financial markets stable through time?
Increasing correlation: Baele and Inghelbre...
Are capital markets more correlated during volatile periods?
Accumulated evidence that the correlations between financial
m...
What is the relationship between macroeconomic variables and
stock market volatility?
Schwert (1989); Hamilton and Lin (19...
Econometric Methods
Returns synchronisation: VMA method of Burns et al. (1998)
Dynamic correlations: DCC model of Engle (2...
Asynchronous Data Problem
Daily data are always measured from one point in time to the
same point 24 hours later
The time ...
Synchronising Returns
Consider synchronising MSCI France Index returns with the returns
on MSCI USA Index, which closes la...
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Following Burns et al. (1998) the unobserved component is
estimated using the linear projection of the observed
nonsynchro...
The expected price at t + 1 is also an unbiased estimator of the
synchronised price at t, provided that further changes in...
Galbraith et al (2002) show that M can be estimated based on a
vector autoregressive approximation of order p, VAR(p).
The...
By applying a VAR approximation, VMA coefficients from those of
the VAR can be obtained.
The VAR(p) model with p > 1 is fitte...
Dynamic Conditional Correlation Model
Assume that the n−vector of returns rt has a time-constant vector
of means µ and tim...
The covariance matrix is the quadratic product of the volatilities
and correlation matrix:
Ct = Diag[st]ΩtDiag[st]. (7)
st...
The model for Ωt proposed in Connor and Suurlaht (2013) is as
follows:
Ωt = Ω0 + mt−1(U − Ω0), for − 1 < mt−1 < 1 (8)
Let ...
Consider the average correlation at time t, found by averaging the
off-diagonal elements of the time-t correlation matrix:
...
As in Engle et al (2009), a linear structure is imposed on mt based
on a low-dimensional vector xt of explanatory variable...
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
Summary
For the full sample, empirical evidence shows that
G7 markets show a significant positive trend toward higher
inter...
Questions and comments welcome
Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
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Anita Suurlaht (UCD School of Business). Correlation Dynamics in the G7 Stock Markets

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Michael Smur t Graduate Business School
University College Dublin
Eesti Pank, February 2019

Published in: Economy & Finance
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Anita Suurlaht (UCD School of Business). Correlation Dynamics in the G7 Stock Markets

  1. 1. Correlation Dynamics in the G7 Stock Markets Anita Suurlaht Michael Smurfit Graduate Business School University College Dublin Eesti Pank, February 2019 Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  2. 2. Introduction This paper explores the changing magnitude of synchronised equity index return correlations within the G7 stock markets in response to dynamic variation in the economic environment in response to secular trends toward greater capital market integration Use synchronised daily returns of G7 stock market indices, January 1st 1980 - December 31st 2017 France, Germany, Italy, Japan, the United Kingdom, the United States, Canada Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  3. 3. Literature Review Is correlation between financial markets stable through time? Increasing correlation: Baele and Inghelbrecht (2010) - 1970’s to mid-2000’s within the developed markets; Christoffersen, Errunza, Jacobs, and Langlois (2012) - 1989 to 2009 Increasing return correlation only among the subsample of European stock markets: Bekaert, Hodrick, and Zhang (2009) - 1980 to 2005 No increasing trend in correlation except during market crashes: King, Sentana, and Wadhwani (1994) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  4. 4. Are capital markets more correlated during volatile periods? Accumulated evidence that the correlations between financial markets are significantly higher during period of volatile markets: Karolyi and Stulz (1996); Ang and Chen (2002); Longin and Solnik (1995); Capiello, Engle and Sheppard (2005) Do correlation levels vary in different states of financial markets? Correlation between capital markets is higher during bear markets than during bull markets: Erb, Harvey and Viskanta (1994); Longin and Solnik (2001); And and Chen (2002) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  5. 5. What is the relationship between macroeconomic variables and stock market volatility? Schwert (1989); Hamilton and Lin (1996); Paye (2012); Christiansen, Schmeling, and Schrimpf (2012) Asynchronous data problem Scholes and Williams (1977); Lo and MacKinlay (1990); Burns, Engle and Mezrich (1998); Martens and Poon (2001); Audrino and Buhlmann (2001) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  6. 6. Econometric Methods Returns synchronisation: VMA method of Burns et al. (1998) Dynamic correlations: DCC model of Engle (2002) with the univariate measure of multivariate correlation magnitude of Connor and Suurlaht (2013) Conditional volatilities: MIDAS-GARCH model of Engle, Colacito, Ghysels (2008) Detecting structural breaks: Splitting the sample into pre-crisis and crisis period Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  7. 7. Asynchronous Data Problem Daily data are always measured from one point in time to the same point 24 hours later The time of measurement differs between markets with different trading hours Any news that occurs in the market closing later will not show up in the closing prices of market that close earlier Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  8. 8. Synchronising Returns Consider synchronising MSCI France Index returns with the returns on MSCI USA Index, which closes later. The synchronised return on the French index can be defined as ˆrt = rt − εt−1 + εt (1) where rt is the observed, unsynchronised return on French index at t and εt is the return we would have observed from the closing time of French index at t to the closing time of MSCI USA Index at t. Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
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  10. 10. Following Burns et al. (1998) the unobserved component is estimated using the linear projection of the observed nonsynchronous return on the full information set of all recorded prices at time t.The synchronisation model is then a (VMA(1)) model: ˆrt = εt − Mεt−1 (2) where M is the moving average matrix and εt is the unpredictable part of returns from the perspective of time t − 1. The unsynchronised returns are defined as the change in the log of unsynchronised prices, rt = log(Pt) − log(Pt−1) and the synchronised returns are defined as the change in the log of synchronised prices, ˆrt = log( ˆPt) − log( ˆPt−1). Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  11. 11. The expected price at t + 1 is also an unbiased estimator of the synchronised price at t, provided that further changes in synchronised prices are unpredictable, i.e. log(Pt+1) = E(log(Pt+1) | It). Thus, the synchronised returns are given by ˆrt = Et(log(Pt+1)) − Et−1(log(Pt)) = Et(rt+1) − Et−1(rt) + log(Pt) − log(Pt−1) = Mεt − Mεt−1 + rt = εt − Mεt (3) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  12. 12. Galbraith et al (2002) show that M can be estimated based on a vector autoregressive approximation of order p, VAR(p). Therefore, M is estimated as follows. The VMA(1) is represented as the following infinite order VAR process rt = ∞ j=1 Bj rt−j + εt, (4) where the coefficients of the matrices Bj are given by B1 = M1 (5) Bj = −Bj−1M1 for j = 2, ... Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  13. 13. By applying a VAR approximation, VMA coefficients from those of the VAR can be obtained. The VAR(p) model with p > 1 is fitted by least squares. From the p estimated coefficient matrices of dimension N × N of the VAR representation rt = B1rt−1 + ... + Bprt−p + εt, N × N dimensional M is estimated by the relation ˆB1 = ˆM1 based on (5). In this application, VAR(2) was chosen. Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  14. 14. Dynamic Conditional Correlation Model Assume that the n−vector of returns rt has a time-constant vector of means µ and time-varying nonsingular covariance matrix Ct : ˆrt = µ + C 1/2 t ηt (6) where ηt is an i.i.d. mean-zero n−vector time series process with covariance matrix equal to the identity matrix. Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  15. 15. The covariance matrix is the quadratic product of the volatilities and correlation matrix: Ct = Diag[st]ΩtDiag[st]. (7) st = (σ1t, ..., σnt) is the n−vector of individual asset return volatilities Ωt = {Covt−1(rit/σit, rjt/σjt), i, j = 1, ..., n} is the returns correlation matrix Connor and Suurlaht(2013) propose a model for Ωt with a simple one dimensional state variable mt capturing the time variation in Ωt Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  16. 16. The model for Ωt proposed in Connor and Suurlaht (2013) is as follows: Ωt = Ω0 + mt−1(U − Ω0), for − 1 < mt−1 < 1 (8) Let U denote the nxn matrix consisting entirely of ones. Let Ω0 denote the time-constant unconditional correlation matrix: (Ω0)ij = cov0[ rit σit , rjt σjt ]i,j=1,..,n = E0[rt((Diag[st])−2 )rt] (9) The variable mt−1 must lie in the interval (−1, 1). To meet the condition that Ωt a positive linear combination of positive semi-definite matrices suppose that the following condition holds: 2Ω0 − U is strictly positive definite. (10) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  17. 17. Consider the average correlation at time t, found by averaging the off-diagonal elements of the time-t correlation matrix: avecorrt = 1 n(n − 1) i=j [Ωt]ij (11) Define the correlation ratio ratiot = avecorrt − avecorr0 1 − avecorr0 = mt (12) which combined with Ωt = Ω0 + mt−1(U − Ω0) provides a univariate measure of correlation dynamics in our model. Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  18. 18. As in Engle et al (2009), a linear structure is imposed on mt based on a low-dimensional vector xt of explanatory variables: ratiot = bxt (13) Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
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  29. 29. Summary For the full sample, empirical evidence shows that G7 markets show a significant positive trend toward higher inter-market correlations over the 1980-2017 period There is significant time-series autocorrelation in the magnitude of cross-market return correlations Correlations are higher when cross-country average variances are higher Correlations tend to be lower when a larger proportion of the economies are in a negative-growth quarter Capital markets are more correlated during recessionary times An increase in TED spread is positively associated with the capital markets’ correlation level Anita Suurlaht Correlation Dynamics in the G7 Stock Markets
  30. 30. Questions and comments welcome Anita Suurlaht Correlation Dynamics in the G7 Stock Markets

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