Convergence and Divergence
in European Bond Correlations
by Schwendner P., Schüle M., Hillebrand M.
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European Bond Yields
̶ Euro convergence for bonds yields during end of 1990s
̶ European sovereign debt crises 2010-2012: spreads reappeared.
̶ Since 2015, bond spreads primarily signal political divergence
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European Bond Return
Correlations 2008 - 2013
Containment of the 2010 sovereign bond crisis
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European Bond Return
Correlations 2014 - 2019
From financial crisis to political divergence
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Problems with correlations
̶ They are unstable in time
̶ Common factors may lead to spurious correlations
̶ Too many links: each market is correlated to any other
market. Who is driving what?
Solution:
̶ Correlation influence based on partial correlations
shows driving factors
̶ Bootstrap filter (“wild bootstrap”) to reduce unstable
links in correlation matrix
̶ Influence networks to identify the markets that drive the
correlations of other markets
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Bootstrap-filtered partial
correlation
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Correlation influence
̶ The partial correlation measure is defined as
̶ Correlation influence is defined as
̶ The average correlation influence is defined as
Ref.: Kenett D. Y. et. al.: Dominating clasp of the financial sector revealed by partial
correlation analysis of the stock market. PLoS ONE 5(12): e15032.
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rij:k =
Cij CikCkj
q
Cik
q
Ckj
.
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di,j:k = Cij rij:k.
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di:k = di,j:kj6=i,k.
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rij:k =
Cij CikCkj
q
Cik
q
Ckj
.
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di,j:k = Cij rij:k.
I
di:k = di,j:kj6=i,k.
I
rij:k =
Cij CikCkj
q
Cik
q
Ckj
.
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di,j:k = Cij rij:k.
I
di:k = di,j:kj6=i,k.
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Generate Filtered Correlation
Influence Network
Method overview: from bond yields to influence networks
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3 -31-Dec-2013
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01-Jan-2014 -31-Dec-2014
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01-Jan-2015 -28-Aug-2015
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Bond yield time
series
Correlation matrix of
yield changes
Bootstrap
filter
Filtered influence network
1990 1995 2000 2005 2010 2015
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-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
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Correlation
influence
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03-Jan-2011 -30-Dec-2011
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02-Jan-2012 -31-Dec-2012
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01-Jan-2014 -31-Dec-2014
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01-Jan-2015 -28-Aug-2015
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We use influence networks to identify the markets that drive the
correlations of other markets.
As correlations are very unstable, we use a bootstrap filter to
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Filtered Correlation Influence
Correlation influence networks of daily bond yield changes 2010 - 2015
Blue arrows:
dominating positive
correlations =>
reinforcing
movements
Red arrows:
dominating negative
correlations =>
diverging
movements
2010. 2011 2012
2013 2014 2015
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Odds vs Exchange rate
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Brexit Referendum: correlations
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Brexit Referendum: dendrogram
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Brexit Referendum: influence
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Odds vs FR-DE bond spread
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French Elections: correlations
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French Elections: dendrogram
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French Elections: influence
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Conclusions
̶ Since 2010, European bonds cluster into core and periphery
groups according to their return correlations. We use filtered
correlation influence networks to show the most significant drivers of
convergence and divergence.
̶ During the European sovereign debt crisis 2010 - 2012, negative
correlation influences between the core and periphery groups are the
dominating force. Since 2013, the situation improved a lot.
̶ In 2015 during the negotiations between Greece and the Eurogroup
and in 2018 during the Italian budget negotiations, the warning
signals of negative correlation influences reappeared for short
periods, although the absolute level of spreads is substantially
smaller than during 2010 - 2012.
̶ In 2016, warning signals reappeared in the week before the Brexit
referendum, but disappeared quickly thereafter.
̶ The findings point to markets becoming more politically driven.