Results from a global insurance spillover analysis conducted as part of the April 2016 GFSR's research agenda on banking and insurance inter-linkages.

1. GLOBAL INSURANCE SPILLOVERS
BENJAMIN HUSTON

2. OUTLINE
 Evolution of spillovers over time
 Change in pre- and post-GFC spillovers
 Insurer-to-insurer and insurer-noninsurer spillovers
 Spillover clustering, by region and by sector
 Systemic importance of spillovers, from a network perspective

3. MINUTIA
DATA
 Week-over-week returns for fifteen large sector- and region-specific equity indices
 Coverage spans the period of 2001-2015
METHODOLOGY
 Spillovers: generalized forecast error variance decomposition (Diebold andYilmaz, 2014; Pesaran, 1998)
 Networks: eigenvector centrality (see Diestel, 2005)
ROBUSTNESS
 Performed same exercise using equity returns and changes in equity return log volatilities, both weighted and
unweighted by market cap. Results were virtually identical.
 Results were also highly invariant to selection of VAR lag order, the choice of control variables, and to the
selection of a forecast error variance decomposition method.

4. KEY FINDINGS
• Total spillover levels are on the rise and approaching levels observed prior to the 2008 global financial crisis.
• The largest share of spillovers is attributable to North America. The share attributable to Asia is rising the most rapidly.
• On a net basis, the largest spillover asymmetries occur between Europe and North America and between Asia and Europe.
• Across sectors, the largest spillovers occur primarily between banks, life, and PC insurers.
• The sectors which have witnessed the greatest increases in spillovers since the GFC are North American asset managers and
reinsurers, Asian life insurers, and European PC insurers.
• Insurer-and-noninsurer (“cross-sector”) spillovers, are approximately twice the size of insurer-insurer (“intra-sector”)
spillovers, both within and across regions. Roughly 15 percent of all insurance-related spillovers occur between different
geographic regions.
• Relative to the pre-crisis period of 2001-08, the systemic importance of North America and Asia has grown, while that of
Europe has somewhat diminished. North America remains the most systemically important region.
• North American asset managers and reinsurers have seen a marked increase in the systemic role they play in the global financial
system, as have Asian life insurers and banks.

5. AM BANKS LIFE PC RE
2004 2008 2012 2016 2004 2008 2012 2016 2004 2008 2012 2016 2004 2008 2012 2016 2004 2008 2012 2016
0
25
50
75
100
2002 2004 2006 2008 2010 2012 2014 2016
p
EVOLUTION OF SPILLOVERS
Left: spillover time series calculated using a 1-year rolling window with overlapping monthly increments. Dashed black lines denote approximate peak dates of the global financial crisis and the European sovereign debt crisis,
from left to right respectively. AM = asset managers, BANKS = banks, LIFE = life insurers, PC = property-casualty insurers, RE = reinsurers.
• Total spillover levels amongst asset managers, banks, life insurers, property-casualty
(PC) insurers, and reinsurers are on the rise and approaching the levels observed prior
to the 2008 global financial and 2012 European sovereign debt crises.
• Across regions, the largest share of spillovers are attributable first to North America
and then to Europe. Historically,Asia has contributed the least to spillovers, but its
share is rising the most rapidly.
• Across sectors, banks are the greatest originators of spillovers, followed by life and
property-causality insurers. Spillovers from asset managers are on par with those from
PC insurers and at a near historic-high. Reinsurer spillovers are the lowest in
magnitude.
ASIA EUROPE NORTH AMERICA
0
10
20
30
2004 2008 2012 2016 2004 2008 2012 2016 2004 2008 2012 2016
p
Spillovers, by sector
Total spillovers
Spillovers, by region
SpilloverindexSpilloverindex

6. CHANGE IN PRE- AND POST-GFC SPILLOVERS
Note: fanplot showing changes in region/sector spillover index levels between the periods 2001-08 and 2010-15. Plot segment length corresponds to region/sector spillover index values. Green and red denote increases and
decreases, respectively, in spillover index values between the pre- and post-GFC periods. Segment width does have a semantic role and is merely used to emphasize differences. GFC = “Global Financial Crisis”.
Asia
AM
Asia
Banks
Asia
Life
Asia
PC
Asia
RE
Europe
AM
Europe
Banks
Europe
Life
Europe
PC
Europe
RE
NorthAm
AM
NorthAm
Banks
NorthAm
Life
NorthAm
PC
NorthAm
RE
Relative to the pre-crisis period of 2001-08:
• In North America, spillovers from banks, asset managers
and reinsurers, have increased in magnitude while those
from life and PC insurers have fallen slightly.
• In Europe, asset manager, life/PC insurer, and reinsure
spillovers have increased in magnitude whereas bank
spillovers have marginally declined.
• In Asia, bank, life insurer, and reinsurer spillovers have risen
as those from asset managers and banks have deceased.
Globally, the sectors which have witnessed the greatest rise in
spillovers in the current period are North American asset
managers and reinsurers, Asian life insurers, and European PC
insurers. Spillovers from North American PC insurers have
experienced the largest decline.

7. INSURANCE SPILLOVERS, 2010-PRESENT
• Insurer-and-noninsurer “cross-sector” spillovers (red), are
approximately twice the size of insurer-insurer “intra-sector”
spillovers (yellow), both within and across regions.
• Roughly 15 percent of all insurance-related spillovers occur
between different geographic regions.
• Within a given region, roughly two-thirds of all spillovers
occur between an insurer and a non-insurer (red).
• In absolute terms, North America and Europe exhibit the
greatest levels of cross-sector spillovers. In relative terms,
Asia experiences the greatest share of such spillovers.
Note: red = spillovers between insurers and non-insurers, yellow = spillovers amongst insurers. Black arrows indicate spillover direction and point from spillover originator to spillover recipient. The numeric values which border each
plot section display regional spillover index values.
Cross-sector and intra-sector
spillovers

8. CROSS-REGIONAL SPILLOVERS, 2010-PRESENT
Outward spillovers, clustered by region
The greatest magnitude spillovers occur primarily between sectors
belonging to the same region. Across regions, large spillovers are observed
between Asian banks/life insurers and virtually all North American sectors.
Left: colors denote low (white), medium (yellow), and high (red) levels of spillovers across region/sectors. Right: colors denote net positive (green) and net negative (red) bilaterial spillovers. Spillover directionality is read from matrix column
to matrix row. AM = asset managers, BANKS = banks, LIFE = life insurers, PC = property-casualty insurers, RE = re-insurers.
On a net basis, the largest spillover asymmetries occur between
Europe and North America and between Asia and Europe. North
America is a net recipient of spillovers from Europe, and Europe is in
turn a net recipient of Asian spillovers.
North
America
Europe Asia
North
America
Europe
Asia
Net spillovers, clustered by region
North
America
Europe Asia
North
America
Europe
Asia

9. CROSS-SECTOR SPILLOVERS, 2010-PRESENT
Outward spillovers, clustered by sector
Left: colors denote low (white), medium (yellow), and high (red) levels of aggregate spillovers across sectors. Right: colors denote net positive (green) and net negative (red) bilaterial aggregate spillovers. Spillover directionality is read from
matrix column to matrix row. AM = asset managers, BANKS = banks, LIFE = life insurers, PC = property-casualty insurers, RE = re-insurers. See supplementary charts in the Annex for analogous graphs showing region/sector detail.
Net spillovers, clustered by sector
Across sectors, the largest spillovers occur primarily between banks, life
insurers, and PC insurers. Spillover from asset managers to banks and life
insurers are also quite large.
On net basis, banks and life insurers are vulnerable to virtually every
other sector. Life and PC insurers have the largest bilaterial impact on
banks and PC insurers have the largest such impact on life insurers.

10. CHANGE IN PRE- AND POST-GFC SYSTEMIC IMPORTANCE
Eigenvector Centrality
Note: The figure displays a centrality plot of insurance spillovers. Node positions are determined using eigenvector centrality scores and a node’s proximity to the center of the network signifies its importance (i.e., closer nodes are more important).
Colored nodes and empty nodes denote post-GFC and pre-GFC centrality scores, respectively. Arrows display the change in systemic risk posed by a given sector between the two periods. The symbols , , correspond to high, medium, and
low levels of systemic risk, respectively, and ring colors are used for solely for visual emphasize. See Diestel (2005) for background information on the graph-theoretic concept of centrality. A = asset managers, B = banks, L = life insurers, P =
property-casualty insurers, R = re-insurers.
Relative to the pre-crisis period of 2001-08 (gray arrows), the
systemic importance of North America and Asia has grown, while that
of Europe has somewhat diminished.
• In North America, asset managers and reinsurers, and to a lesser
extent banks, have seen a marked increase in the systemic role they
play in the global financial system.
• In Asia, life insurers and banks have also begun to play a much
larger systemic role, as have PC insurers.
• In Europe, asset managers and PC insurers remain as important as
they have in the past, however the centrality of European banks, life
insurers, and reinsurers have mitigated since the pre-GFC period.
North America remains the most systemically important region,
followed by Europe and then by Asia.
= Asset managers
= Banks
= Life insurers
= PC insurers
= Re-insurers
= North America
= Europe
= Asia

11. SUMMARY
• Total spillover levels amongst asset managers, banks, life insurers, property-casuality (PC) insurers, and reinsurers are on the rise and
approaching historic highs.
• Across regions, the largest share of spillovers are attributable first to North America and then to Europe. Historically,Asia has
contributed the least to spillovers, but its share is rising the most rapidly. On a net basis, the largest spillover asymmetries occur
between Europe and North America and between Asia and Europe. North America is a net recipient of spillovers from Europe, and
Europe is in turn a net recipient of Asian spillovers.
• Across sectors, the largest spillovers occur primarily between banks and life and PC insurers. Spillovers from asset managers to banks
and life insurers are also quite large.
• Globally, the sectors which have witnessed the greatest increase in spillovers since the GFC are North American asset managers and
reinsurers, Asian life insurers, and European PC insurers. Spillovers from North American PC insurers have moderated the most.
• Insurer-and-noninsurer (“cross-sector”) spillovers, are approximately twice the size of insurer-to-insurer spillovers, both within and
across regions. Roughly 15 percent of all insurance-related spillovers occur between different geographic regions.
• Relative to the pre-crisis period of 2001-08, the systemic importance of North America and Asia has grown, while that of Europe has
somewhat diminished. North America remains the most systemically important region.
• In North America, asset managers and reinsurers have seen a marked increase in the systemic role they play in the global financial system.
In Asia, life insurers and banks too have witnessed a large uptick in the systemic importance of their operations.

12. REFERENCES
Diebold, Francis X., and KamilYılmaz, 2014, "On the network topology of variance decompositions: Measuring the
connectedness of financial firms." Journal of Econometrics 182, no. 1: 119-134.
Diestel, Reinhard, 2005, GraphTheory (3rd ed.), Berlin, NewYork: Springer-Verlag, ISBN 978-3-540-26183-4.
Pesaran, H. Hashem, andYongcheol Shin, 1998, "Generalized impulse response analysis in linear multivariate
models." Economics Letters 58, no. 1 (1998): 17-29.

13. ANNEX

14. SPILLOVER METHODOLOGY
 Spillover values are determined using an order independent generalized FEVD (Diebold and
Yilmaz, 2014; Pesaran, 1998).
 Region/sector equity indices used as endogenous variables in the followingVAR model
specification:
 A spillover from j to i is defined as the portion of i’s total forecast error variance that is
attributable to a shock from j:
matrixiondecompositanceerror variforecastahead-stepHtheis][
],[X
][Y
)()(
t
t
H
ij
H
t
ti
ttt
dD
GlobalVIXWORLD
r
XLBYLA



 
.
i
ijijij dds

15. NETWORK METHODOLOGY
Let be a network with associated sets of vertices and edges and . The eigenvector
centrality score, , of a given vertex ∊ is defined as
1
,
∊
where
 is a vertex which shares an edge with ,
 , is the entry in , the adjacency matrix of , which corresponds to the vertices and ,
 and the eigenvalue is a constant which is satisfies the relationship . The value of
is not necessarily unique and is numerically estimated using the Power Iteration algorithm.
Higher eigenvector centrality scores signify greater network importance. When is a financial
network, eigenvector centrality is interpreted as a proxy for systemic risk.

16. SUPPLEMENTARY CHARTS
Detailed net spillovers,
clustered by sector
Detailed outward spillovers,
clustered by sector