## _wp1481 — Appendix I: Shock Propagation Mechanism (and related appendices)

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### I. Purpose, data coverage, and preprocessing
- Focus:
  - Role of “safe havens” in spreading or containing contagion in asset prices via asset price correlations as proxy networks for underlying exposures and to capture high-frequency stress signals.
- Sample and time span:
  - 50 sovereigns; 331 banks; daily data; time span 2000-2013; sample divided into six-month intervals from H1 2000 to H2 2013.
- Asset series:
  - Daily changes in 5-year bond yields of 39-50 sovereigns.
  - Daily log changes in bank equity prices of 331 individual banks.
- Regional composition:
  - About one-third of banks and one-half of sovereigns are European; about one-quarter of both are Asian; three quarters of banks and one-half of sovereigns are emerging markets.
- Preprocessing and matching:
  - Adjusted daily data for time zones and exchange rate changes.
  - North America shocks: match North American data with average of same-day and next-day data for Europe and with next-day data for Asia.
  - Europe shocks: match European data with average of same-day and next-day data for Asia.

### II. Correlation-network construction and methodological choices
- Correlation measurement:
  - Bilateral Pearson correlation coefficients computed for each pair (bank/bank, sovereign/sovereign, bank/sovereign) over each six-month subperiod.
  - Correlations outside own-country sovereign/bank pairs set to zero to eliminate spurious correlations.
  - Network represented by matrix S where diagonal elements are zero; time-adjusted data render S not symmetric (directed network).
- Methodological choices and limitations:
  - Focus on correlations rather than causal measures (e.g., Granger causality or Diebold-Yilmaz spillovers) to preserve sample size and comparability with asset price literature.
  - Semi-annual windows used to reduce volatility bias highlighted by Forbes and Rigobon (2002).
- Directional scaling and size adjustments in propagation framework:
  - Correlations scaled by relative size of source’s and destination’s total assets (for banks) or government debt (for sovereigns); weight capped at one.
  - To contain exploding paths, each propagation step is scaled by the number of nodes.

### III. Stylized empirical facts (summary)
- Significance distribution:
  - Bulk of correlations are inside the 95% confidence interval [-0.196, +0.196] and hence statistically insignificant.
  - Insignificance especially pronounced for bank-sovereign and, to a lesser extent, bank-bank correlations.
  - More than half of sovereign-sovereign correlations are significantly positive, with very few significantly negative ones.
- Relative strengths:
  - Sovereign-sovereign correlations > bank-bank correlations > bank-sovereign correlations in general.
  - At 2008H2 peak of the global financial crisis, bank-bank correlations spiked to almost match sovereign-sovereign correlations on average; bank-bank correlations declined thereafter.
  - Sovereign-sovereign correlations fell with onset of the euro area crisis in early 2010.
- Geography and clustering:
  - Highest positive sovereign-sovereign correlations (above 0.8) are almost exclusively among European sovereigns; exceptions include Australia and New Zealand throughout the sample, and large emerging markets and Canada during periods of stress in advanced countries.
  - Very few significantly negative sovereign-sovereign correlations, predominantly with the US (2000-2007, 2013), Japan (2007-10), and Hong Kong (2002-03, 2012-13).
  - Random walk centrality: average random walk centrality declined noticeably in the late 2000s as some previously most central European countries lost centrality and the periphery gained centrality.
  - Clustering coefficient (Barrat et al. 2004):
    - Increased noticeably in 2000-2004.
    - From 2004-06, average clustering coefficient around 97 percent.
    - Three episodes of decoupling: 2007–mid-2008 (temporary), H2 2011 (sharp decline), post-2012 (weakened clustering with temporary reversal in H1 2012).
    - Despite declines, composition of most important clusters remained remarkably stable (a grey-shaded global cluster contained all euro area countries through the sample).
- Bank network specifics:
  - Bank equity price network much less clustered than sovereign bond yield network.
  - Until 2006, banking systems were essentially clustered by nationality (except global banks in Western Europe, Eastern Europe, and the US).
  - Asian and non-US North American banking systems began integrating into a widening global cluster of bank equity prices starting in 2006; this global bank cluster began to shrink from 2010 onwards.

### IV. Safe havens: definition and observed properties
- Operational two-criterion definition used:
  - Country has a triple AAA credit rating from at least two of the three major rating agencies (Fitch, S&P, Moody’s).
  - Sovereign bond yield changes correlate negatively with returns on a risky asset during times of stress (negative beta), using US banking equity price index as benchmark and stress events: Q4 2000; Q3 2001 and 2002; H2 2008; H1 2010; and Q3 2011.
  - Safe havens in this paper: countries that meet both criteria.
- Distinctive empirical properties:
  - Sovereign bond yields in safe havens are, on average, more strongly correlated with other countries’ sovereign bond yields (both safe havens and non-safe havens) than non-safe haven sovereigns.
  - Safe havens’ bank equity prices tend to be more strongly correlated with other banks’ equity prices than non-safe havens; the safe-haven/non-safe-haven gap is smaller for bank-bank correlations than for sovereign-sovereign correlations.
  - Sovereign bond yields in safe havens are on average more strongly positively correlated with their home banks’ equity prices; in non-safe havens these correlations are uncorrelated or in very few cases negative.
  - Representative averages (advanced-country comparisons reported in text):
    - Average sovereign-sovereign correlation for advanced country safe havens: 0.55.
    - Average sovereign-sovereign correlation for advanced country non-safe haven: 0.38.
    - Average bank-bank correlation for advanced country safe havens: 0.31.
    - Average bank-bank correlation for advanced country non-safe haven: 0.19.
    - Average bank-sovereign correlation for advanced country safe havens: 0.17.
    - Average bank-sovereign correlation for advanced country non-safe haven: 0.06.
  - Country-specific notes:
    - US: exceptionally low cross-country sovereign-sovereign correlations (even below non-safe havens); pre-crisis domestic bank-sovereign correlations well above average safe-haven or non-safe-haven countries.
    - Euro-area safe havens: higher-than-average cross-country sovereign-sovereign and bank-bank correlations; since the financial crisis somewhat lower domestic bank-sovereign correlations.
- Implication:
  - Because safe havens exhibit higher correlations in sovereign-sovereign, bank-bank, and bank-sovereign dimensions, they can propagate shocks to other countries faster than non-safe havens; degree of propagation depends on source/recipient country and time period.

### V. Stylized shock-propagation model and experiments
- Framework and assumptions:
  - Stylized model from disease-spreading literature (Jammazi and Aloui (2012)): every period each node propagates the cumulative shock it has received to all adjacent nodes; impact weighted by link strength (correlation-based).
  - Simplifying assumptions: nodes are neutral (cannot stop propagation); no buffers (nodes cannot slow propagation).
  - Initial shock: simulated as a 1 percent increase in either sovereign bond yields or in daily bank equity prices.
  - Iterative propagation: destinations become origins in next step; cumulative effects tracked step-by-step.
  - Iterations reported: impacts after 5 iterations and after 10 iterations.
- Shock origin scenarios simulated:
  - Shock in any individual country (average of shock in any country of the network).
  - Simultaneous shock in all GIIPS countries (Greece, Ireland, Italy, Portugal, Spain).
  - Shock in the US alone.
- Baseline simulation stylized findings:
  - Except for a sovereign bond yield shock in the US, shocks are gradually amplified as they reverberate around global sovereign bond and bank equity markets.
  - Amplification strongest for a sovereign bond yield shock in the GIIPS (initially transmitted mainly to European bond markets, later to rest of world).
  - Sovereign bond shocks (average country, GIIPS, US) peaked in impact in H1 2005 and even higher in H2 2010 (additional peak for US shock in H2 2002).
  - Average impact of a bank equity price shock peaked in H2 2008.
  - Bank equity price shocks produce very similar impacts across source-market scenarios because bank-bank and bank-sovereign correlations are more homogeneous across countries than sovereign-sovereign correlations.
  - Cross-country heterogeneity example: 2013 H1 US sovereign bond yield shock would have initially raised sovereign bond yields in advanced Asia-Pacific and had mostly negative/no impact on most European sovereigns; in 2013 H2 the same shock would have taken longer to build positive impact in advanced Asia-Pacific and would have reduced euro area sovereign bond yields more than in 2013 H1.
  - Representative numeric illustrative statistic: 93 percent correlation reported between changes of the 5-year sovereign bond yields of Ireland and Germany in 2010-12 (used to motivate directional scaling).

### VI. Feedback loops between banks and sovereigns
- Counterfactual experiment:
  - Compare actual network (with bank-sovereign links) to counterfactual network with all bank-sovereign links set to zero (no feedback loops).
- Main findings:
  - Feedback loops have on average amplified the impact of sovereign bond yield shocks (difference positive across average country, GIIPS, US scenarios).
  - Feedback loops amplify both sovereign bond and bank equity shocks, but strength varies:
    - By source: feedback loops are an order of magnitude stronger for shocks originating in the average country than for shocks originating in the GIIPS or the US (reflecting predominance of highly-interconnected European sovereigns and banks).
    - By market: since 2010, feedback loops amplified bank equity price shocks more strongly than sovereign bond yield shocks when shocks originate in the GIIPS or the US.
  - Mechanism:
    - GIIPS and US banks (with significantly negative and positive bank-sovereign correlations, respectively) transmit shocks into the strongly correlated sovereign bond network where they propagate quickly and then feed back into bank equity prices.
    - GIIPS and US sovereigns transmit shocks into the only mildly correlated bank-bank network where propagation is slower; thus feedback loops amplify bank shocks more than sovereign shocks.
  - Recipient-country heterogeneity:
    - Feedback-loop amplification of external bank shocks varies by recipient region and over time (e.g., in 2008-09 feedback loops strongest for core euro area; more recently strongest in non-euro area advanced Europe; GIIPS-origin shocks most amplified in euro area; US-origin shocks most amplified in Latin America).

### VII. Role of safe havens in propagation and counterfactuals
- Counterfactual “no-safe havens” experiment:
  - Replace all safe havens’ correlations with average correlations of non-safe-haven countries (for sovereign-sovereign, bank-bank, bank-sovereign links) and compare propagation.
- Results summary:
  - Sovereign bond shocks (average country and GIIPS): shocks propagate more strongly in the actual network with safe havens than in the counterfactual without safe havens.
    - Narrowing of safe-haven group since 2011 reduced the gap between actual and counterfactual impacts.
  - US sovereign bond shock:
    - Pre-crisis (when US had mildly negative sovereign-sovereign correlations), a US sovereign bond shock propagated more slowly than if the US were an average non-safe-haven country.
    - Since the crisis, increased US bank-sovereign correlations and sovereign-sovereign correlations approaching non-safe-haven levels reduced this difference.
  - Bank equity price shocks:
    - Presence of safe havens accelerates shock propagation in all three source scenarios (average country, GIIPS, US).
    - US banking shocks propagate faster in the actual network than in one without safe havens because US bank-bank correlations are above average non-safe-haven levels.
- Intuition for amplification via safe havens:
  - A bond-yield shock originating in a non-safe haven that arrives in a safe haven raises safe-haven sovereign yields and, via positive bank-sovereign correlations in safe havens, raises bank equity prices there.
  - These bank-price changes transmit through bank-bank correlations to other safe havens and loop back into sovereign yields via bank-sovereign links—generating amplification and cross-class propagation.

### VIII. Mapping network structure, contagion chains, and regional examples
- Sovereign-sovereign interconnectedness (2000-06, 2007-09, 2010-12 highlights):
  - Pre-crisis (2000-06): Singapore and, less directly, Korea acted as bridges between Emerging Asian and European sovereign bond yields.
  - Since H1 2008: sovereign bond yields in Asia (Korea, Indonesia, India, Philippines, China, Malaysia, Thailand, Japan) have become less correlated with advanced-country group.
  - Europe: European sovereign bond yields remained the most closely intertwined; correlations between European sovereign bond yields and US sovereign bond yields strengthened since pre-crisis period.
- Bank-bank interconnectedness:
  - Pre-crisis (2000-06): few strong bank-bank correlations; mostly regional (Europe) or within-country.
  - 2007-09: global financial crisis tightened disparate pre-crisis groups into one knot of cross-border bank equity correlations.
  - 2010-12: European banks remain tightly intertwined; Asian and Latin American banks decoupled from some advanced-economy banks; persistent Asia cross-country groupings identified (Australia–Singapore–Korea–Malaysia; Hong Kong–China).
- Sovereign-bank linkages and contagion chains:
  - Emerging Asia: at the height of the global financial crisis (2007-09), sovereign-bank linkages strengthened in almost all emerging Asian economies; shocks from European banks could transmit through Singapore to other Asian banks and then to Asian sovereigns via bank-sovereign feedback loops.
  - Emerging Europe and Turkey/Poland/Hungary: Turkish, Polish and—to a lesser extent—Hungarian bank equity prices were highly correlated with their own countries’ sovereign bond yields; stress could propagate across banking channels to neighboring sovereigns and banks.
  - GIIPS and Cyprus: pre-crisis sovereign-bank interconnections weak; during 2007-09 Spanish and Italian banks became highly correlated with core European banks while Greek and Cypriot banks formed a separate group; as European crisis deepened (2010-12) sovereign-bank inter-linkages strengthened, enabling multi-step contagion chains (e.g., Portugal bank → Portugal sovereign → other banks → Italian bank).
- Appendix Table 2: country-bank coverage lists preserve exact bank-count brackets for each country and period (representative entries include Argentina(6) → Argentina(7), Austria(5), Belgium(3) → Belgium(4), Canada(6), China(6/7), Colombia(7/8), Germany(5), Spain(5), Ireland(2/3), Korea(South)(7/8), Taiwan(9/10), Turkey(8/9), United States(4/5), Venezuela(7/8), Viet Nam(6/7), etc.).

### IX. Conclusions and open questions for further research
- Main conclusions:
  - Cross-country sovereign-bond yield correlations > bank-bank correlations > bank-sovereign correlations, implying rapid cross-country propagation once the sovereign bond network is hit.
  - Safe havens tend to have stronger sovereign-sovereign, bank-bank, and bank-sovereign correlations than non-safe havens (the US shows distinctive patterns), making them potential shock propagators in price-based networks.
  - Changes in the distribution of correlations over time map into changes in shock propagation (e.g., bank equity price correlation peak in H2 2008 and subsequent fall correspond to implied propagation changes).
- Open research issues noted:
  - How safe havens’ roles change with their “neighborhood” in the network (e.g., deeply interconnected Europe vs Asia).
  - How policy actions altered the shape of the correlation network and changed shock propagation (policy interventions are implicit in estimated correlations but not modeled here).
  - Improving causal identification of directions in spillovers (authors plan to use Diebold-Yilmaz spillover coefficients or Granger causality measures in future work).

*Source: Appendix I: Shock Propagation Mechanism and accompanying appendices from the provided IMF working paper excerpt (_wp1481).*

### Appendix I: Shock Propagation Mechanism ...........................................................................32

### Appendix I: Shock Propagation Mechanism

### I. Introduction
- Focus: role of "safe havens" in spreading or containing contagion in asset prices via asset price correlations as proxy networks for underlying exposures and to capture high-frequency stress signals.
- Rationale:
  - Asset price correlations proxy fundamental ties when granular exposure data are missing or lagged.
  - Asset price correlations can trigger macroeconomic effects (example: sovereign bond yield increases raise domestic long-term financing costs affecting investment and consumption).
- Contribution:
  - Document stylized facts on sovereign-sovereign, bank-bank, and sovereign-bank correlations across a large sample (50 sovereigns, 331 banks) over 2000-2013.
  - Illustrate implications of heightened asset price correlations for shock propagation and feedback loops, with emphasis on properties of safe haven countries.

### II. Data and Methodology
- Data:
  - Daily changes in 5-year bond yields of 39-50 sovereigns.
  - Daily log changes in bank equity prices of 331 individual banks.
  - Time span: 2000-2013; sample divided into six-month intervals from H1 2000 to H2 2013.
  - Regional composition: about one-third of banks and one-half of sovereigns are European; about one-quarter of both are Asian; three quarters of banks and one-half of sovereigns are emerging markets.
- Preprocessing and matching:
  - Adjusted daily data for time zones and exchange rate changes.
  - For shocks originating in North America: match North American data with the average of the same-day and next-day data for Europe and with next-day data for Asia.
  - For shocks originating in Europe: match European data with the average of same-day and next-day data for Asia.
- Correlation measurement:
  - Bilateral Pearson correlation coefficients computed for each pair (bank/bank, sovereign/sovereign, bank/sovereign) over each six-month subperiod.
  - Correlations outside own-country sovereign/bank pairs set to zero to eliminate spurious correlations.
  - Network represented by matrix S where diagonal elements are zero; time-adjusted data render S not symmetric (directed network).
- Methodological choices and limitations:
  - Focus on correlations rather than causal measures (e.g., Granger causality or Diebold-Yilmaz spillovers) to preserve sample size and comparability with asset price literature.
  - Semi-annual windows used to reduce volatility bias highlighted by Forbes and Rigobon (2002).

### III. Stylized Facts (summary of empirical findings)
- Overview:
  - Figure 1 (described) summarizes correlations between daily sovereign bond yield changes (“sovereign-sovereign”), daily bank equity price changes (“bank-bank”), and daily changes in sovereign bond yields and same-country bank equity prices (“bank-sovereign”).
- Five stylized facts:
  1. Statistical significance distribution:
     - Bulk of correlations are inside the 95% confidence interval [-0.196, +0.196] and hence statistically insignificant.
     - Insignificance especially pronounced for bank-sovereign and, to a lesser extent, bank-bank correlations.
     - More than half of sovereign-sovereign correlations are significantly positive, with very few significantly negative ones.
  2. Relative strength of correlation types:
     - Sovereign-sovereign correlations > bank-bank correlations > bank-sovereign correlations in general.
     - At 2008H2 peak of the global financial crisis, bank-bank correlations spiked to almost match sovereign-sovereign correlations on average; bank-bank correlations declined thereafter.
     - Sovereign-sovereign correlations fell with onset of the euro area crisis in early 2010.
  3. Geography of strongest sovereign-sovereign correlations:
     - Highest positive sovereign-sovereign correlations (above 0.8) are almost exclusively among European sovereigns, possibly reflecting a common exchange rate.
     - Exceptions: Australia and New Zealand sovereign bond yields throughout the sample, and large emerging markets and Canada during periods of stress in advanced countries.
     - Very few significantly negative sovereign-sovereign correlations, predominantly with the US (2000-2007, 2013), Japan (2007-10), and Hong Kong (2002-03, 2012-13).
  4. Bank-bank correlation patterns:
     - Bank-bank correlations are highest in Europe; most significantly positive bank-bank correlations are found between Europe and the rest of the world.
     - Many significant bank-bank correlations are small in magnitude.
     - Bank-bank correlations within countries tend to be larger than between countries; the within-vs-between gap narrowed in Europe in 2004 but widened with the euro area crisis.
  5. Bank-sovereign correlation characteristics:
     - Approximately four-fifths of bank-sovereign correlations are statistically insignificant.
     - Of the few significantly positive bank-sovereign correlations, about two-thirds fell into the euro area before the euro area crisis.
     - Few significantly negative bank-sovereign correlations; prior to the euro area crisis these were predominantly outside the euro area but have appeared in the euro area periphery since (examples: banks in Spain, Belgium, France, Greece, Ireland, Italy, Mexico, Russia during 2009-13; Brazil, China, Mexico in 2007/08; several emerging markets throughout the sample).

### IV. Network Structure, Centrality, and Clustering
- Centrality:
  - Random walk betweenness centrality (probability a country lies on a random path between any two others) used to measure country centrality in the sovereign bond yield network.
  - Average random walk centrality declined noticeably in the late 2000s as some previously most central European countries lost centrality and the periphery gained centrality.
- Clustering:
  - Clustering coefficient (Barrat et al. 2004 definition) measures strength of connections among neighbors.
  - Clustering evolution:
    - Increased noticeably in 2000-2004.
    - From 2004-06, clustering was high, with average clustering coefficient around 97 percent.
    - Three episodes of decoupling:
      - 2007 to mid-2008: temporary decline reversed after Lehman.
      - Second half of 2011: sharp decline at height of euro area crisis as markets discriminated between core and peripheral Europe.
      - Post-2012: clustering weakened further with a temporary reversal in H1 2012.
  - Despite declines in clustering strength, composition of most important clusters remained remarkably stable.
    - A grey-shaded global cluster contained all euro area countries through the sample, and typically included Japan (except early in the decade), the UK, Switzerland, non-euro Nordics, advanced commodity exporters (except late 2002/early 2003), and Eastern Europe (except late 2002).
    - The US was outside this global cluster for much of the period but rejoined during heightened global stress in 2008-2012.
  - Bank equity price network:
    - Much less clustered than sovereign bond yield network.
    - Until 2006, banking systems were essentially clustered by nationality (except for global banks in Western Europe, Eastern Europe, and the US).
    - Asian and non-US North American banking systems began integrating into a widening global cluster of bank equity prices starting in 2006; this global bank cluster began to shrink from 2010 onwards.

### V. Safe Havens: Definitions and Observed Properties
- Definitions applied:
  - Hedging against stock market risk (assets that hedge returns on risky portfolios during times of financial stress or rising risk aversion).
  - Sovereign credit ratings by rating agencies.
- Observed distinctive properties of safe havens in dataset:
  - Sovereign bond yields in safe havens are, on average, more strongly correlated with other countries’ sovereign bond yields (both safe havens and non-safe havens) than non-safe haven sovereigns.
  - Safe havens’ bank equity prices tend to be more strongly correlated with other banks’ equity prices than non-safe havens; the safe-haven/non-safe-haven gap is smaller for bank-bank correlations than for sovereign-sovereign correlations.
  - Sovereign bond yields in safe havens are on average more strongly positively correlated with their home banks’ equity prices, whereas in non-safe haven countries these correlations are uncorrelated or in very few cases negative.
    - Interpretation: In safe havens, credit risk is of negligible concern; expectations about future growth and monetary policy dominate. An improving growth outlook can raise bank equity prices and simultaneously raise expectations of monetary tightening, putting upward pressure on sovereign bond yields — yielding a positive correlation (rather than the negative correlation expected if credit risk drove the relation).
  - Implication for shock propagation: Due to higher correlations in three dimensions (sovereign-sovereign, bank-bank, bank-sovereign), safe havens can propagate shocks to other countries faster than non-safe havens, with the degree of propagation depending on source/recipient country and time period.

### VI. Illustrative Shock-Propagation Insight
- Relative feedback strengths:
  - Cross-country sovereign-sovereign correlations are stronger than individual bank equity price correlations.
  - Bank-bank correlations are stronger than bank-sovereign (domestic) correlations.
  - Consequence:
    - A shock within the sovereign bond yield network would propagate quickly and strongly across countries.
    - If a bank equity price shock raised local sovereign bond yields through bank-sovereign links, strong feedback loops between asset classes and across countries could ensue.
    - Conversely, a sovereign bond yield shock that depressed local bank equity prices would be amplified less strongly by feedback loops from the more mildly correlated global bank equity price network.

*Source: Appendix I: Shock Propagation Mechanism (pages 32–) of the provided IMF working paper excerpt.*

### Appendix Figure 4 and green in Appendix Figure 5).

### IV.   MAPPING THE NETWORK OF SOVEREIGN BOND YIELDS AND BANK EQUITY PRICES

### Method and data selection
- Clusters in Appendix Figures 1-5 define broad groupings; greater granularity achieved by examining individual countries within clusters for subperiods.  
- Appendix Figures 6-10 show pairwise links for intervals: 2000-06, 2007-09, and 2010-12.  
- To ensure representation, the strongest 10 percent of sovereign-sovereign, bank-bank, and bank-sovereign (negative only) links are selected.  
- Empirical regularity: sovereign-sovereign correlations tend to be much higher than bank-bank correlations and bank-sovereign correlations tend to be the weakest.

### Sovereign-sovereign interconnectedness (Appendix Figure 6)
- Pre-crisis (2000-06):
  - Singapore and, less directly, Korea acted as main “bridges” between Emerging Asian and European sovereign bond yields.
- Since the first half of 2008:
  - Sovereign bond yields in Asia (Korea, Indonesia, India, Philippines, China, Malaysia, Thailand, Japan) have become less correlated with the group of advanced country sovereign bond yield correlations.
- Europe:
  - European sovereign bond yields have remained the most closely intertwined, despite some recent weakening of links with some of the periphery (see also Box 1 for euro area countries).
  - Correlations between European sovereign bond yields and US sovereign bond yields have strengthened since the pre-crisis period.

### Bank-bank interconnectedness (Appendix Figure 7)
- Pre-crisis (2000-06):
  - Few strong bank-bank correlations; mostly confined to region Europe or individual countries.
- Global financial crisis (2007-09):
  - Tightened disparate pre-crisis groups into one knot of cross-border correlations between bank equity returns.
  - One Singaporean bank tied this tight global group to Asian-Pacific banks.
- Post-crisis (2010-12):
  - European banks remain tightly intertwined; other countries’ bank equity prices have drifted out of the dense global grouping.
  - Asian and Latin American banks have decoupled from banks in other advanced economies.
  - In Asia, two persistent cross-country bank groupings:
    - one including banks in Australia, Singaporea, Korea, and Malaysia;
    - another including banks in Hong Kong and China.
  - In Europe, banks in Greece and Cyprus separated from the main European grouping.
  - Few strong cross-border correlations outside Europe: in Asia-Pacific (Singapore and Australia) and North America (Canada and the US).

### Sovereign-bank linkages and cross-country contagion chains (Appendix Figures 8-10)
- General:
  - Appendix Figures 8-10 parse cross-country chains of correlations between banks and sovereigns for individual country groups.
  - Significant (negative) correlations between sovereign bond yields and bank equity prices were present within each country in Emerging Asia (Appendix Figure 8).10
- Emerging Asia (Appendix Figure 8):
  - Prior to the global financial crisis, cross-country sovereign-sovereign and bank-bank correlations were relatively weak.
  - At the height of the global financial crisis (2007-09), sovereign-bank linkages strengthened in almost all the emerging Asian economies.
  - Transmission example: shocks from European banks could be transmitted through Singapore to other Asian banks which, through bank-sovereign feedback loops, could have propagated them to Asian sovereigns.
- Emerging Europe and Turkey/Poland/Hungary (Appendix Figure 9):
  - Turkish, Polish and—to a lesser extent—Hungarian bank equity prices were highly correlated with their own countries’ sovereign bond yields.
  - During the global financial crisis (2007-09), both sovereign-bank links and cross-country banking sector linkages strengthened further.
  - Stress in Turkey’s tightly-linked banking sector could affect both sovereigns and banks in Poland and Hungary through the banking channel.
  - During the subsequent European crisis (2010-12), Turkey decoupled from Poland and Hungary which remain together in a tightly interconnected cluster.
  - Turkey and Romania developed into two highly correlated within-country groups.
- GIIPS and Cyprus (Appendix Figure 10):
  - Prior to the global financial crisis, sovereign-bank interconnections were weak.
  - During the global financial crisis (2007-09):
    - Spanish and Italian banks became highly correlated with core European banks.
    - Greek and Cypriot banks formed a separate group of strong bank-bank correlations.
    - Sovereign-bank linkages remained quite weak.
  - As the European crisis deepened (2010-12):
    - Aside from higher interconnectedness of global banks, sovereign-bank inter-linkages strengthened.
    - Contagion chain example: stress in bank 2 in Portugal could travel to Portugal’s sovereign, propagate to Portuguese bank 3, which is highly correlated with Italian bank 2, etc.
    - Similar contagion chains can be drawn for Belgium, Spain, Italy and Austria.
    - Greece and Cyprus remained decoupled from the other European banks and sovereigns during this period.

*Source: Appendix Figures and accompanying text in the content unit.*

### Box 1. Clustering and declustering of the Eurozone community in Sovereign Bond Yields

### Box 1. Clustering and declustering of the Eurozone community in Sovereign Bond Yields

### Clustering evolution of Eurozone sovereign bond yields
- Sample period begins in 1994; network constructed for 12 countries: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Slovakia and Spain.
- Community detection method: random-walk algorithm of Rosvall and Bergstrom (2008).
- Timeline of core cluster:
  - 1994-1996: core EMU cluster comprised Austria, Belgium, France, Germany and the Netherlands; separate from remaining countries.
  - 1997-1999: Italy and Spain joined the core EMU cluster.
  - 2000-2006: Greece, Ireland, Portugal, Finland joined the core cluster; Slovakia did not join (late euro member in 2009).
  - 2010-2012: core cluster partly dissolved—Belgium, Greece, Ireland and Portugal separated completely; Italy and Spain formed a common cluster.

### Defining safe havens (two-criterion definition)
- Two common definitions:
  - Credit-rating based: country has a triple AAA credit rating from at least two of the three major rating agencies (Fitch, S&P, Moody’s).
    - This criterion excludes Japan in the sample period (none of the three agencies rated it triple A during the sample).
  - “Negative beta” based: sovereign bond yield changes correlate negatively with returns on a risky asset during times of stress.
    - Benchmark risky asset: US banking equity price index.
    - Stress events used: Q4 2000; Q3 2001 and 2002; H2 2008; H1 2010; and Q3 2011.
- Operational definition used in this paper: safe havens are countries that meet both criteria (at least two triple AAA ratings AND negative beta during stress).
  - Authors also tested alternative definitions (three triple AAA ratings OR negative beta) and report robustness.
- Empirical note: Spain and Ireland were considered safe havens in the wake of Lehman’s bankruptcy; Switzerland and Denmark briefly stopped being safe havens until the euro area crisis regained momentum in the second half of 2011.

### Empirical differences: safe havens vs non-safe havens
- On average, safe haven correlations are higher than non-safe haven correlations for:
  - sovereign-sovereign correlations,
  - bank-sovereign correlations,
  - and, to a lesser extent, bank-bank correlations.
- These higher correlations apply both with safe-haven partners and with non-safe-haven partners.
- Distributional differences:
  - Non-safe-haven correlation distributions approx. normal.
  - Safe-haven correlation distributions have very fat tails with high positive correlations.
- Advanced-country comparison (averages reported in text):
  - Average sovereign-sovereign correlation for advanced country safe havens: 0.55.
  - Average sovereign-sovereign correlation for advanced country non-safe haven: 0.38.
  - Average bank-bank correlation for advanced country safe havens: 0.31.
  - Average bank-bank correlation for advanced country non-safe haven: 0.19.
  - Average bank-sovereign correlation for advanced country safe havens: 0.17.
  - Average bank-sovereign correlation for advanced country non-safe haven: 0.06.
- Country-specific notes:
  - US: exceptionally low cross-country sovereign-sovereign correlations (even below non-safe havens); pre-crisis domestic bank-sovereign correlations well above average safe-haven or non-safe-haven countries.
  - Euro-area safe havens: higher-than-average cross-country sovereign-sovereign and bank-bank correlations; since the financial crisis somewhat lower domestic bank-sovereign correlations.

### Modeling shock propagation: assumptions and methodology
- Shock-propagation framework: stylized model from disease-spreading literature (Jammazi and Aloui (2012)).
  - Every period each node propagates the cumulative shock it has received to all adjacent nodes; impact weighted by link strength (correlation-based).
- Simplifying assumptions for this exercise:
  - Nodes are neutral (cannot stop propagation).
  - No buffers (nodes cannot slow propagation).
- Directional scaling for size differences:
  - Correlations scaled by relative size of source’s and destination’s total assets (for banks) or government debt (for sovereigns); weight capped at one.
- Numerical/operational details:
  - Initial shock simulated as a 1 percent increase in either sovereign bond yields or in daily bank equity prices.
  - Iterative propagation: destinations become origins in next step; cumulative effects tracked step-by-step.
  - To contain exploding paths, each step is scaled by the number of nodes (countries and individual banks).
  - Averages: for GIIPS and US shock origins the source country of the shock is excluded; in the average-country setting the size of the initial shock is subtracted from all nodes to focus on net propagation.
- Shock origin scenarios simulated:
  - Shock in any individual country (average of shock in any country of the network),
  - Simultaneous shock in all GIIPS countries (Greece, Ireland, Italy, Portugal, Spain),
  - Shock in the US alone.
- Iterations highlighted in results: impacts reported after 5 iterations and after 10 iterations.

### Baseline simulation results (stylized findings)
- Amplification over iterations:
  - Except for a sovereign bond yield shock in the US, shocks are gradually amplified as they reverberate around global sovereign bond and bank equity markets.
  - Amplification strongest for a sovereign bond yield shock in the GIIPS (initially transmitted mainly to European bond markets, later to rest of world).
- Cross-source differences:
  - Sovereign bond shock in GIIPS produces strong global amplification; contrast with US sovereign shock which had modest average impact and changed little after 5 iterations (owing to US’s special safe-haven properties and mildly negative correlations with other sovereigns pre-2006 and again in 2013).
- Time variation:
  - Impact of sovereign bond shocks (average country, GIIPS, US) peaked in the first half of 2005 and even higher in the second half of 2010 (additional peak for US shock in the second half of 2002).
  - Average impact of a bank equity price shock peaked in the second half of 2008.
- Cross-market differences:
  - Bank equity price shocks produce very similar impacts across source-market scenarios (average country, GIIPS, US) because bank-bank and bank-sovereign correlations are more homogeneous across countries than sovereign-sovereign correlations.
- Cross-country heterogeneity:
  - Example: 2013 H1 US sovereign bond yield shock would have initially raised sovereign bond yields in advanced Asia-Pacific and had mostly negative/no impact on most European sovereigns; in 2013 H2 the same shock would have taken longer to build positive impact in advanced Asia-Pacific and would have reduced euro area sovereign bond yields more than in 2013 H1.
- Representative numeric illustrative statistic:
  - 93 percent correlation reported between changes of the 5-year sovereign bond yields of Ireland and Germany in 2010-12 (used to motivate directional scaling).

### Feedback loops between banks and sovereigns
- Experiment compares actual network (with bank-sovereign links) to counterfactual network with all bank-sovereign links set to zero (no feedback loops).
- Findings:
  - Feedback loops have on average amplified the impact of sovereign bond yield shocks (difference positive across average country, GIIPS, US scenarios).
  - Feedback loops amplify both sovereign bond and bank equity shocks, but strength varies:
    - By source: feedback loops are an order of magnitude stronger for shocks originating in the average country than for shocks originating in the GIIPS or the US (reflecting predominance of highly-interconnected European sovereigns and banks).
    - By market: since 2010, feedback loops amplified bank equity price shocks more strongly than sovereign bond yield shocks when shocks originate in the GIIPS or the US.
  - Mechanism explanation:
    - GIIPS and US banks (with significantly negative and positive bank-sovereign correlations, respectively) transmit shocks into the strongly correlated sovereign bond network where they propagate quickly and then feed back into bank equity prices.
    - In contrast, GIIPS and US sovereigns transmit shocks into the only mildly correlated bank-bank network where propagation is slower; thus feedback loops amplify bank shocks more than sovereign shocks.
- Recipient-country heterogeneity:
  - Feedback-loop amplification of external bank shocks varies by recipient region and over time (e.g., in 2008-09 feedback loops strongest for core euro area; more recently strongest in non-euro area advanced Europe; GIIPS-origin shocks most amplified in euro area; US-origin shocks most amplified in Latin America).

### Role of safe havens in shock propagation
- Key structural property: average safe havens exhibit stronger sovereign-sovereign, bank-bank, and (since 2007) bank-sovereign correlations than average non-safe havens (except the US has distinctive patterns).
- Counterfactual experiment:
  - “No-safe havens” network: replace all safe havens’ correlations with average correlations of non-safe-haven countries (for sovereign-sovereign, bank-bank, bank-sovereign links).
  - Compare shock propagation in actual network vs counterfactual network.
- Results summary:
  - Sovereign bond shocks (average country and GIIPS): shocks propagate more strongly in the actual network with safe havens than in the counterfactual without safe havens (continuous line above dotted line in figures).
    - The narrowing of the safe-haven group since 2011 reduced the gap between actual and counterfactual impacts.
  - US sovereign bond shock:
    - Pre-crisis (when US had mildly negative sovereign-sovereign correlations), a US sovereign bond shock propagated more slowly than if the US were an average non-safe-haven country.
    - Since the crisis, increased US bank-sovereign correlations and sovereign-sovereign correlations approaching non-safe-haven levels have reduced this difference.
  - Bank equity price shocks:
    - Presence of safe havens accelerates shock propagation in all three source scenarios (average country, GIIPS, US).
    - US banking shocks propagate faster in the actual network than in one without safe havens because US bank-bank correlations are above average non-safe-haven levels.
- Intuition for amplification via safe havens:
  - A bond-yield shock originating in a non-safe haven that arrives in a safe haven raises safe-haven sovereign yields and, via positive bank-sovereign correlations in safe havens, raises bank equity prices there.
  - These bank-price changes transmit through bank-bank correlations to other safe havens and loop back into sovereign yields via bank-sovereign links—generating amplification and cross-class propagation.

### Conclusions and issues for further research
- Stylized facts documented:
  - Cross-country sovereign-bond yield correlations > bank-bank correlations > bank-sovereign correlations, implying rapid cross-country propagation once sovereign bond network is hit.
  - Safe havens tend to have stronger sovereign-sovereign, bank-bank, and bank-sovereign correlations than non-safe havens, making them potential shock propagators in price-based networks.
  - The US is a distinctive safe haven with negative sovereign-sovereign correlations until the mid-2000s that would have slowed sovereign shock propagation in that period.
  - Changes in the distribution of correlations over time map into changes in shock propagation (e.g., bank equity price correlation peak in H2 2008 and subsequent fall correspond to implied propagation changes).
- Open questions for further research:
  - How safe havens’ roles change with their “neighborhood” in the network (e.g., deeply interconnected Europe vs Asia).
  - How policy actions altered the shape of the correlation network and changed shock propagation (policy interventions are implicit in estimated correlations but not modeled here).
  - Improving causal identification of directions in spillovers (authors note plans to use Diebold-Yilmaz spillover coefficients or Granger causality measures in future work).

*Source: Box 1. Clustering and declustering of the Eurozone community in Sovereign Bond Yields (excerpt).*

### References:

### _wp1481 - References

### Key bibliographic references
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- Acharya, Viral V. and Drechsler, Itamar and Schnabl, Philipp, 2011. "A Pyrrhic Victory? - Bank Bailouts and Sovereign Credit Risk," Journal of Finance (forthcoming).
- Basurto, Miguel A. Segoviano and Caceres, Carlos and Guzzo, Vincenzo, 2010. "Sovereign Spreads: Global Risk Aversion, Contagion or Fundamentals?” IMF Working Papers 10/120, International Monetary Fund.
- Bauer, Michael D. and Rudebusch, Glenn D. (2013), “What Caused the Decline in Long-term Yields?”, FRBSF Economic Letters.
- Baur, Dirk G. and McDermott, Thomas K, 2010. “Is gold a safe haven? International evidence,” Journal of Banking and Finance, Vol. 34, pp. 1886-1898.
- Beck, Roland and Rahbari, Ebraim, 2008. “Optimal reserve composition in the presence of sudden stops: The euro and the dollar as safe haven currencies,” Working Paper Series 0916, European Central Bank.
- Caballero, Julian, 2012. ”Banking Crises and Financial Integration”, Research Department Publications 4816, Inter-American Development Bank, Research Department.
- Caporin, Massimiliano and Pelizzon, Loriana and Ravazzolo, Francesco and Rigobon, Roberto, 2012. "Measuring sovereign contagion in Europe" Working Paper 2012/05, Norges Bank.
- Chinazzi, Matteo and Fagiolo, Giorgio, 2013. "Systemic Risk, Contagion, and Financial Networks: A Survey” LEM Papers Series 2013/08.
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- Cunningham, A.; Dixon, L.; Hayes, S., 2001. “Analysing yield spreads on emerging market sovereign bonds”, Bank of England Financial Stability Review, Issue 11, pages 175-86.
- Drainville, Brian; Khatchadourian, Eric; Torrey, Matthew, 2011. “The Case for Balanced Investing in Emerging Markets”, Leadership Series, Investment Insights.
- Ejsing, Jacob and Lemke, Wolfgang, 2011. "The Janus-headed salvation: Sovereign and bank credit risk premia during 2008-2009," Economics Letters, vol. 110(1), pages 28-31, January.
- Forbes, Kristin J. and Rigobon, Roberto, 2002. “No Contagion, Only Interdependence: Measuring Stock Market Comovements,” Journal of Finance, vol. 57(5), pages 2223-2261.
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### Appendix I — Shock propagation mechanism (illustration and mechanics)
- Network example:
  - Nodes: 7.
  - Link weight (equal for all links): 0.25.
  - Initial conditions: Before shock, all nodes equal 0.
  - Shock: In step 1, node A is hit by a shock of magnitude one.
- Propagation rules and steps:
  - After step 1: The leftmost node becomes a source propagating 25% of its initial magnitude with an appropriate sign.
  - After step 2: There are three sources of the shock (the three left-most nodes), each propagating 25% of the initial shock accumulated.
  - After step 3: All nodes except the two rightmost ones become shock propagators.
  - Process: The propagation is repeated for an arbitrary number of steps; after each step the cumulative impact in each node is calculated.

### Appendix Table 2 — Countries and banks used in the analysis (period coverage and bank counts)
- Table description:
  - Title: "List of all countries and banks used in the analysis, available in different periods. The number of banks for a particular country is given in brackets."
  - Period columns shown: 2000-2006; 2007-2009; 2010-2012; 2013.
- Representative listings (as shown in the table; entries preserve exact bracket counts where provided):
  - Austria; Argentina(6) (2000-2006) → Argentina(7) (2007-2009, 2010-2012, 2013)
  - Australia; Austria(5) (2000-2013)
  - Belgium; Australia(5) (2000-2013); Belgium(3) (2000-2006) → Belgium(4) (2007-2013)
  - Canada; Canada(6) (repeated entries across periods)
  - Switzerland; Switzerland (multiple period entries)
  - China; Bahrain(7) (2000-2013) and China entries across periods with China(6) and China(7)
  - Colombia; Brazil(4) (2000-2013) and Colombia with changing bank counts (e.g., Colombia(7), Colombia(8))
  - Germany; Switzerland(4/5) across periods and Germany with Germany(5) for banks
  - Spain; China(6/7) across periods
  - Finland; Colombia(7/8) across periods
  - France; Cyprus(3) (2000-2013)
  - Greece; Germany(5) (2000-2013)
  - Hong Kong; Denmark(4) (2000-2013)
  - Indonesia; Egypt(11) and Spain-related bank counts evolving (e.g., Indonesia Spain(6/7))
  - Ireland; Spain(5) (2000-2006) and Ireland with Finland(2/3) bank listings across periods
  - India; France(5) and India with United Kingdom(6) listings across periods
  - Italy; United Kingdom(6) (2000-2006 and later)
  - Japan; Hong Kong(4) (multiple periods)
  - Korea (South); Croatia(5) and Korea(South)(7/8) entries
  - Malaysia; Indonesia(6) and Malaysia with Ireland(3) entries
  - Mexico; Indonesia(6) and Mexico with Indonesia(6) across periods
  - Netherlands; Indonesia(6) and Netherlands(2) entries across periods
  - Norway; Ireland(3) and Norway(2) across periods
  - New Zealand; Israel(6) and New Zealand(1) entries
  - Philippines; India(6) and Philippines(9) in later periods
  - Pakistan; Iceland(4) and Pakistan with changing bank counts (e.g., Pakistan(9), Pakistan(11))
  - Peru; Italy(7) and Peru(5) entries
  - Poland; Sri Lanka(7) and Poland with varying counts (Poland(10/11))
  - Portugal; Luxembourg(2) and Portugal(4/5) across periods
  - Qatar; Qatar(7) in some periods
  - Romania; Romania(3) in several periods
  - Russia; Russia (3/5) across periods
  - Singapore; Sri Lanka(7) and Singapore(3) across periods
  - Slovakia; Netherlands(2) and Slovakia(5) in later periods
  - Slovenia; Slovenia(1/3) across periods
  - South Africa; Netherlands(2) and South Africa(3) in later periods
  - Spain, Sweden, Taiwan, Thailand, Turkey, Ukraine, United States, Venezuela, Viet Nam — multiple entries with explicit bank counts shown in the table (e.g., Taiwan(9/10), Turkey(8/9), United States(4/5), Venezuela(7/8), Viet Nam(6/7)).
- Note: The table spans many country-bank pairings across the four period columns; the above are representative entries preserving the bracketed bank counts exactly as presented.

### Appendix figures — cluster and correlation snapshots (labels and periods)
- Appendix Figure 1: "US in sovereign bond yield clusters" — snapshots for 2010H1, 2005H1, 2000H1.
- Appendix Figure 2: "Asia in sovereign bond yield cluster, 2007-2013".
- Appendix Figure 3: "European and US banks in bank equity price clusters" — snapshots for 2010H1, 2005H1, 2000H1.
- Appendix Figure 4: "Asian banks in clusters of bank equity prices" — snapshots for 2010H1, 2005H1, 2000H1.
- Appendix Figure 5: "Non-US American banks in clusters of bank equity prices" — snapshots for 2010H1, 2005H1, 2000H1.
- Figure 6: "Sovereign Interconnectedness".
- Appendix Figure 7: "Bank Interconnectedness" — periods shown: 2000-06, 2007-09, 2010-12. Notes:
  - 2000-06: European banks cluster together; All banks cluster together.
- Appendix Figure 8: "Sovereign-Bank Correlations in Emerging Asia" — periods shown: 2000-06, 2007-09, 2010-12.
- Figure 9: "Sovereign-Bank Correlations in Emerging Europe" — periods shown: 2000-2006, 2007-09, 2010-12.
- Figure 10: "Sovereign-Bank Correlations in Euro Area" — periods shown: 2000-06, 2007-09, 2010-12. Text notes included:
  - "Sovereign-bank correlation also strengthened in Spain, Austria, Belgium, Italy (Soft core), PortugalGRC and CYP decoupled."
  - "Sovereign-bank correlation strengthened in Greece and Ireland."

*Source: _wp1481 - References (appendices and reference list).*

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