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Sovereign debt crisis in the European Union: A minimum spanning treeapproachAbstractIn the wake of the financial crisis, sovereign debt crisis has emerged and is severely affecting some countries in the European Union, threatening the viability of the euro and even the EU itself. This paper applies recent developments in econophysics, in particular the minimum spanning tree approach and the associate hierarchical tree, to analyze the asynchronization between the four most affected countries and other resilient countries in the euro area. For this purpose, daily government bond yield rates are used, covering the period from April 2007 to October 2010, thus including yield rates before, during and after the financial crises. The results show an increasing separation of the two groups of euro countries with the deepening of the government bond crisis.Highlights► Recent government bond crises affected some countries in the euro area.►The most touched four countries exhibit an increasing separation from the euro core.► Minimum spanning tree analysis clearly shows this separation.Keywords:Minimum spanning tree; Sovereign debt; Government bonds; Crisis1. IntroductionIn the aftermath of the recent financial and economic crisis, many European Union (EU) member states, as well as countries in other regions, have significantly raised their budget deficits and public debts. One such example is the case of Greece, which recorded a government debt and budget deficit representing 126.8% and 15.4% of Gross Domestic Product (GDP) respectively in 2009. This unsustainable situation created difficulties in accessing international financial markets and a new crisis emerged, this time related to government bonds.After Greece, Ireland became the next country to draw on financial assistance from the EU and the International Monetary Fund (IMF), with Portugal following some months later. Spain also has been impacted by high government bond yield rates although its budget and debt problems are not of the same magnitude as those of the other three countries. Nevertheless, strong pressure has loomed over the euro area, given that other countries, such as Italy or Belgium, have also accumulated large public financial imbalances. There is now an increasingly widespread fear that the Euro might be in jeopardy, with even the European Union itself called into question as a project for economic and political integration in Europe, should this crisis not be contained.In this paper, sovereign debt crisis in the European Union is analyzed with tools developed and largely applied in the field of econophysics. The euro area is of particular concern and, thus, the main focus of the paper lies in the network topology of the eurozone members. The minimum spanning tree (MST) provides the main analytical approach and the dynamics of daily government bond yields are investigated using rolling windows of three months, from April 2007 through October 2010. Our methodology is similar to that used in a recently published paper in thisjournal [1], related to comovements in government bond markets over 1993–2008. Like in this latter paper, we also base our analysis on minimum spanning trees, hierarchical trees and use rolling windows. However, our subject is different, since we are interested in the analysis of the current sovereign debt crisis in the EU. Although we use 10-year government bold yield rates as well, the country composition (only EU countries), period under analysis (last four years) and even frequency of data (daily values) are quite distinct. Besides, we use a larger set of measures in the rolling windows.In addition to this Introduction, the paper is structured as follows. Section 2 briefly describes the data used. Section 3 explains the methodology adopted and Section 4 presents the results obtained. Finally, Section 5 draws the main conclusions.2. Data characterizationWe analyze daily yield rates on 10-year government bonds for nineteen EU countries. Thirteen of them belong to the euro area: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Slovakia, Slovenia and Spain. However, Slovakia and Slovenia only recently became members of the eurozone. The six non-Euro countries are the Czech Republic, Denmark, Hungary, Poland, Sweden and the United Kingdom. Table 1 lists all the countries and groups in the sample, their abbreviations and the year they adopted the euro.The data for all countries corresponds to the Thomson Reuters Government Bond Indices and are end-of-day 10-year government bond yields as calculated by Datastream. All data are valued in local currencies and were obtained from this last database.The sample covers the last four years, from the beginning of April 2007 to the end of October 2010, with a total of 933 observations. This corresponds to distinct phases in the current economic and financial crisis, although we do not pretend here to provide any rigorous characterization of it. Accordingly, the sample is split into three periods. The first (P1P1) includes the observations from April 2007 up to the end of August 2008 and largely corresponds to pre-crisis data, even though the last months already show significant declines in stock markets all over the world. Period two (P2P2) covers the most critical financial crash from September 2008 up to December 2009. Finally, the last period (P3P3), from January to October of 2010, shows some economic and financial recovery in many countries but exposes deep budget problems in others and gives rise to a new crisis, this time related to government bonds.Fig. 1 illustrates this periodization with the evolution of the S&P 500 index (S&P500) and 10-year government bond yield rates for Greece (Greece_Y10). In the first period, in spite of a substantial reduction in the stock market index, no clear trend is observed in the case of bond yield rates, whose values ranged from 4.21 to 5.31. During the second period, the crash also generated some concerns with government bonds and yield rates jumped to a maximum of 6.18. However, the recovery in stock markets was accompanied by some pressure relieve on government bond yield rates during most of the second half of 2009. These rates exploded in the third period, from a minimum of 5.55 to a maximum of 12.27 and this peak was followed by somedecline in the S&P500.European debt crisis makes everyone frustratedMARIO DRAGHI, the head of the European Central Bank (ECB), appears to be winning his bluff with the markets since he declared that he would do “whatever it takes”to save the euro. Bond yields in Spain and Italy have fallen significantly since the beginning of September, although borrowing costs in Spain are higher than they were at the beginning of the year. Unfortunately for the peoples of the euro zone, it is becoming increasingly clear that “whatever it takes” is not actually being considered. Two recent stories support the pessimistic view.First, consider this article from yesterday’s Financial Times:Addressing a German mutual banking event in Frankfurt, Mr Draghi said: “Financial union does not have to imply the pooling of deposit guarantee schemes, an issue that I know is of concern in this country. Organising and funding deposit guarantee schemes can remain a national responsibility, with comparable effectiveness.” While Mr Draghi’s comments chime with the thinking of officials in Brussels, it was the most explicit acknowledgment yet that plans for a single deposit guarantee scheme, already shelved, may not be revived. Establishing a common backstop for the €5tn of deposits in the eurozone has proved by far the most politically contentious element of Europe’s drive to form a banking unio n. Since the autumn, member states led by Germany have been gradually scaling back ambitions for when and how a single deposit insurance scheme should be established...Germany’s council of economic advisers to the government, known as the “wise people”, al so backed the view that a pooled deposit guarantee scheme should be avoided. “Introducing such an insurance scheme would entail significant risks, since losses would be mutualised after the fact,” they wrote in their annual report, published on Wednesday.Many in Europe appear to misunderstand the entire point of deposit insurance, which is that it minimises losses by preventing bank runs. Whether or not the extant banking system is what anyone would design if starting from scratch, the fact is that most intermediaries fund long-term illiquid asset portfolios with short-term liabilities, including consumer and corporate deposits. This is not a problem as long as those short-term liabilities behave like long-term liabilities. In plain English, depositors have to feel so confident in the safety of their bank accounts that they choose not to withdraw any significant proportion of their funds at a single time, which would cause the bank to collapse. Given our knowledge of what bankers actually do, there is no reason for anyone to have this sort of confidence in a bank without a government guarantee.Of course, this guarantee itself has to be credible. The waves of deposit flight from the euro zone’s periphery to its core (and to Switzerland) are proof that many governments are incapable of convincing their citizens that their money is safe. At bottom, the problem can be traced to the single currency itself. In the absence of central banks standing behind them, the euro zone’s separate national depositinsurance schemes are meaningless. Consider the experience in Spain as compared to America. Both endured nasty housing bubbles and busts, which got their banks into trouble. Americans moved some money into gold but there was no widespread flight from the dollar. In fact, the dollar is basically unchanged in value against the trade-weighted basket of foreign currencies. A big part of the reason is that American savers need dollar-denominated assets to hedge against dollar-denominated liabilities. By and large, those assets are only issued in America, so capital flight was never an option.In the euro zone, it is a very different story. Spaniards rightly suspect that their nation might choose to leave the currency union. Even if the risk is small, there is no cost—yet—to taking the reasonable precaution of moving their savings to Germany or the Netherlands (or Switzerland, thanks to the currency peg). Adjusted for devaluation risk, a euro saved in a Dutch bank is worth more, potentially much more, than a euro saved in a Spanish bank. If Spain leaves the euro, deposits held in Dutch and German banks will remain secure, or become far more valuable when brought back into Spain. Unsurprisingly, deposits have been fleeing Spain for years.This capital flight exacerbates the underlying problem by weakening the Spanish banks and Spanish economy, thereby making an exit more likely. Moreover, it puts significant strains on the existing deposit insurance scheme, which endangers the fiscal position of the Spanish government, thereby encouraging yet more capital flight. There is no way Spain can break this vicious circle by itself, unless it actually leaves the euro zone and prints new pesetas with abandon. The ECB could help stem the capital flight by explicitly selling insurance against devaluation risk, but this seems extremely unlikely. Given all this, it is nearly impossible to imagine the euro holding together without the “Europeanisation” of bank deposits through the introduction of a common insurance scheme backed by the entire zone, particularly the ECB. The people of Europe might not want to accept these consequences of the single currency but they ought to know that this is the choice they must face.Why does the ECB need to be involved? After all, aren’t most schemes pre-funded by collecting fees from banks? Pre-funding might seem like a great idea, but it is insufficient in practice. As Sheila Bair, the former head of America’s Federal Deposit Insurance Corporation, recounts in her memoir Bull by the Horns, there are strong incentives among regulators and bankers to prevent the collection of sufficient fees. When times are good and risks are building, bankers often persuade their overseers that they are being needlessly overcharged. But when times are bad, no one wants to extract fees from solvent banks to cover the losses of the failed institutions. Therefore, while pre-funding might sound good in theory, no government can expect to amass a sufficiently large rainy-day fund in practice. This helps explain why the apparently prudent fiscal management of the Spanish and Irish governments before 2008 did little to help them in the years that followed.The other disturbing story out of Europe comes from Bloomberg:There is little doubt that Weidmann lost the argument over the ECB’s latest response to the sovereign debt crisis. He was the only one of the bank’s 22 Governing Council members to vote against Draghi’s unlimited bond-purchase plan, arguing it istantamount to printing money to finance governments. Yet the Bundesbank was actively involved in designing the specifics of the program and supported strong conditionality, said two central bank officials who spoke on condition of anonymity. Weidmann’s concerns were “vital” to the design of the bond program, ECB chief economist Peter Praet told Germany’s Handelsblatt newspaper on Oct. 31. The ECB will only buy bonds if a country signs up to budget consolidation and structural reforms, he said.Draghi stressed the “strict conditionality”of the program in a speech in Frankfurt yesterday as he seeks to assuage German concerns. Conditions were put in place “largely to please Germany,”said Jennifer McKeown, senior economist at Capital Economics in London, who also thinks the decision to sterilize the bond purchases was due to Weidmann. “Given that the Bundesbank has only one vote at the ECB, one might argue that it has actually exerted undue influence in these matters,” she said. Under so-called Outright Monetary Transactions, the ECB will only buy a nation’s bonds on the secondary market if the government requests aid from Europe’s rescue fund and signs a Memorandum of Understanding to meet certain fiscal targets. Even then, there is no guarantee the ECB would intervene.Given what we know has happened so far in Europe as a result of self-defeating austerity and myopic deficit targets, this seems like madness. If the Bundesbank successfully holds the ECB hostage and demands further fiscal bleeding as the price of additional monetary stimulus.。