Unless you've been living under a rock, you would probably have noticed (or read) about the gyrations in global capital markets as a result of the Greek sovereign debt crisis  (and, to a lesser extent, electoral uncertainties  in Britain). This was alleviated somewhat by the whooping EUR 720 billion financial stability package  designed to cow financial market contagion into submission. For added (ironic) effect, EUR 440 billion of the assistance is to be effected  (PDF) through a special purpose vehicle (SPV)---the very entity (ab)used by private sector banks prior to the crisis to maintain large risky assets off their balance sheets.
One major justification for the massive size of the stabilization package was the need to send a credible signal to financial markets that have been jittery and increasingly testing the asset markets in other EuroPeriphery states, leading to fears of contagion that could spread beyond the periphery and perhaps even to core or Eastern Europe. Since the SPV is funded not so much from money already in the bank but rather will be raised from the markets (having been covered by government guarantee), it remains to be seen whether markets will comfortably digest the package, or whether their nervousness will return after a lull. In the meantime, it is interesting to ask what the extent of contagion has been, in order to gauge whether fears of contagion were truly justified.
To do so, we need some measure of asset market contagion. Of course, this question is not new to the economics literature (indeed, the issue of identifying comovement in aggregate economic series is likely as old as macroeconomics itself ). But it is not purely academic nitpicking to want to distinguish the broader study of the extent of synchronicity in the evolution of macroeconomic variables from the narrower concern of how the comovement of indirectly-related variables may change as a result of some major shock in one of the variables. In other words, there are legitimate reasons to want to study how closely two market variables are related before and after a significant event (such as a financial crisis). We thus take a small academic digression.
The empirical literature has adopted several approaches toward testing for for these contagion effects. The most straightforward method is to compare pre- and post-shock relationships between two markets, generally by taking correlations (Calvo and Reinhart  is a good example of this strategy). Other approaches that attempt to capture the extent of market comovement include papers using cointegration  techniques (see Longin and Solnik  and Yang and Lim  (PDF) for applications to the OECD and East Asian stock markets, respectively), and those favoring ARCH and GARCH  (PDF) modeling (Hamao, Masulis and Ng  for developed equity markets, and Edwards  (PDF) for Latin America). Finally, a whole literature tries to capture how different economic linkages---such as the size of trade and financial flows between countries---may matter in transmitting crises between countries (Eichengreen, Rose, and Wyplosz  is one of the seminal attempts; Chinn and Forbes  and Caceres, Guzzo and Segoviano Basurto  are two more recent efforts).
Now, one shortcoming with much of the academic work is that they generally do not offer real-time diagnosis of contagion as they arise (this is of course not a shortcoming for the academic papers themselves, since their focus is on uncovering fundamental relationships and building our knowledge of the phenomenon, rather than providing contemporaneous diagnosis). Still, such real-time takes on the high-frequency data may be helpful for policymakers watching an economic disaster unfold elsewhere, and wondering if their countries could be the next target.
One method here is to stare long and hard at the economic fundamentals in related economies, and to ask to what extent we can expect future deterioration in these fundamentals. In this regard, several research bodies housed in investment  banks  (PDF) have offered some rapid analysis of Greeek contagion concerns. Another method is to look at what the currently-evolving data are telling us, and to make inferences based on what such patterns reveal.
Ground zero for the Greek crisis was, well, Greece. More specifically, most would probably agree that concerns began in the Greek government bond market, where the Hellenic Republic first announced, on November 5, 2009, that irregularities in earlier budgets would mean that Greece's deficit would come to 12.7 percent of GDP, more than twice the amount previously believed. Yield speads on Greece have been on a roller-coaster, but generally upward, trajectory ever since. As we all know, this re-examination of Greek public sector debt and deficits has been accompanied by re-assessments of the fiscal positions of the EuroMed nations and Ireland, and changes in spreads between Greek and EuroPeriphery began to display a disturbing coincidence (see figure)---the dreaded contagion. What's worse, the strength of the correlation between changes in these spreads peaks in response to events in Greece: For example, the Fitch downgrade of Greek debt  (free registration required) on December 8, 2009 led to a noticeable spike in correlations between Greek spreads and those of Portugal, Italy, Ireland, and Spain. Ditto for the more recent downgrade of Greece to junk status  on April 27.
Source: World Bank staff calculations, from J.P. Morgan .
Notes: 60-day rolling correlation on changes in yield spreads (on German Bunds) of 2-year sovereigns for Hellenic Republic government bonds with: Portuguese government bonds, Italian BTPs, Irish NTMAs, and Spanish government bonds.
As it turns out, contagion spillovers have been somewhat more limited relative to the Eurozone core, as well as other major developed markets, such as the United Kingdom and United States (see figure). With the exception of the France---where the trend since March has risen somewhat more strongly---there is little discernible uptick in the past month or so for correlation between changes in CDS spreads on Greece vis-a-vis other countries in the European core or the United States. In fact, the trend for the U.S. has been downward since the collapse of Lehman, and correlations with Greece have fallen since the end of March (which likely reflects a flight-to-quality response).
Source: World Bank staff calculations, from Datastream .
Notes: 30-day rolling correlation on changes in CDS spreads of 5-year sovereigns for Hellenic Republic government bonds with: German bunds, French OATs, UK Gilts, and US Treasuries.
What about emerging Europe? As noted in a previous post , sovereign risk in emerging Europe was a concern, especially given the high debt/GDP ratios of many ECA countries (both current and projected). The concern here, of course, is whether these nations could be susceptible to contagion from the Greek crisis. Here, we see once again that correlations between the Athens Stock Exchange index and a basket of ECA stock market indexes have risen in recent days, especially since the downgrade of Greece (see figure). The pattern is similar for sovereign risk, as proxied by correlations between CDS spreads on Greek bonds and a basket of ECA nations' CDS. It is key to recognize, however, that these correlations remain significantly below highs attained due to the Lehman failure, and that current correlations are not at intra-period highs, either. While it is important for ECA policymakers to remain vigilant, it does appear that contagion effects have not quite spilled over into ECA, either.
Notes: 30-day rolling correlation on returns on the Athens Stock Exchange with a GDP-weighted basket of returns from the: Bulgarian Stock Exchange SOFIX index, Prague Stock Exchange PX index, Budapest Stock Exchange BUX index, Warsaw Indeks Giełdowy (WIG) index, and the Bucharest Exchange Trading BET-10 index; and 30-day rolling correlation on changes in CDS spreads of 5-year sovereigns for Hellenic Republic government bonds with a GDP-weighted basket of CDS spread changes for: Bulgarian, Czech, Hungarian, Polish, and Romanian government bonds.
In addition to contagion between countries, however, we have also seen contagion across asset classes. Changes in Greek government bond spreads have clearly seen a marked strengthening in its relationship with EuroPeriphery equity markets, especially with the Lisbon Stock Exchange and Bolsa de Madrid. Foreign exchange has also been hammered by contagion effects, with the euro and pound showing increased synchronicity. Although this may seem entirely self-evident, recall that the Greek economy is only 2 percent of Euro area GDP, with a fairly healthy German economy serving as the regional anchor. Furthermore, the UK is not even a part of the eurozone (although, as alluded to earlier, weaknesses in the pound may have been due to British electoral uncertainties).
Notes: 30-day rolling correlation on changes in yield spreads (on German bunds) of 2-year Hellenic Republic government bond with the returns on the: Lisbon Stock Exchange PSI general index, Irish Stock Exchange ISEQ overall index, Borsa Italiana MIB index, Bolsa de Madrid IBEX 35; and changes in the: EUR/USD exchange rate, and GBP/USD exchange rate. Correlations on bond spreads with equity returns have been inverted for expositional purposes.
Before closing, it is useful to raise some caveats to our discussion above. The measure used in this post---simple rolling correlations---is hardly rocket science; and I'm well aware that higher-power methods can better address some concerns that have arising in the literature: for example, cointegration tests allow for the possibility of short-term deviations in opposite directions, while imposing ultimate reversion, and by focusing on the volatility element, GARCH and conditional correlation /dynamic conditional correlation  models better correct for heteroskedasticity biases that may be prevalent during periods of market turmoil (and which is ignored by simple rolling correlations). But these are technical issues that, while addressing will undoubtedly improve the quality of the measure, should not take too much away from the main qualitative message we have made here.
Importantly, it should pointed out that the indicator does not distinguish between periods where markets display comovement in response to positive news, as opposed to negative news: Hence, indicators such as this should always be used in conjunction with some measure of fundamentals, in order to ascertain whether markets are responding coincidentally to some external factor, which may well be positive (and hence may be of lesser concern to a policymaker worried about contagion due to market panics). Here, pairing the analysis we have done here with an index based on underlying fundamentals would make the picture far more complete. Thankfully, an index that directly fulfills this purpose has already been developed by our group, and is described---in amazing dynamic detail---by Hans  in this recent blog post . Efforts by teams elsewhere to provide measures with a similar flavor include NYU Stern 's recently-launched systemic risk measure  (the methodology, while general, has thus far only been applied to U.S. financials); along with the Scale of Market Quakes , a measure of shocks experienced by currencies in response to political and economic events, developed by Olsen and Associates , a Zurich-based FX-centric outfit.