With all the bail out packages of the PIIGS, the tail risk is still “stubbornly high”. SOme more on the subject via Voxeu.

Mutualising sovereign bonds is equivalent to forming a linear combination of the underlying bonds, i.e. a portfolio of them. Hence the risk associated to the portfolio is a function of the risks of the constituents and their correlations.

• In tranquil periods these risks have a linear nature,
• In periods of turmoil non-linearities appear, namely due to extreme events, that induce non-linear -or tail- risks.

Figure 1 shows the quarterly cross-sectional average correlations (from 2005Q1 to 2012Q2) for the Sovereign bond yields of all the Eurozone countries (solid blue), the core countries (dotted red), the peripheral countries (doted and dashed green), and the peripheral countries but Greece (dashed purple).

Prior to the crisis correlations were very close to unity, reflecting the almost perfect co-movements among the yields. Since the beginning of the crisis the correlations have sharply decreased for all countries and groups of countries. From a risk perspective, the creation of the Eurobonds may be seen as appropriate since the benefits (creditworthiness, resilience, stability, and liquidity) offset the slight increase of risk associated to the small correlations.

Figure 1. Average linear correlations

…and tail risks up

In periods of turmoil, it is not enough to watch the linear relationships – non-linearities appear; tail risks increase. Indeed, when tail events occur, their effect is spread over the system. In recent work, Luca Ricci and I have recently introduced TailCoR, a new measure of tail correlation (Ricci and Veredas 2012).

• TailCoR is a function of linear and non–linear contributions, the latter characterised by the tail behaviour.
• It is based on quantiles and has a number of useful properties, such as simplicity, distribution freeness, and no need of optimisations.

Figure 2 shows the quarterly cross-sectional average tail contribution to TailCoR for the same groups of countries as in Figure 1. Values below unity refer to thin tails, and hence low portfolio tail risk. Values above unity correspond to high portfolio tail risk. Prior to the crisis all the dependence among Sovereign yields was linear since the tail contributions were smaller or in the vicinity of one; the only exception being 2008, at the height of the financial upheaval. More importantly, since the beginning of the crisis the tail risk associated to all the Eurozone countries has increased substantially (blue and solid line), and the trend is positive. As a consequence, pooling Eurozone sovereign bonds today may be seen as too risky since a negative tail event in the yields of one country may cause a cascade of tail events in the yields of the other countries, increasing the probability of a large negative and generalised extreme event in the Eurozone as a whole.

Figure 2. Average tail contribution to TailCoR – part I

Note: Quarterly cross-sectional average tail contribution to TailCoR of all Eurozone sovereign bonds (solid blue line), core bonds (dotted red), peripheral bonds (dotted and dashed green), and peripheral but Greece bonds (dashed purple).

Full article here.

Tail chart; PIMCO