Testing the “risk-freeness” of sovereign bonds


Alexander Ludwig

The treatment of EU sovereign debt continues to trouble the capital calculations of insurers under Solvency II. In research published in ‘Applied Financial Economics’*, Alexander Ludwig, Actuary (DAV), argues that there is an economic justification for treating the government debt of some Member States as risk-free, but for other varying degrees of “risk-freeness” exist.

Despite the debt crisis in the Eurozone that led to quasi-defaults and bailouts of countries such as Greece, Portugal, Ireland and Cyprus – and direct recapitalization of Spanish banks by a rescue measure that the Spanish state was not able to shoulder alone – government bonds of all EU Member States still have a zero per cent capital charge under the Solvency II standard formula.

It is obvious that for these crisis-hit countries there cannot be an economic justification of this assumption. But for other Member States that faced similarly deep recessions in 2009 but are now showing signs of recovery, the economic reliability of this assumption should not be rejected instantly. If one accepts that there are still assets that can be perceived as (at least close to being) risk-free, then there are suitable econometric techniques whose outputs can justify the propagation of the risk-free property of such assets in relation to other assets under examination.

Testing the “risk-freeness” of sovereign bonds

In my research I set out to examine the level of “risk-freeness”, if you like, of individual EU government bonds. An asset can be empirically justified to be risk-free if one finds an equilibrium relationship with another asset that is risk-free or is assumed to be risk-free by most market participants. Equilibrium relationships can be detected using cointegration techniques, often applied in economics and finance. If two time series are cointegrated, they are driven by the same stochastic trend meaning that every short-run deviation from their common equilibrium path is followed by a re-adjustment of the series back to their long-run equilibrium.

In other words, if the spread of the yields of the considered asset over the yields of the risk-free asset has converged to a certain value to which it returns after each short-run deviation, the asset under examination can also be deemed risk-free. In a statistical sense, the spread has to be shown as stationary around a mean value. Applying this analysis to EU government bonds is complicated by events such as the introduction of the Euro, the Great Financial Crisis of 2008-9 and the subsequent sovereign debt crisis in Europe as they impact the statistical reliability of standard tests for cointegration and stationarity of time series.

One should therefore first identify structural breaks in the relation between time series, applying appropriate econometric techniques that are able to detect multiple structural breaks.

The test inference of the risk-freeness of an asset should then be based on the most recent period as this guarantees that strong co-movements, which may have been the case before the last structural break (e.g. before the financial crisis), are not mixed with the most current developments.

My research tested this assumption by comparing the yields of 10-year government bonds of 25 EU Member States against the yield of 10-year German government bonds. Germany is generally perceived as the “safe haven” in Europe, which is reflected by the fact that its 10-year yields have been the lowest in the EU (disregarding short-run deviations) already since 1995, and its yields were lower than those of the risk-free rate at the valuation dates used for QIS 5 in 2010 and the EIOPA Long-Term Guarantees Assessment in 2013. The test for multiple structural breaks shows shifts to regimes with larger degrees of convergence with German yields for many Eurozone countries in the wake of the introduction of the Euro as a result of the disappearance of exchange rate risk in the monetary union.

But the shift is also observed for the United Kingdom, Sweden and Denmark, which did not join the Eurozone. Until the outbreak of the Great Financial Crisis in 2008, only few country specific regime-shifts can be observed. Most breaks in the relation with German yields occurred as a consequence of the crisis and the subsequent debt crisis in Europe. Examining the relation with German yields for each country in the most recent period (i.e. after the last structural break), long-run convergence can only be observed for five countries: Luxembourg, the Netherlands, the United Kingdom, the Czech Republic and Poland, with largest mean spreads for the latter two countries. The yields of Sweden and Denmark gradually caught-up with German yields and assumed similar values in previous years. These seven countries are hence suitable candidates for the zero risk charge.

For Austria, Finland, Belgium and France, spreads over Germany are still relatively small but increased since 2008 such that there is currently no convergence with German yields. The zero risk charge for the bonds of these countries can thus not be supported. For all other countries the rejection of the validity of this central assumption of the standard formula is even more evident.

The zero risk charge to government bonds of EU member states is likely to have relevant implications for the asset allocation of insurance undertakings. Unlike EU government bonds, risk charges for corporate bonds increase with the duration of the bond and decrease with the creditworthiness of the issuer.

The preferential treatment of government bonds in this respect may lead to unintended consequences such as the rise of refinancing costs of corporate undertakings and banks if returns adjusted to the new risk charges become unattractive for insurance firms. Moreover, as a consequence of the market-consistent valuation approach under Solvency II insurance firms will face smaller available own funds in times of market downswings and have the incentive to reduce overall solvency capital requirements by increasing their government debt exposure which in turn leads to larger systematic risks in the financial sector.

On the other hand, the ORSA requires a critical reflection of the adequacy of the standard formula assumptions for the specific undertaking. The results of the research provide the justification of this zero risk charge for some EU member states. The analysis can be repeated on a frequent basis as part of the ORSA process of the undertakings.

The views expressed are the author’s own. Alexander Ludwig, Actuary (DAV), is a manager at the management and IT consultancy firm zeb. The research was conducted as part of his studies in Mathematics and Economics at the Dresden University of Technology, Germany and published in 2014 in ‘Applied Financial Economics’. *Ludwig, A. (2014) Credit risk-free sovereign bonds under Solvency II: a cointegration analysis with consistently estimated structural breaks, Applied Financial Economics, 24, 811-823