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Annex 1 – Pricing Purple and Red Bonds
Intra-euro area sovereign bond spreads reflect three distinct, but not mutually exclusive risks; debt restructuring, currency redenomination and liquidity. Debt restructuring can take place both inside the euro area and in the risk scenario of a euro exit. Currency redenomination, however, would only occur if a euro area member state exits the euro. The remaining risks relate to the risk that an investor is unable to exit a position due to poor trading conditions (liquidity risk), Credit Default Swap (CDS) counterparty risk and CDS contract uncertainty.
To illustrate how Purple and Red bonds might price under out proposal, we find it useful to consider the three premiums listed below.
1) ESM premium: This covers the risk that a member state applies for an ESM programme and debt is restructured. Purple bonds are not exposed to this risk while Red bonds are.
2) Euro exit premium: In a euro exit scenario, a member state can restructure its debt and/or repay it in a newly devalued national currency. We distinguish these two risks in our analysis. Both Purple and Red bonds are exposed to this risk.
3) Market friction premium: This includes market liquidity risks, counterparty risks and contract uncertainty.
We discuss redenomination and restructuring risks below and then present our framework to illustrates how Purple and Red bonds might price. We have purposefully kept the framework simple to allow our readers to easily replicate our methodology and enter their own assumptions if so desired. The first step in developing our approach is to consider how intra-euro area sovereign spreads can be broken down to reflect the different premiums. Our framework takes its starting point in Credit Default Swap (CDS) spreads, albeit that we recognise for the onset that these markets are far from perfect due both to contract uncertainty, counterparty risks and liquidity issues.
Credit Default Swaps in brief
Credit Default Swaps (CDS) offer the buyer protection against a credit event against the payment of an insurance premium (generally referred to as the CDS spread) to the seller. If a credit event occurs, the buyer will receive the difference between the par value of the bond and its post-credit event value. As we discuss below, CDS spreads are useful in analysing both redenomination and restructuring risks but various segments of the market often suffer from low liquidity and counterparty risk. On the later risk, it should be noted that CDS may be exposed to the sovereign-financial institution doom loop when there are close ties between the sovereign on which the CDS is sold and the financial institution selling the CDS8.
A distinction must, moreover, be made between CDS issued under, respectively, the 2003 ISDA definitions and the 2014 definitions9. At the height of the euro area debt crisis in 2011/12 there was a great deal of discussion as to what would constitute a credit event. Amongst other issues, it was not entirely clear that, in all cases clear, a euro area sovereign CDS issued under the 2003 rules would protect from redenomination risk (i.e. the risk that the bond is repaid in a new national currency than is devalued against the euro).
Despite these various issues, CDS spreads are nonetheless, to our minds, the best available proxy to gauge market pricing of the risks reviewed without having to rely on complex quantitative models to extract the premium, which brings its own model uncertainty. For further discussion of issues relating to sovereign CDS spreads, we refer to Duffie (1999), Fontana and Scheicher (2010) and De Santis (2015).
Isolating restructuring risks
The differential between the cash government bond yield and the CDS spread is referred to as the basis. If the CDS offers 100% full protection against all restructuring and redenomination risks, then this spread should in theory be equal to zero as arbitrage should remove any differences. This would of course only be the case if markets are frictionless with unlimited access to unimpeded funding for arbitrage and no counterparty risks. The market reality is quite different, however.
A positive basis would logically arise if the CDS does not offer full coverage against all restructuring and redenomination risks. A negative basis would typically reflect counterparty risk. Market frictions, moreover, may also influence the basis. Respective liquidity risks may also impact the basis.
The chart below shows how the 10-year benchmark government bond spread between Italy and Germany, breaking it down between the CDS spread and the basis. Note that all our analysis below uses a dataset from Datastream that is based on CDS issued under the 2003 ISDA rules. As such, the CDS spread below should only reflect restructuring risks (debt default) and not redenomination risks.
Chart A.1 Breaking the bond spread into a CDS spread and a Basis
Source: Datastream and own calculations
A useful feature of CDS spreads is that these can be used to derive probabilities applying certain assumptions about loss given default. Applying a typical loss given default of 50%, we can thus derive a probability for debt restructuring from CDS spread. We here assume that the markets fully understood that the ISDA 2003 definition would not cover redenomination risk, albeit that we recognise that there was some uncertainty on this, as already mentioned above, during the crisis. At present, the market is implicitly pricing an accumulated restructuring probability of around 12% on Italian 10-year debt equivalent to a CDS spread of just over 60bp. Note, that restructuring can take place both in a risk scenario where the member states is assumed to remain in the euro area and in a scenario where the member states exits the euro. To be able to price Purple and Red bonds, respectively, this premium must be split between the two restructuring risks. We return to this point after discussing redenomination risks.
Isolating redenomination risks
As proposed by De Santis (2015), redenomination risk can be estimated by taking the difference between individual member states quanto-CDS relative to Germany. The quanto-CDS for a euro area member state is defined as the differential between its dollar-denominated and euro-denominated CDS spreads. Absent redenomination risk, the quanto-CDS should trade identically across individual euro area member states. An alternative means to derive redenomination risks would be to take the spread between the CDS issued under, respectively, the 2014 and 2003 ISDA rules.
The basis spread in Chart A.1 above includes redenomination risk. We can thus strip this out to be left with a “pure” basis, which should in theory reflect only the various other frictions discussed above.
As seen from Chart A.2, the 10-year quanto spreads of Italy over Germany widened significantly during the crisis and narrowed sharply after President Draghi delivered his now famous “whatever it takes speech” in London on 26 July 2012. More recently, this spread has widened again for Italy. Assuming an eventual new devalued currency trades at 30% below the euro, we can again derive an implied probability. At present, this suggests a redenomination risk of just over 6% drawing on the 10-year Italian-German quanto spread, translated into a spread of around 20bp.
Chart A.2 Breaking down the 2003 basis into redenomination and a “pure” Basis
Source: Datastream and own calculations
With these observations in mind, we now return to the pricing of Purple and Red bonds.
To give a sense of how probabilities translate into CDS spreads, the chart below shows the spreads for various probabilities of credit events and a loss given default (restructuring or redenomination) of, respectively 30%, 50% and 70%. To derive these measures, we use the reduced form formula as shown in equation A.1 below. As seen, the function is exponential.
Chart A.3 10-year CDS spreads for various probabilities as a function of loss given default (LGD)
Where P is the implied default probability, S is the CDS spread (in percentage terms), t is the years to maturity and R is the recovery rate in percentage terms (note, LGD=1-R).
Pricing Purple and Red bonds
In pricing Purple and Red bonds, we are interested in two distinct risk. The first reflects the risks that a member state will apply to the ESM and as result potentially see Red bonds restructured, but not the Purple ones as these benefit from the no restructuring guarantee under an ESM programme. The second risk reflects euro exit risk; this would see both Purple and Red bonds exposed to both redenomination and restructuring risks.
The redenomination risk can as outlined be directly derived from the quanto spread. To estimate this component in our simple price model. We simply apply a probability that sovereign debt will be repaid in a new devalued national currency combined a 30% devaluation assumption. This, however, is not the full euro exit risk as a member state leaving the euro could opt to repay its debt in euros but only after having restructured it. Indeed, as discussed above, restructuring risk can relate both to the risk scenario where the member state remains in the euro and the scenario where the member state exits the euro.
De Santis (2015) shows that during the peak of the crisis about 40% of Italian sovereign spreads could be linked to euro exit risks. Of course, varying appreciations of the risks could lead to very different probabilities on such a scenario. What is clear is that in our pricing model, we must attach a separate probability hereto.
There is also an element of restructuring risk that relates to the case where a member state applies for an ESM programme. As shown in our summary table below, this risk is only relevant for Red bonds as the Purple ones enjoy a no restructuring guarantee under an ESM programme. We assume a loss given default for Red bonds of 70% under this scenario reflecting that market participants would likely see a higher restructuring risk related hereto given its smaller share of the total sovereign debt.
The final element in our pricing model is market frictions. We conservatively set this to always be positive and here define it as 30% of the sum of the other risk premia and a flat premium that we here set to 20bp, reflecting a general pre-crisis spread relative to Germany across the euro area. The table below summarises the assumptions of our pricing framework.
Table A.1 – Pricing Purple and Red bonds
The price of, respectively, the Purple and Red bonds would thus vary with the market probabilities attached to (1) an ESM programme. (2) debt redenomination under a euro exit scenario and (3) debt restructuring under a euro exit scenario. The market frictions premium varies with the size of the ESM and euro exit premiums.
In breaking down the current 10-year Italian benchmark spread of 130bp over Germany (8 May 2018), we can observe the quanto spread (20bp), the CDS spread (62bp) and what we term market frictions (48bp). The quanto spread reflects the risk of the bond being repaid in a new devalued currency (which would only happen under euro exit). Assuming the new currency would trade 30% lower than the euro, then this implies a probability of 6% on this scenario.
The CDS spread of 62bp reflects a restructuring risk premium linked both the to the risk of restructuring under an eventual ESM programme and to a potential euro exit. Assuming a loss given default (restructuring) of 50%, this implies a probability hereof at around 12%. This needs to be broken down into restructuring risks linked to an ESM programme and to a euro exit, respectively. In our example illustrated in Chart 4.1, we have set these probabilities so that around 1/3 of the risk premium is linked to euro exit risks and 2/3 debt restructuring under an ESM programme, inspired by De Santis (2015). This is, however, is a purely subjective split and not an exact science. Moreover, this will change with market perceptions of different risks over time. The point to note is that if all the risk implied by the CDS spread is linked to a euro exit scenario, then Purple bonds would offer no gain. Conversely, if some of the premium (as we assume) is linked to debt restructuring risks under an eventual ESM programme, then Purple bonds would trade at a discount as they would not contain this risk factor.