Case Study: The Default of Greece

In Section 5.4.1 we used the debt of Greece as an example on how to price bonds to recovery. Next to what we have said, which stands true, as an added feature we can use the default itself of the government of Greece as an important tool in the understanding of credit events. At the end of a drawn- out process and with little surprise on the part of the markets, Greece agreed to restructure its debt on March 19, 2012.

In the case of events so recent and so charged with different meanings and interests to different parties, it is difficult to point the reader to formal literature other than the major financial newspapers and specialist sites such as Vox or Breakingviews. A few key issues render the situation of Greece particularly difficult:

┠Defaults by developed sovereign entities are extremely rare and there is a general wish for them to remain so. This has resulted in an unwillingness on the part of the public and the politicians to accept the fact that a default was unavoidable, and in the default itself, taking place well after the market had taken it for granted. The lateness of the default brought with it all the problems of a self-fulfilling prophecy: contagion of other European countries' debt, capital flight from Greece, and so on.

┠Greece is part of the Euro zone: the membership resulted in a series of considerations and discussions that probably would not have taken place had Greece been unattached. (There are, of course, those arguing that Greece's membership in the Euro zone is precisely the reason for its default.) The general effort was directed toward finding voluntary arrangements that would minimally disrupt the complicated links between sovereign debtors and corporate creditors.

┠The majority of Greece's debt is in Euros, which, as we have mentioned before, can be considered at the same time a domestic currency, but also as a foreign currency since the Greek government has no monetary control over it.

Instead of focusing on the economics of the issue, which not only are controversial but also subject to change resulting in statements easily obsolete, let us discuss a few numbers and figures in order to illustrate what we have discussed about distressed and illiquid debt.

In Figure 5.8a we show a plot of the price of the bond in EUR paying a coupon of 6.14% and expiring on April 14, 2028, together with the (EUR) up-front premium needed to purchase five-year protection against the default of Greece. In Figure 5.8b we show the plot of the price of the bond in USD paying a coupon of 4.625% and expiring on June 25, 2013, together with the (USD) up-front premium needed to purchase five-year protection against its default.

Let us remind ourselves that Greece has defaulted on its EUR, not USD, denominated debt.^[1] We see that near the default, the price of the USD bond is (relatively speaking considering the abysmal levels) considerably higher than the EUR bond. Both plots are striking in their being X-shaped from the summer of 2010 when the sovereign debt crisis roughly began: the price of the bonds starts veering off the par value and the price of the up-front protection increases accordingly.

In the previous section we introduced a rough relationship between protection premium, recovery, and probability of default, namely

This means that in a situation nearing default, since the probability of default is essentially 100% and the recovery is very close to the bond price, the sum of protection premium and bond price should be close to 100% of the bond's face value. We plot this in Figures 5.8a and 5.8b and we find our view broadly confirmed. There are, however, some details that are interesting to focus on. First of all is the difference between the EUR and USD scenarios. Since the probability of default cannot be more than 100% we would expect the sum of bond price and protection to be below 100: this is because the protection premium must also involve the scenarios where the underlying does not default. An event cannot be more than certain, to be certain is the most probable it can be, therefore protection must be progressively cheaper as we move away from certitude and therefore the sum of bond price and protection should have, according to this very simple reasoning, 100 as an upper bound.

(5.20)

FIGURE 5.8 A plot in time of the market price of the Greek government bond, the up-front premium to buy five-year protection against the default of Greece, and the sum of the two for a) the 2028, 6.14% bond (EUR) and b) the 2013, 4.625% bond (USD).

Of course this is very simple reasoning indeed since it does not take into account the estimate of the recovery level, liquidity, or the effect of interest rates (and the coupon value) on the bond price (we have assumed that in a situation like this one credit trumps any other consideration). We notice that in the case of EUR the sum tends to be below 100, whereas in the case of USD the sum tends to be above. This could be because the price for protection is very similar in the two currencies whereas the bond price in USD is considerably higher.

Protection is determined with respect to a pool of reference obligations, that is, debt instruments whose default triggers the protection payment. The USD bond we are considering is essentially the only USD bond issued by Greece: this means that the five-year protection premium, being of a tenor much longer than the maturity of the bond, is an approximation. Moreover, the protection premium is linked to the reference obligations but is also very much driven to market feeling: once accounted for FX basis and the like, it only makes sense that the cost of protection in USD would follow closely the cost of protection in EUR. This irrespective of the fact that repaying its USD debt is a drop in the ocean of obligations facing the Greek government.

Relating to what we have just mentioned about the fact that 100 should be an upper bound for the sum of bond price and protection, let us observe another characteristic of the shape of each curve. Judging from Figure 5.8a, by the end of December 2011 the market seemed to have settled on the price at which Greece would eventually default (21.5% of face value). Figure 5.8b shows that, similarly, the USD bond price reaches a more or less stable price at the same time. Despite the fact that these values remained stable for more than three months before the actual (EUR) default, the protection premia are not as stable. For more than a year before the actual default of Greece the market believed that it was unavoidable, yet, more than once, the European governments managed to rescue the situation and postpone its solution for a brief period. This means that the default possibility, while present, was not seen in the immediate future (in this context immediate really means immediate). This means that, since we said that the further away from certitude, even for a small period, the cheaper protection must become, protection level would be lower than it should be judging by bond prices.^[2]

In Figures 5.9a and 5.9b we show the plot of a two-year strategy beginning in the summer of 2010 and ending at the time of default. We imagine

FIGURE 5.9 The cumulative profit and loss resulting from holding bond and protection from August 16, 2010, up to the default of Greece for a) EUR-denominated debt and b) USD-denominated debt.

that in the summer of 2010 we bought our two bonds and at the same time we purchased the corresponding protection against their defaults. In the two plots we show the P/L (profit or loss) deriving from holding bond and CDS, that is, hedging the bond with its corresponding CDS.

The P/L associated with the possession of a bond is fairly easy to understand: if the price of the bond increases we could make a profit by selling it at a higher price than the one we bought it at. Should the price decrease the opposite would be true. What does P/L mean in the case of protection? It means roughly the same thing: if we bought protection at a certain price, should the cost of protection increase, we make a profit because we are holding something that has become more valuable than when we bought it. In order to realize the profit (i.e., monetize it) we could sell protection at the new (higher price) and, a process made even more transparent by the new CDS quotation convention, we would gain the difference between the upfront premia. It might not seem obvious and tangible, but as far as judging the worth of our strategy is concerned, we mark a profit or loss even if we do not physically realize it.

A perfect hedge in which the price of the bond and its corresponding protection move in perfect sync would result in a net P/L, which is a fairly constant line near the zero level.^[3] Of course this is not possible since there are considerations such as liquidity, the assumption of recovery rate, and the effect of interest rate that affect the two prices in different ways. Having said that, we would still expect the line to be roughly constant and end (this is the interesting aspect of doing this exercise on the obligation of a borrower who has defaulted) at zero. Both plots confirm the final part, as in both situations the final net P/L is close to zero. Otherwise the two plots illustrate in a different way what we have already mentioned. The cost of protection at the beginning differs little between the two currencies, however, the EUR bond drops in price more quickly and sooner than the USD bond. The strategy therefore during the first half shows a net loss in the case of the EUR and a profit in the case of USD. Later both turn negative and reach the final, zero, net value from below, that is, confirming the fact that the bond prices reached a stationary value sooner than the corresponding protection premia.

The example of Greece has been very useful to understand the movement of bond and CDS levels when the dynamic is driven mainly by credit. The exercise has been helped by the fact that there is a great availability of data.

We shall now concentrate on situations where the credit situation not only- might be dire but also where the data is scarce.

• [1] This is also because the size of the EUR debt dwarfs by roughly two hundred times the size of its USD-denominated debt
• [2] This option-like argument based simply on the time value of protection is compounded by legal arguments centering around the possibility that a non-CDS- triggering default could take place.
• [3] How constant and how near zero would depend on some secondary factors such as the size of the running coupon in the CDS (indicating the relative weight of the up-front premium in the cost of protection), the time to maturity, the distressed level of the debt (the more distressed the more credit plays the dominant role), and so on.