## Tuesday 4 October 2011

### Greek Default Probabilities

In the past few weeks a flurry of articles have hit the popular press regarding the probability of default of Greece. Headlines like, “Markets predict Greek Default probability 99.99%” or “CDS markets predict 100% probability of default for Greece” inspired fear to the hearts of investors and to Greek depositors who rushed to take their money out of Greece. Most of these stories have originated from the financial press[1] and from traders who used a well known mathematical formula that computes the probability of default given the bond Price.
One cannot argue the correctness of this number or the mathematical involved which have been checked by many practitioners and academics alike (including me). There is however, great ambiguity and controversy at applying this mathematical formula and interpreting this number as the market’s prediction for the probability of default for the Hellenic Republic. The reason is simple. Many of the underlying assumptions, which unfortunately are almost never mentioned, are violated in this case.

Market Liquidity and Efficiency

Figure 1. Monthly traded volume of GGB's

The credit spread of any bond whether corporate or sovereign is comprised of the following components:

a)    Risk of Default.
b)   Optionality if any.
d)   Other, like Convexity, Repo specialness, etc.

In the case of almost all Greek bonds the credit spread is simply (a) and (c). I.e. Risk of Default plus Liquidity Premium.
So how much is the Liquidity risk or premium embedded in the spread. Do we know? Can we somehow estimate its value? Most academic studies have shown that it is significant but unfortunately no satisfactory model exist (to the best of my knowledge) that can separately price it.
So, how liquid are the Greek bonds and the Greek Bond market. Greece has about 350 billion of debt. In the form of tradable bonds around 280billion as the bailout package have so far transformed 60billion into bilateral loans and there are also around 10billion in short term Tbills. How many of these bonds are traded on a monthly basis now and how many a year ago. The graph below (Figure 1) is revealing. From a high of around 45billion in March 2010 (when the debt crisis erupted) we are down to 1.7billion in March 2011 (Data are from the major providers, HDAT, MTS, Brokertec, BGC, ICAP). This is an absolute staggering reduction in liquidity to the once vibrant Greek bond market. Why did it happen? Why are these bonds not traded? Why do investors shy from them even at extremely low prices and why are scared holders don’t sell them?

The problem is that as prices dropped, many banks holding Greek bonds moved them to the banking book (accrual) and marked them at PAR. By moving them to the banking book, they also shielded them from the infamous stress tests. Thus, it was impossible for them to sell them at 70 (say) as it would mean taking a loss that most European banks could ill afford.
The recent EBA (European Banking Authority) tests imply that around 85% of the Bonds held by Greek banks were marked at Par (before the PSI writedown) and 60% of the bonds held by European banks. Then we have the funds, mutual or pension. The majority of the European funds bought the Greek bonds on an asset swap basis taking advantage of the credit spread at the time. The asset swap package is marked at Par and selling the bond not only would incur a loss on the bond side but also on the swap side. Finally, other institutional investors like insurances may or may not have taking the mark to market losses. Anecdotal evidence suggests that not all of them have taken the losses.
How about the repo market? In principle investors could find the bonds there. Well, around 85billion are with Greek Financial institutions, which are locked out of the market (no lines). They can only repo with the ECB. The ECB owns a further 45billion. Most of the other banks prefer to repo with the ECB for credit crunch reasons.

So, who remains in the market to determine the price?
a.    Funds and insurances that own them outright and have real MTM and have redemptions.
b.    Banks that have them in the trading book.
c.    Private banking investors who are easily spooked.

These bondholders are a small subset of the market and they do not represent a good sample anyway. On the buyers side, the problem is that most Institutional investors are not allowed by their rules to invest in low quality bonds. True, they are stuck with the Greek ones, but they cannot add to them no matter how great the opportunity is.
In conclusion, the Greek bond market is a totally dysfunctional market with separate dynamics from the ones most modellers assume.

Information availability and valuation

One of the basic tenets of mathematical pricing theory, is that all information is available to the market at any point in time and that market participants have equal access to it. Valuing this information is the job of the trader who can easily shift through the credible from the ludicrous. Unfortunately, most market participants have been caught in the dark here. After 2000 with the introduction of the Euro most investment banks scaled down their coverage on individual countries (and peripheral) as they shifted their resources into covering the ECB.  The result was a huge mispricing of the Greek risk (and other countries), which now the market tries to correct in panic.
Now that we have a malfunctioning bond market, together with a malfunctioning of the information flow the bond price reflects mainly the ignorance of the risk of default rather than the true probability of it.

Conclusion
I am not arguing that Greece does not have a high probability of default. Their fiscal situation speaks louder than anything else. I am only saying that unqualified usage of the models is wrong and it gives totally the wrong message to the easily spooked and impressionable market participants.

Apart from the sensationalist value of these reports one should not attach any credence to the numbers obtained. There is information content in the Price of the Greek bonds, however the interpretation is far more complex than the naïve and simple Probability of Default.

[1] See for example, 1) http://www.bloomberg.com/news/2011-09-12/greece-s-risk-of-default-increases-to-98-as-european-debt-crisis-deepens.html, 2) http://money.cnn.com/2011/09/19/news/international/greek_default/?source=cnn_bin