# When The Cost Of Sovereign Default Plunges

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Includes: ARGT
by: Felix Salmon

CMA is out with its quarterly Global Sovereign Debt Credit Risk Report, which includes this league table:

Click to enlarge

CPD stands for cumulative probability of default, which means that according to the market, Argentina has an 84.5% chance of defaulting at some point in the next five years. Calculating these probabilities is more art than science: Thomson Reuters puts the 5-year default probability at 71%, but both TR and S&P agree that the one-year default probability is about 50%.

How can that be, in a world where it seems all but certain that Argentina is going to default this year?

Well, for one thing, life is never as sure as bloggers make it out to be. But also, all the standard default probabilities assume that if Argentina defaults, bondholders will get back only 25 cents on the dollar. Which is improbably low. Argentina has both the ability and the willingness to pay its debts; it just doesn't want to pay holdouts, and is likely to be forced into technical default as a result. This is a long way from the kind of outright debt repudiation that we've recently seen in countries like Ecuador, and it's fair to assume that if and when it defaults, Argentina will try its hardest to ensure that its bondholders (holdouts excepted, of course) get repaid in full on everything they're owed.

So let's look at the 1-year CDS, which is currently trading at about 38 points up front. That means that if you want to insure \$100 of Argentine debt, you need to pay \$38 to do so. On top of that, if Argentina does default, you're going to need to deliver a bond in order to get your \$100 back. The way that default probabilities are calculated, they assume that defaulted bonds are going to cost about \$25 each. So if you buy protection for \$38, and then spend another \$25 on the bond you have to deliver, you're paying \$63 in order to get your \$100 payout, for a profit of \$37. On the other hand, if Argentina doesn't default within a year, you lose your \$38 insurance policy, for a loss of \$38. Since the profit and the loss are roughly equal, that means the probability of default is roughly 50%.

What happens, however, if the price of the defaulted bonds doesn't fall to \$25? Right now the cheapest-to-deliver bond is trading at about \$33, and I doubt that it'll fall much further than that, even if Argentina doest default. In that case, the profit to someone who bought protection drops to \$29, while the loss if Argentina fails to default within a year remains \$38. You wouldn't take that trade if the probability of default was only 50%: the implied probability of default now rises to something more like 60%. And remember too that the price of the cheapest-to-deliver bond could conceivably rise post-default, depending on the actions of the Argentine government and how it decided to intervene in the markets. After all, the Argentines have a strong political interest in minimizing the profits of those who have bet against them.

The fact is that the markets know full well that countries like Argentina can and will default occasionally, despite the fact that standard CDS calculations always think of defaults as one-off events. (Just look at the presence on the league table of Argentina, Pakistan, Ukraine, and Iraq, all of which have defaulted in recent years and seem to be reasonably likely to do so again within the next half-decade.)

In a fascinating new paper, for the Deutsche Bundesbank, Klaus Adam and Michael Grill try to calculate an optimum sovereign default strategy: they try to work out when it makes sense for a sovereign to default, and when it doesn't. And it all comes down to what they call λ, a variable which measures the cost of default to a country. They write:

We first consider - for benchmark purposes - a setting without default costs (λ=0). As we show, the full repayment assumption is then suboptimal under commitment and sovereign default is optimal for virtually all productivity realizations. This holds true independently of the country's net foreign asset position. We then show for "prohibitive" default cost levels with λ≥1, default is never optimal.

The thing to remember, as you read this, is that λ is a variable, even though for the purposes of the paper it's treated as though it doesn't change. And while λ might well be relatively high for a country like Germany, the more that a country defaults, the lower it becomes. After all, a lot of the cost of default is related to the lack of market access, and countries like Argentina have precious little market access even if they don't default.

What we're seeing in countries like Argentina and Ecuador, I think, is a rational response to λ falling to levels very close to zero. When that happens, such countries will default quite often - and that frequent default will be baked in to bond prices no matter how healthy the country's broader economy. As a result, the "official" default probabilities for serial defaulters like Argentina are almost always going to be understated. Although I still think that buying 1-year protection on Argentina right at current levels is probably quite a good bet.