## How to compute sovereign default probabilities

My article mentions invesetors’ estimates of the probability the U.S. will default based on spreads on credit default swaps. Some readers have asked how I computed the probabilities. What follows is a guide but should not be considered authoritative.

I computed straight default probability rates without any assumption for recovery; as such they probably understate the true implied probability, as does the lack of any allowance for counterparty risk. But there are other reasons why the market may be overstating investors’ true expectations. Since I couldn’t decide the net effect of these opposing influences, I simply said that there were technical reasons not to assume this was a precise measure of expectations, and focused on the trend instead.

Here’s how I got my calculations, and I don’t claim to be authoritative; it’s just based on my best understanding. The CDS premium (or spread) should be equal to the expected loss on the insured bond multiplied by the probability of default. Assume for now a recovery rate of zero. That means, in any given year, the probability that the bond will NOT default is 1-premium. The probability it will not default after *x * years is (1-premium)^*x* (where ^ means “to the power of”). Thus, the probability it WILL default after *x* years is 1-(1-premium)^*x*. So if the premium on Treasury CDS is 62 basis points (as it was early last week), then the probability of default after 10 years is 1-[(1-.0062)^10]=6%.

Now, relax the assumption of zero recovery. The premium should be equal to the expected loss minus recovery multiplied by probability of default. Since OECD defaults are so rare (much less U.S. defaults) there is very little precedent from which to derive recovery rates. I’m told that the presumed recovery rate for European sovereigns is 35-40%. Let’s assume for now 40% for the U.S. Incorporating this into the above formula gives us 1-[(1-.0062/(1-0.40))^10] = 9.9% (approximately). The second reason the probability might be higher is counterparty risk. There is a nonzero possibility that the party from which you bought protection will not be in business to pay you when a default is triggered and your position is not sufficiently collateralized. I assume this is even more likely in the event it’s a sovereign defaulting (as Dean Baker notes). That being the case, the buyer of protection would pay less for protection than its true economic value and the premium and thus the above calculation would understate the implied probability of default. In theory the creation of a federally-backed clearing house for CDS should reduce counterparty risk, but not below zero.

All that said, 6% and certainly 10% seems high and probably overstates investors’ actual expectation of default. Sovereign CDS have apparently become a popular way to trade systemic risk and the likelihood of further government financed bailouts as opposed to a pure bet on default. Still, I find this explanation a bit unsatisfying; boiled down, that’s another way of looking at the factors that could one day impair a sovereign’s ability to pay. When Moody’s downgrades a country from AAA to AA, it is not a prediction of default; merely an assessment that the odds of default, though still miniscule, have risen. And, leaving aside the actual levels, what is interesting to me is not the actual number but the trend: it’s going up. Why? Apart from the fundamental factors, events of the last year may have awakened the investor community at large to the realization that default events

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http://tinyurl.com/primsharp20359February 2, 2013 at 10:43 pm