Streetwise Professor

As the periodic debt ceiling game of chicken proceeds, you might read about the credit default swap (CDS) rate on US government debt. This is commonly (even by economists) used to quantify the market’s estimate of probability that the US government will default. Although it is related to this probability, it is not a direct measure of the “true” probability. So interpret with extreme care. Especially in the case of US government debt.

As a little background, a CDS is a contract that pays off if the underlying entity–in this case, the US government–defaults on its obligations. In that event, the purchaser of protection receives the face value of the debt minus the price of the defaulted security. If the defaulted security is worth 40 cents on the dollar at default, the “recovery rate” is 40 percent and the protection buyer receives 60 cents on the dollar.

If the protection currently costs X, you might reason that your expected payoff is p(1-R), where p is the probability of default and R is the recovery rate. Thus, you can estimate p=X/(1-R).

The problem with this logic is that p is not the real world–“physical measure” or “true”–probability of default. It is the probability of default in the so-called “equivalent measure.” Roughly speaking, this p includes a risk adjustment, a risk premium if you will. In theory the p estimated this way could be less than the actual probability of default, meaning that the premium is negative. But usually the p implied this way will be above the objective probability of default. Put simply, just like when you insure your car you will pay a premium that exceeds your expected claims, with CDS the protection purchaser will pay a premium that exceeds the expected payoff.

Indeed, the risk premium embedded in Treasury CDS is likely to be quite large. The reason is that this type of CDS will pay off in bad states of the world–and likely very bad states of the world. That is, if the US government defaults, economic chaos and a recession (perhaps a severe one) is a likely outcome. The marginal utility of income (or wealth) is high when income (or wealth) is low, as during a large recession. Thus, protection sellers are required to perform on their contracts when the marginal utility of income/wealth is higher, so they are going to charge a high price in order to assume such an obligation. The worse the economic consequences of default, the higher the risk premium, and hence the price, that they will charge.

That is, the USG CDS price must exceed the expected payout, likely by a lot, because the payouts occur in bad economic times.

Corporate CDS spreads tend to be “upward biased” measures of default rates for companies, precisely because payoffs tend to be more likely during bad economic times because that’s when companies default. This bias is likely to be especially great for USD CDS precisely because a default will likely cause a severe economic contraction.

Another way to visualize this is to realize that there is considerable “systematic risk” in USG CDS. The risk in CDS payouts cannot be diversified away, and are highly correlated with the overall financial markets. Put differently, a US government default is not really an insurable risk. Classic insurance works by diversification and pooling of independent risks. That is not possible with USG CDS.

There’s another factor at play here–counterparty risk. How much would you pay for insurance from a financially shaky insurance company? Probably not much, because it may not be around to pay when you need it.

Since a US government default is likely to have severe consequences for the financial sector, there is a material probability that the seller of protection will be unable to perform in the event of a USG default.

This would tend to work in the opposite way as the risk adjustment described earlier, that is, it would tend to reduce the cost of protection. The protection is worth less because of the risk it would not be there when you need it. This reduces your willingness to pay for it.

These risk adjustment and counterparty risk issues are likely to be particularly acute for US Treasuries, given the potentially serious economic consequences of a government default. Meaning that USG CDS rates are very unreliable measures of the likelihood of a government default: they are impacted by both the probability of default and the economic consequences thereof.

Yes, a rising CDS spread–like we’ve seen recently–likely reflects a rising estimate of the true probability of a default. But you just can’t back out that probability from the rate.