"Why would anyone buy credit default swaps on the U.S. government? If the U.S. ever defaulted it would be because the world ended, so no one would be around to pay you on your CDS," is a thing that people more or less used to say.

Not so much any more? Now it's like, "Why would anyone buy credit default swaps on the U.S. government? If the U.S. ever defaulted it would be because of stupid debt-ceiling procedural problems, and they'd fix it quickly, and treasury bonds would only have payments delayed by a couple of days, so they wouldn't lose any value, so your CDS wouldn't pay you anything."

And yet, U.S. CDS has ticked up a bit over the last few days as we've all remembered about the debt ceiling. So there's gotta be an actual answer to those disbelieving questions.

Those questions rest on the notion that credit default swaps are a hedge against credit risk -- as my colleague Matt Klein puts it in his post on the subject today, "the contracts are supposed to offset investor losses" -- but this is only true to a first approximation. If you own $100 worth of government bonds, and you buy $100 notional of CDS on that government, then to a first approximation:

  • If the government doesn't default, your bond pays off 100 and your CDS pays off zero.
  • If the government defaults, your bond pays off X and your CDS pays off 100 minus X, where X is whatever your bonds are worth after default.
  • If the government sorta defaults but not really, X is basically 100, so you make 100 on the bonds and zero on CDS, just like if there wasn't a default. So your CDS isn't worth much.
  • If the government totally totally defaults, X is like 40 or 0 or whatever, so you make 40 or 0 on the bonds and 60 or 100 on the CDS. So your CDS is worth a lot.
  • Except that whoever sold you that CDS has to pay you, and if the government is the U.S. government then its default means that we're all running from zombies and using bitcoins to pay for ammunition and whatever, so good luck getting paid. If you don't get paid your CDS is worth zero.
  • So CDS on the U.S. government, in either of the two most plausible U.S.-government-default scenarios -- brief technical default or zombie apocalypse -- is worth zero.
  • So don't buy it, dope.

One possible explanation for why (1) people buy it and (2) more people have been buying it recently as technical default becomes more likely, pushing up the price, is that those people are all dopes. This is an unsatisfying explanation, as it is never great to assume that a market exists entirely due to stupidity, though of course sometimes that assumption turns out to be correct.

It seems wrong here though. Schematically, a normal CDS contract's value is made up of:

  1. Credit protection, plus
  2. Structural nonsense in the CDS contract unrelated to credit protection.

In U.S. government CDS, the value of the credit protection is more or less zero, for the reasons described above. This means, first, that U.S. CDS isn't worth much -- I see 1-year CDS bid and offered at 28/38 basis points running, with the 5-year at 28/33*; the price of 5-year CDS seems never to have exceeded about 100 basis points running (in early 2009), compared to 505 bps for Portugal now, or 25,960 for Greece in early 2012. And it means, second, that whatever it is worth comes from the structural nonsense.

Fortunately, CDS contracts are full of structural nonsense! The main piece of structural nonsense is the cheapest-to-deliver option: When a government defaults, the CDS contract allows its owner to deliver any bond of that government and get back 100 minus the value of that bond.** So you find the cheapest bond, you buy it, you deliver it into the CDS contract, and you get back 100. If the cheapest bond is cheaper than 100, you make money. (It is!)

The cheapest-to-deliver option exists for historical and liquidity reasons, but is sort of weird in practice. It is so weird that people who write about CDS often forget it. People who trade CDS do not. To a second approximation, the entire value of a CDS contract on the U.S. government is made up of the value of that cheapest-to-deliver option.

The thing is that this option doesn't require a massive, "real" government default. The CDS contract will trigger if the government misses a payment on any Treasury bill or note (though not, say, a social security check or amount due to a contractor or whatever) by more than three business days. There's at least one payment due a week, meaning that CDS would trigger between three and seven business days after a debt-ceiling hit that actually stops payments on Treasuries: a long time, but not an unthinkably long time. Once it triggers, the CDS procedures go into effect, an auction is held, CDS holders get paid off, and the cheapest-to-deliver option becomes valuable -- even if, as Klein says, the government "eventually raised the debt ceiling and paid back creditors with interest, as it almost certainly would." Even if it did that four business days after missing a payment.

You can sort of look at the value of the cheapest-to-deliver option. The cheapest bond is, intuitively, a long-dated bond with a below-market coupon. An RBC Capital Markets rates research note from yesterday notes that the lowest-dollar-priced U.S. government bond is the 2.75 of November 2042, trading at a yield of about 3.72 percent or a dollar price of around 82.75.***

One thing you could do is:

  1. Buy $100 face amount of those bonds for $83 (just rounding),
  2. hedge out the interest rate risk, and
  3. buy $100 notional of 6-month U.S. government CDS for about $0.19 (38 bps per year for half a year).

If the government doesn't default within six months, you're out (1) the $0.19 you paid for the CDS, plus (2) bid/offer on getting in and out of the bonds (maybe a few pennies), plus (3) your cost of funding and interest rate hedging, call it another 10 cents.**** Let's say your all-in cost is $0.30, just illustratively.

If the government defaults, you deliver those bonds that you bought for $83 into the CDS, and you get back $100. So you make $17.*****

Simplistically speaking, the fact that a bet that pays off $17 costs about $0.30 suggests that the CDS market prices the probability of a temporary default at around 2 percent. That doesn't mean that that's the actual probability. For one thing, that math was sort of half-baked. For another, that's just, like, the CDS market's opinion, man, and as Klein says, the market for U.S. government CDS is not a particularly deep or serious market. (Yet?) The notional amount of U.S. government CDS outstanding is pretty small, around $21.6 billion of gross notional ($3.1 billion net) as of last Friday.

For another other thing, that probability is probably overstated because this market is a useful hedge, and hedge demand is driving up the price beyond its pure speculative equilibrium. You can see why you might overpay for this sort of protection: If the government actually does miss a payment on Treasuries, even for a few days, Bad Things Will Happen. It'll be chaos. Not zombie-apocalypse chaos, but, y'know, traders-with-hands-on-their-faces chaos. The sort of chaos where a lot of your other positions lose value in scary and unpredictable ways. The sort of chaos where (1) you'll probably still get paid on your CDS and (2) you'll be glad you are, because everything else is going wrong. Which is of course exactly the point of the contract.

* That's ZCTO CDS EUR SR 1Y Corp CDSV, if you're following along on your Bloomberg terminal.

** Technically you don't have to deliver it, there's an auction, but thinking of it as delivery works fine.

*** RBC Capital Markets, US Economics and Rates Focus, "DC: Dysfunctional Circus," September 25, 2013. Here is a very good post by Cardiff Garcia at FT Alphaville referring to this note, with a link to the note. RBC also notes that (1) the 2.75 of August 2042 is almost as cheap (I see it at 82-29ish vs. 82-24ish for the November, as of 12:18pm today) and (2) there are cheaper TIPS, but TIPS are weird and "many holders of CDS may be less familiar with this market." TIPS, which have an accreting principal amount, are somewhat confusing to deliver into CDS.

**** You could hedge the interest rate risk with a swap, or by selling short another bond, say the 3.75 of August 2041, which trades a bit north of 101. Here is a Bloomberg screen (FIHZ) that I think says that doing that for six months will cost you about $99 per $100,000, or call it ten cents for $100:

There's no real reason to do this trade for six months; the debt ceiling should come to a head in the next month or two. I'm just using six months for simplicity, because a six-month CDS contract trades.

***** You lose a portion of your 30 cents, though not all of it, since a lot of those costs (carry on the bonds, the CDS) are running costs and if the government defaults quick you don't lose most of them.

Incidentally, you could do this trade without buying the bonds! That's cheaper. You just buy the CDS and hope that if there's a default the cheapest bond is still at $83, or lower. This has some appeal: After all, normally when a company defaults, its bonds get cheaper. But of course when the U.S. gets closer to default, people flee to risk-free assets, and as those are ironically Treasury bonds, rates tend to go down, so there's a decent chance the value of the cheapest-to-deliver bond would trade up. (Even leaving aside technicals where it trades up as people want to buy it for this trade. Note that the November '42 has $42 billion outstanding, more than the total amount of U.S. government CDS, so technical effects seem unlikely.)

[Update: Also US CDS is denominated in euro, so you have some currency effects. In a zombie-apocalypse scenario you might expect the euro to strengthen against the dollar; in a technical default I'm not so sure. I just ignored currency here.]