Why would anyone buy credit default swaps on the U.S.?

"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:

  • Credit protection, plus
  • 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.

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