## CDS chart of the day, Portugal edition

Many thanks to my colleague Eric Burroughs for sending over this chart, showing how Portugal’s CDS curve has evolved over the course of this year:

The black curve is how Portugal looked in April: a pretty standard upward-sloping curve, with default more likely the longer you go out.

By June, however, with the onset of the Greece crisis, things looked very different. (This is the green curve.) Obviously default probabilities were higher across the board. But they were highest at the short end of the curve: 6 months to a year out. If Portugal could make it that far, markets were saying, then it would become steadily less likely to default thereafter.

Today, with the red curve, it’s very different yet again. The contrast from just a few months ago is striking: while the 1-year CDS showed the *highest* default probability back then, today it’s the *lowest*. The EU bailout of Ireland confirms that Portugal will probably not be allowed to default any time soon.

But then look at where Portugal’s CDS curve goes after that: straight up, to the point at which the country is now considered more likely to default at 3 years out, and on from there.

The implication is clear: any bailout now only serves to make a future default more likely.

Which is not, I’m pretty sure, the message that the EU is really intending to send.

So a CDS at 5yr doesn’t payout if the default happens at 3yrs? That seems silly.

@tedtwong, the 5Y does pay out on credit events any time in the 5Y period. But that does not mean credit spreads cannot be downward-sloping. If you hold recovery rates fixed (the convention), then you can take the credit spread as qualitative proxy for term (integrated) hazard rates, analogous to term zero-coupon rates in an IR curve. A downward-sloping credit spread would then imply declining forward hazard rates, just as a declining zero curve implies declining forward rates. The limitation is on the degree of the slope; too steep a slope would imply negative hazard rates, just as too steeply declining a zero curve implies negative forward rates.

Oops. Perhaps a definition is wanted. “Hazard rate” mans “probability of default given prior survival.”

greycap: given the yields on Eric Burroughs’ graph what would you calc today’s hazard rates on the 1Y, 2Y, 3Y, and 10Y Portugal CDS?

@greycap, I think I mistook this as the price of the CDS instead of the yield on the CDS. Thanks for the clarification.

I’m not sure I understand how to read the yield curve and get the implied probability. If the yield is 3%, the risk-free rate is 1% and I’m a risk neutral investor, that tells me that the probability of default is [p(1.03)=1.01] — only around 2%. Am I reading this correctly?

Excuse me as I am totally ignorant of this CDS stuff, but is’nt there a problem with the amount of potential liability and the means of insurers to compensate the insured?

And if this were not accurate then how are the insurers assets currently held? Could those assets be liquidated for anywhere near the book value in a global sovreign debt melt down?

“I’m not sure I understand how to read the yield curve and get the implied probability.”

That is not easy to do. The qualitative shape of the curve is easy to read (Felix has already done so in the post), but backing out a hazard curve involves some assumptions and some calculation. I already mentioned recovery rate. In addition, you need to assume something about the form of the hazard curve, e.g. piecewise-flat, with the points at the quoted CDS tenors. Then at each successive tenor, you solve for the current additional piece of the hazard curve that makes the expected value of the credit event payment equal to the expected value of the swap coupons (plus the upfront amount, in the case of a standardized post-”big bang” quote.)

@tedtwong: “I think I mistook this as the price of the CDS instead of the yield on the CDS.” They are the same. “Spread” is probably a better word than yield in this context. Risk-neutral default probabilities are typically derived from assuming a constant recovery rate (e.g. 40 cents on the dollar instantly upon default) and a piecewise flat term structure of hazard rates (instantaneous annualized rate of default, conditional on survival). A cheap (though inexact) calc for a hazard rate is CDSSpread/(1-RecoveryRate). The link between hazard rate and risk-neutral cumulative default probability at time T is simply [1-e^(-haz*T)].

@tonydd: “isn’t there a problem with the amount of potential liability and the means of insurers to compensate the insured?” Yes, and there’s even a name for it: counterparty risk, and it’s extensively studied and managed–which isn’t to suggest that it’s managed *well* by protection buyers, or sellers for that matter.

“Could those assets be liquidated for anywhere near the book value in a global sovreign debt melt down?” Good question. Again, there’s a name for that: wrong-way risk (see also: Armageddon insurance). But it may be worth asking whether a “global sovereign debt meltdown” is the *only* scenario in which a particular sovereign might default, and if so, whether, in such scenario, one’s CDS payoff would be the most important thing on one’s mind (or even anywhere near the top). This is why it is sometimes joked that CDS on the US treasury might more appropriately be denominated in (take your pick:) bullets/gasoline/spam/tinfoil (the latter for hat-making).

How about the CDS charts of Spain, Italy, and France? Are they all like this one?

@Sandrew: “I think I mistook this as the price of the CDS instead of the yield on the CDS.” They are the same.

I don’t think they would be. Why would you sell me a 10 year CDS for less than a 5 yr one? If it’s a graph of price, that’s what the graph would be saying.

@tedtwong I meant only that the conceptual price of bearing credit risk can be reflected by a spread. You are correct that there is a relevant distinction between an up-front cash payment and a running spread. As greycap alluded to, the CDS market conventions changed last (dubbed the CDS “Big Bang”) s.t. single-name CDS ar now be quoted in a combination of up-front cash payment (points) and a standardized rolling spread (of either 100 or 500 bps, depending on the credit). Sorry if my explanation obfuscated rather than clarified.