# CDS Implied Probability of Default – Be Careful

Unless something changes in the next 24 hours, I expect we will hear more and more talk about default, not only of Greece but of other countries and of banks. Just in case that happens, here is some information that may help you make good decisions. There will be lots of chatter about the “likelihood of default” the CDS market is implying, but although it can be a useful statistic, it can also be very misleading. Before jumping into trades based on erroneous assumptions, it is worth spending a few minutes reading this. If all it does is confuse you, maybe that is a good thing in itself, because you won’t take a headline about default probability as fact.

### Recovery is Key and is often assumed away making default probability calculations less useful

Let’s start with a simple example. You have bonds of 2 different companies, each maturing in the near term, both trading at 70. What is the probability of default of each of these companies? You don’t know because that isn’t enough information. You know the bonds are trading at 70, and without a default they would pay par, providing a 30 point return. What you need to know to figure out the probability of default, is what the recovery value will be. Let’s assume that the recovery value for one company is going to be 60 and for the other will be 10. Then in the first case, the default probability is 75%. There is a 75% chance an investor would lose 10 points, and a 25% chance that they would gain 30 points, giving an “expected” value of 0 (today’s risk free rate). In the second case the default probability is only 33% (66% chance of 30 point gain plus a 33% chance of a 60 point loss).

So recovery is a key element of determining what default probability the market is pricing in. Yet, although it is key, it is often assumed to be 40% or some other number based on historical averages. That is a reason to be very concerned when you see a default probability mentioned. It is useless without looking at the recovery value, and recovery value isn’t easy to figure out. Recovery value is figuring out the enterprise value of a company after it has defaulted. It is not any easier than figuring out enterprise value of a company that is not in default, so treat estimated recovery values with the respect they deserve.

In the CDS pricing model, there are 3 key variables: the spread, the recovery value, and the up-front premium. If you know any 2 of those 3, then you can solve for the other. The market trades with the assumption of 40% recovery. That let’s traders quote a spread, and then the up-front premium is just a calculation. This is done more out of convenience than anything else. Agreeing to a recovery rate on each trade would be time consuming, and 40% seems reasonable enough for the purposes of calculating the up-front.

For high quality (tight spread names) the up-front premium is not very sensitive to recovery.

For names that trade at 400 over (BAC for example), the probability to default over 5 years is 21% with a 10% recovery, and 51% with a 70% recovery. So you need to take any probability of default derived from CDS prices with a grain of salt. Without a rational assumption for recovery, the probability of default is somewhat meaningless. Since changing recovery would change the “up front” premium, you could try and argue that the recovery must be valid. I would argue that the smartest credit investors figure out what premium they need to earn to take the risk, based on their assumptions, and then figure out what spread in a 40% recovery model world gives that up-front premium.

At the other extreme, names will eventually trade in “points”. With a 40% recovery in the model, there is no spread that can give an up-front premium of more than 60. If a dealer was willing to buy protection and pay 55 points up front, or sell that protection at 57 points up front, most investors wouldn’t complain about the liquidity. It would be as good as in the bond market. On the other hand, if the same dealer quoted that market as 3470/4430 some client might argue that 1000 bps seems egregious. Also, if a company has a bond trading at 35, dealers will not want to floor recovery at 40 since a bond trading at 35 shouldn’t exist if recovery is 40. So as default becomes more likely, the model becomes less useful.

### The Curve is also important

For simplicity and market convention, the 5 year cumulative default probability is based on a flat curve. As a situation deteriorates it becomes more important to look at each point on the curve. Two names trading at 1000 in 5 year CDS would have the same implied probability of default from the standard model. But if one is trading “inverted” at the short end, and the other is steep, then at the very least the timing of default that is being priced is very different. An inverted curve means the risk of default in the near term is much higher. If you, as an investor are going to make decisions based on default probability headlines, you need to look at the curve. The 5 year default probability is a nice headline, but the devil is in the details.

### Sovereigns are even more problematic when divining default probabilities

Sovereign CDS for Eurozone countries trades in USD. CDS on US government debt trades in Euros. This helps explain why CDS trades so wide for many sovereign names. If you bought €10 million of a European sovereign at par, and it defaulted, recovering 40%, you would have lost €6 million. If you had bought CDS in Euro that trade would basically offset it. If you bought protection in $’s and the exchange rate was unchanged, you would break even on the trade. But many investors believe that a default of a European sovereign would cause the Euro to get a lot weaker. So let’s say at the time of the trade the FX rate was 1.40. You would need to purchase $14 million of CDS to cover the €10 million bond position. If the default occurs and the FX rate went to 1.20, then you would have made $8.4 million on the CDS trade, which when converted back to Euros at 1.2 is now €7 million.

If investors believe an FX move is highly correlated with default, they will pay more for CDS. They make more on their negative view than they would if the FX trade wasn’t embedded. Similarly they lose less if the market rebounds. Their position in the bonds will go up, while their losing position in CDS gets converted back into more expensive Euros, thus mitigating their losses.

So on sovereign CDS, particularly at times of stress where the market clearly believes that a default is bad for the currency, the CDS spread is not just pricing in default, it is pricing in default with a currency move, making implied default probability less useful.

On top of that, recovery for sovereigns is purely guesswork. Creditors have NO rights. There is nothing they can do to try and collect on their bad debts. It is purely a negotiation. That is why the distressed investors don’t do much in sovereigns, because they are used to playing by rules, and in a sovereign default there are no rules. In some sovereign defaults, shorter dated bonds have received better treatment than longer dated bonds. That is uncommon in corporate defaults, but not uncommon in sovereign defaults, making picking a recovery value even more difficult.

### Cheapest to Deliver Bonds

For banks, financials, and sovereigns the cheapest to deliver option embedded in CDS has less impact on daily CDS prices because they are such frequent issuers. For companies with fewer bonds, the cheapest to deliver option can impact CDS prices, without really impacting probability of default in the real world. If two very similar companies existed, but one had only issued bonds at times of high coupons, and the other had issued when rates were very low, the CDS on the low coupon bond company should trade a bit wider. Investors who like the “basis package” where they buy bonds and buy CDS generally prefer to buy lower priced bonds because they can benefit from a “jump to default” and lock in their basis trade profits sooner than later.

Copyright © 2011 · Peter Tchir

*** * ***

25/09/2011 at 4:29 pmYou need to correct your opening calculation or your readers ARE going to get confused. You have: “There is a 75% chance an investor would lose 10 points, and a 25% chance that they would lose 30 points”; what you mean is: “There is a 75% chance an investor would lose 10 points, and a 25% chance that they would GAIN 30 points”.

25/09/2011 at 4:49 pmCorrected!

Thanks for the heads-up!

26/09/2011 at 8:51 amThanks! As a non-trader, it would really help if you could:

1. Expand on this bit:

“In the CDS pricing model, there are 3 key variables: the spread, the recovery value, and the up-front premium. If you know any 2 of those 3, then you can solve for the other. The market trades with the assumption of 40% recovery. That let’s traders quote a spread, and then the up-front premium is just a calculation. This is done more out of convenience than anything else. Agreeing to a recovery rate on each trade would be time consuming, and 40% seems reasonable enough for the purposes of calculating the up-front.”

What is the up front premium? Can you do an example of solving for the third variable. And explain how this lets traders quote a spread. Most importantly, what is the significance of agreeing the 40% recovery rate. Is this just a pricing convention? So if I can make a better estimate I’m likely to make money?

2. Explain why: “For high quality (tight spread names) the up-front premium is not very sensitive to recovery.”

3. What does it mean to “trade at 400 over”?

Many thanks – W.