Why CDS–Bond Basis Analysis Uses Z-Spread Instead of Coupon

# Importance of z-spread in CDS-Bond Basis trading


# Importance of z-spread in CDS-Bond Basis trading












Consider the following:

A bond with a 9% coupon and a price of $98. Let's say the zero swap curve is flat at around 7% (e.g. the zero swap curve is high because we're at the end of a business cycle). Let's say this gives the bond a z-spread of 2%.

Now say the CDS spread is 7.5%.

The CDS-Bond basis using the z-spread is positive (7.5-2 = 5.5%), but if we were to just use the coupon rate of 9% as our reference rate and bought both the bond and the CDS we would have a risk-less trade (ignoring upfront payments, etc.) Pocket 9%, pay out 7.5%. In the case of default, price goes from 98 to 40, but CDS pays you 60 (100-40). So what's the big deal with the z-spread?

Why do we use the z-spread and not just the coupon in these scenarios?

## Answer by VanillaCall (score 2)

https://quant.stackexchange.com/a/46592

Z-spread is a valuation tool. It's not traded but is used as a measure of relative value.

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/46599

First, please note that in a standardized credit default swap, you do not pay (in your example) 750 bps every year for protection. The 750 is just a "market standard quote" (MSQ), but you pay every year a standard "running spread" (usually 100 bps; for high-yield credit it might be 500 bps) (with 4 payments a year on standardized dates: March, June, September, December 20th). So if you're looking at the cash flows of a relative value trade that involves both a cash bond and a CDS, you should assume that the protection buyer will pay a lot upfront and then pay a running spread that'll be less than the bond coupon. You can't just "ignore: the upfront fee. It might well be 20-50% of the notional! (Also observe that if the MSQ is less than the running spread, then the protection buyer would receive a fee.) Many years ago, before the so-called "big bang", you could trade CDS with no upfront fee, zero value at inception, and running spread close to the MSQ - somewhat similar to interest rate swaps. But not anymore, sorry. Second, if some bond's Z-spread is 200 and the CDS market standard quote is 750, this does not automatically mean that you should sell the bond (be short credit) and sell CDS protection (be long credit). Does the bond mature in a few months (little chance of default), while the CDS is for 5 years? Is the bond highly collaterlized or guaranteed by someone else, while the CDS references "senior unsecured" (meaning that in case of default, the recovery on the bond would be substantially higher than the recovery on the CDS)? If none of the obvious reasons for the large bond-CDS basis explain it, then you could take a look at the history of the CDS, and the history of the bond's Z-spread, and if their basis is far from its historical levels, then express the view that the basis would revert to its historical mean. But it is not at all guaranteed to revert. Third, Z-spread may be too simplistic for serious analysis of relative value of credit-risky bonds and CDS because Z-spread looks at everything simply in terms of risk-free interest rates and spreads. There was a good paper by Duffy and Singleton in 1999 and an even better one by Tomas Bielecki on how to look at bond cashflows as defaultable instruments, and to consider probabilities of default, and recovery assumptions. You probably don't need this for your question, though.