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?


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