# Why do we have CDS + Bond = Treasury?

In section 25.1, sub-section "Credit Default Swaps and Bond Yields", of "OPTIONS, FUTURES, AND OTHER DERIVATIVES", John Hull defines "CDS–bond basis = CDS spread - Bond yield spread", and claims "The effect of the CDS is to convert the corporate bond to a risk-free bond (at least approximately). [...] [This] suggests that the CDS–bond basis should be close to zero.".

I cannot find a rigorous justification for this. Let's take a simple example: maturity = 1 year, bond APR = 5%, paid twice a year, CDS rate = 2%, riskless rate = 0% for all maturities. The claim would then mean "Bond + CDS rate = 3% Treasury", and given the CDS is free to enter (issued at par), then that would mean the bond price is 103.

Yet, if we try writing all the cashflows with simple assumptions (recovery rate = 40%, only possible default times are t = 0 and t = 0.5, and payments are made in arrears), then we have the below cashflows: We see CDS + Bond still looks rather different from a one-year, 3% treasury, because the whole position can be extinguished at t = 0.5 in case of an early default, and you would then need to reinvest the proceeds, so you could never exactly replicate a "bond + CDS" position with treasuries only. In fact, in this example, CDS + Bond always has cashflows lesser than a 3% treasury, so the value of the credit should definitely be less than that of a 3% treasury, so the "CDS bond basis" would definitely be positive.

What is wrong with this reasoning? Given these caveats, why are we paying so much attention to the "CDS bond basis"?

Thanks!

• Why are you receiving the recovery payments 6months after the default ? Should be immediate , for a better comparison.
– dm63
Mar 19 at 18:07
• Hull is not a very good book for learning about credit derivatives. Mar 19 at 20:16
• Thanks! We can rewrite the cashflows for the recovery to be immediate but given riskless rate is assumed to be zero at all horizons in this example, I don't think it would change pricing, so the problem remains. Any reference that you recommend instead? Mar 21 at 10:12
• "given the CDS is free to enter (issued at par)" You could start by googling the the Big Bang. Mar 21 at 15:05
• How come the riskless rate is zero and the t bill yield is 3% ? Contradiction
– dm63
Mar 22 at 7:50