Hedging a Long Bond with a Shorter-Maturity CDS
Summary
The document examines how to hedge a 10-year bond when only a 5-year credit default swap is available. It distinguishes two objectives: protection against an issuer default over the CDS term, and reducing sensitivity to changes in market-implied credit risk. A static CDS hedge can cover default losses for the first five years, but leaves the bond exposed afterward if no default occurs.
For a sensitivity hedge, the answer describes matching the bond’s credit sensitivity, or CD01, to that of the CDS. A rough two-times notional ratio follows from the simplified risky-annuity example, but the actual hedge ratio should be based on the quotient of the two instruments’ CD01s. It may need periodic rebalancing as sensitivities change. The proposed ratio is therefore approximate, and the hedge does not remove all risks, including exposure beyond the CDS maturity and differences between bond and CDS behavior.
Key ideas
- A shorter-maturity CDS can hedge default exposure only during its own term.
- A static hedge leaves the bond’s later years exposed if the issuer survives the CDS period.
- A sensitivity hedge matches the bond’s CD01 to the CDS’s CD01.
- The two-times notional example is approximate; actual sizing uses the ratio of credit sensitivities.
- Periodic rebalancing may be needed to maintain the target hedge.
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Full text
# Hedging bond with CDS of different maturity # Hedging bond with CDS of different maturity Say I buy a 10-year bond with a notional of 100k. To hedge my credit risk entirely I could buy a 10-year CDS, also on a notional of 100k. Now, if there are only 5-year CDS trading and no 10-year CDS, then I could still hedge the first 5 years of my bond, assuming that I do not "care" about the years 5 till 10 right now. But the question is, on which notional should I buy the 5-year CDS. Intuitively I would say it should also be 100k. But I heard the following reasoning which I do not fully understand: ``` Making the simplying assumption that the risky annuities (RA) of the two CDS contracts are 5 and 10 respectively one would need to buy a 5-year CDS with a notional of 200k. The reason being that (in its first five years) a 5-year CDS with 2*100k notional and RA of 5 acts like a 10-year CDS with notional 100k and RA 2*5. ``` Could somebody explain this behaviour? Is the reasoning right or wrong? Basically, how would one try to cope with the fact that 10-year CDS are not currently traded, but 5-year CDS are? ## Answer by Brian B (score 4, accepted) https://quant.stackexchange.com/a/15114 It depends on how one is thinking about the hedge. One might be thinking of it as - A hedge against catastrophic risk (default of the issuer), or - A hedge against changes in (market-implied) default intensity or hazard rate In the former case, which seems to be how you are considering it, the hedge is a static hedge, kept for up to 5 years, and insulates you against losses from default. In the (likely) case that no default happens, you will accrue PL at roughly the bond rate minus the CDS rate, and you will be left unhedged after 5 years. In the latter case, a practitioner would be hedging our the CD01 (credit sensitivity) of the bond, effectively stripping it to a risk-free interest rate product for a small amount of time and small default intensity changes. The 2x multiplier is very approximate, and the actual hedge ratio would be taken as the quotient of the bond CD01 by the CDS CD01. In this latter case, one would expect to trade small amounts of bond and/or CDS periodically (probably 1-4 times per year) in order to keep the position matched to the target hedge ratio.
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