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For examples if we bought a 10 years corporate bond and want to hedge the credit risk only using CDS , 1- how can we calculate the hedge ratio (compare the change in the asset credit risk vs what )? Please elaborate. 2- What is the best hedge effectiveness testing method to be used (dollar offset ,Regression, others. CTM or SC ) and why ?

Thanks for your help and support

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just a few considerations from an ex credit / hybrids trader:

Let's assume your CDS and bond are denominated in the same CCY to eliminate quanto risk, and we'll assume any interest rate risk is hedged out. Let's also assume that the CDS and bond are coterminal. Your chief sources of risk are then, for any bond + CDS portfolio:

  1. 'Linear' CR01 risk assuming bond and CDS effectively have the same spread.
  2. Jump to default or default risk at 'market' recovery.
  3. Annuity risk - i.e. the credit risk that emanates from bond and CDS probably having different, and potentially very different premium legs (primarily referring to quantum here than schedule).
  4. Credit convexity.
  5. Recovery risk in the event of a credit event.
  6. Basis risk (bond implied survivals may be significantly different to CDS for a variety of factors - even for sovereigns eg with BTPs (Italian govt bonds) the bond-CDS basis can be tens of bps.

Let's now assume that the bond is deliverable into the CDS contract. This means a bond holder can sell the bond at the ISDA auction at the recovery price at which the CDS will settle - this eliminates (5) so let's get that out of the way.

(3) and (4) are related: If for example the CDS premium leg is materially higher (eg a standardised 500bps for some credits) than the bond coupons then the 'hedged' position will be short risk and short credit gamma (paying an annuity is like buying protection since the annuity obliterates on default, however as the credit widens the default gain is obviously more and more priced in hence the residual short risk position declines. This can be a material effect say equivalent to 1mm notional equivalent on a 10mm 5y CDS pure annuity with a 500bp coupon).

A differing annuity can also mean that the default even is not hedged (the premium legs do not exactly offset on default) giving rise to (2).

(1) is probably the main first order risk you are referring to, and we'll come back to this.

(6) is pretty unhedgeable in many cases and emanates from the funded vs potentially unfunded nature of the CDS vs bond. All sorts of supply and demand factors particular to the heterogeneous nature of bond vs CDS market participants mean that this basis can swing from +ve to negative, sometimes in response to general market movements, sometimes owing eg to central bank policy action providing funding on eg short dated sovereign bonds.

So, from a trading desk point of view, typically the full term structure of CR01 risk measures is generated, annuity differences meaning that the notional flat package is most likely not 'flat', these are hedged out subject to bid/offfer liquidity constraints, and possibly in many cases the bond-cds basis does mean revert over time so this is not too problematic if not run in too massive a size. Hedging out the actual risk measure in my view is better than regression. However, clearly in many cases the basis and outright spread may not be orthogonal, and so there is definitely something to be said, in the context of book with many credits, to adopt a holistic PCA type approach - this may well save 10s of bps in rehedging costs (credit books do have convexity) and initial hedge bid/offer. It's hugely important to remember however that regimes change in credit markets all the time, so to be too wedded to one approach is dangerous.

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