The Negative Convexity of CDS Trading and Why CDOs Chase Markets

Anyone who has ever traded CDS has noticed the self-fulfilling prophecy of accelerated widening or tightening on an initial move in single name spread. This phenomenon has stumped traditional cash credit investors who don't realize the peculiar technicalities of the CDS market. It is explained by dealer-structured credit desks that tend to chase the market, meaning as spreads widen they buy CDS, and vice versa. Because of this, otherwise small moves in single names can lead to profound jumps in spread.

How does it work:

• A client sells a synthetic CDO tranche to a structured credit desk. The desk is now long risk in the CDO. From a transaction perspective, the client bought CDO CDS while the desk sold the protection.


• The dealer has to offset risk and can either buy protection on the same CDO tranche or hedge by proxy thru single-name CDS. As the CDO world is limited and at times very illiquid, usually the easiest trade is to use single-names as hedges.


• Dealers use models to estimate how much a CDO tranche should move for a given move in the underlying spread. The below chart shows amount of single-name CDS a desk needs to buy in order to hedge $100 mm long risk from CDO position. As spreads widen, the dealer has to buy more and more protection to hedge (i.e. negative convexity).
  
  
• Assume the correlation desk bought CDO when spread was 150 bps. To hedge, the dealer bought $250 mm single-name CDS. Now the portfolio spread moves 50 bps wider so average single-name spread is 200 bps. Dealer looks at the model and realizes $250 mm hedge is too small and now needs $300 million, which difference ($50 million) in the single-name he promptly goes to the market and buyss, thereby pushing prevailing offers even wider in the process, starting a feedback loop for other CDO managers in the market. As spreads continue to widen, the dealer (and other comparable CDO desks) are forced to continue buying more and more protection, thereby chasing the market and exacerbating the moves wider.

In practice, the trading dynamics are more complicated but fall along these lines. Dealers are usually buyers of mezzanine tranche protection and hedge by selling single-name CDS. As spreads widen, mezz-tranches become more equity-like and mezz tranche hedge-ratios vs single-name CDS tend to decrease as spreads widen. This implies the size of dealers' single name hedges relative to mezz tranches might end up being too great as spreads increase, and as a result, dealers will need to decrease hedges by buying single-name protection. And vice versa when spreads tighten.

Comments

[Heaven, Hel...:]

I have worked for several companies who have wanted to use CDS as a proxy for cost of credit/economic capital calculations and I have argued that it is too sensitive to technical factors. This excellent article elucidates for me one of the most salient factors, namely the delta hedging of CDO tranches with single-name CDS and associated "negative feedback loop". Many thanks for the additional ammunition!

One question: I am assuming that the necessity to buy a greater amount of single-name CDS vis-à-vis the CDO tranche is driven by the different loss-given-default assumptions for the two tranches, i.e., as losses mount the mezzanine CDO tranches can be wiped out completely whereas each discrete single name CDS will have an implied recovery factor commensurate with senior unsecured bonds. Is this correct?

Feb 19 09:23 AM

[TJB:]

Thank you for summing up a large part of the catastrophe of our financial system. A tranche should be something you dig in your garden. A mezzanine should be cheap concert tickets and the rest of this stuff should go on the trash heap of history.

Feb 19 09:28 AM

[MeMyself:]

Hey - I beleive the necessity arises because buying a mezzanine tranche (selling protection) is effectively positve gamma trade as value starts creeping inside ( due to wider spreads) you are requried to buy more on sigle name CDS side so effectively you are short systemic risk here.
However , if you see the otuehr side where the party has bought protection on a mazz. tranche and sold single name CDSs wrt Deltas as spreads widen ( being positive gamma) they sell more and it helps them with (+) MTM and hence they are efectively long systemic risk.


On Feb 19 09:23 AM Heaven, Hell or Hoboken wrote:

> I have worked for several companies who have wanted to use CDS as
> a proxy for cost of credit/economic capital calculations and I have
> argued that it is too sensitive to technical factors. This excellent
> article elucidates for me one of the most salient factors, namely
> the delta hedging of CDO tranches with single-name CDS and associated
> "negative feedback loop". Many thanks for the additional ammunition!
>
>
> One question: I am assuming that the necessity to buy a greater amount
> of single-name CDS vis-à-vis the CDO tranche is driven by the different
> loss-given-default assumptions for the two tranches, i.e., as losses
> mount the mezzanine CDO tranches can be wiped out completely whereas
> each discrete single name CDS will have an implied recovery factor
> commensurate with senior unsecured bonds. Is this correct?

Jun 12 12:28 PM