Sunday, May 20, 2012

The Wonderful World of Synthetic CDO Strikes Again

ZeroHedge has their take on the JPM trade and it sounds fairly convincing.

http://www.zerohedge.com/news/irony-101-or-how-fed-blew-jpmorgans-hedge-22-tweets

I have tried to make this as simple as I can but the simple truth is ...it is not simple.  Their story is

(1)  JPM was looking for a way to hedge tail risk - the risk of a huge disruption where everything goes wrong as once.  Tail risk is always expensive to hedge because no one wants to be left holding the bag when the shit hits the fan.  To see a good example of this look at the S&P skew in the options market where downside insurance is much more expensive than upside insurance.

(2) JPM found what seemed to be a good hedge in senior tranches of a synthetic CDO on the CDX.NA index.  What does this mean?  For a description of how CDS works see my Credit Default Swaps for Dummies Parts I and II.  Recall that for synthetic CDO the first defaults get paid out of the equity tranche.  When defaults have exceeded the collateral of the equity tranche then the next tranche up starts paying out.  It continues upward through the junior, mezzanine, and senior tranches in a similar manner.  The only way a tranche has to pay out is if all tranches below it have been depleted.  So the only way that a senior tranche pays out is if there are a huge number of defaults which was exactly the situation that JPM wanted to hedge.  ZeroHedge hypothesizes that JPM purchased large amounts of the senior tranches of CDX.NA.  Not sure which vintage.

(3) So what factors influence the price of a CDS/CDO tranche?  First most obviously how close we are to default.  Second how much volatility there is in each of the underlying names.  And finally how correlated are the underlying names.  But the correlation affects the various tranches very differently.  Imagine first that the names are completely uncorrelated in their default probabilities.  Then it is very likely that there will be some losses in the most junior tranches but the probability of defaults eating through all junior tranches up to the senior tranche is very small.  Now imagine the opposite that the names are perfectly correlated.  So if one name defaults then they all default.  Now if the most junior tranche gets hit the most senior tranche also gets hit.  So the value of senior tranches are extremely sensitive to correlation while the junior tranches are much less so.  In math speak the dV / d(correlation) is very high for the senior tranches and much less positive for the junior tranches.  By purchasing large amounts of the senior tranche of CDX.NA Morgan  had bought insurance against a crash but at the cost of making themselves very long dV / d(correlation). If correlation fell then the value of their CDX.NA senior tranche positions would fall as well.

(4)  At some point in time JPM tried to hedge out some of their exposure to correlation.  The hedge instrument that JPM chose was the CDX.NA.IG9.  Since CDX.NA.IG9 includes all tranches it has a much lower dV / d(correlation) than do the senior tranches of CDX.NA.  So JPM had to sell huge amounts of CDX.NA.IG9 in order to offset the long exposure to correlation that they had incurred from their senior tranche position.  Furthermore, the relationship between V and correlation is not linear ie the second derivative of V with respect to correlation is not zero.  This is analogous to the gamma from standard option pricing.  If correlation fell then JPM would have to continue to change their position in CDX.NA.IG9 in order to keep their correlation hedge balanced.  More on this point below.

(5) When the Fed and the ECB took action to reduce the probability of systematic defaults in Europe they effectively reduced the correlation between names.  At this point it is not clear if JPM had fully hedged their correlation.  It is possible that they were not fully hedged - in which case they took a mark to market  loss on their long correlation position in the CDX.NA senior tranches.  In either case since senior tranches are nonlinear in correlation they would have had to rebalance their hedge in CDX.NA.IG.

(5)  Hedge funds saw that IG9 was getting way out of line with fundamentals so they tried to profit by buying IG9 against other indices.  But no matter how much they bought IG9 kept falling as JPM continued selling in an attempt to balance their correlation exposure.  The funds eventually got pissed about the non-convergence and the nicknames The Whale and Voldemort began seeping into the business news.

Ok so what parts of this story still don't make sense to me?

(a) If the original purchase of CDX.NA senior tranches really was a hedge to the JPMs other positions then why change its exposure when correlation changed or hedge out its correlation exposure at all? Yes as correlation fell they would have lost mark to market on their senior tranche hedge but their original portfolio would have been better off - since there would have been less tail risk.  If they could not explain this then how did they explain the rational for the hedge in the first place?

(b) I am no expert in CDO pricing but I think the second derivative of the V with respect to correlation is positive (someone correct me if I am wrong here).  So if correlation increased then dV / d(correlation) should  increase or if correlation fell then dV / d (correlation)  would decrease.   If prior to the Fed / ECB intervention JPM had been hedged then after the intervention (where correlation fell) then they would be short correlation by the second derivative effect.  Hence after the intervention they should have been buying CDX.NA.IG9.  Maybe they were...

(3) Why did JPM's alarm bells not go off when they put on the CDX.NA.IG9 hedge?  It seems like they replaced the tail risk with correlation risk, and then replaced correlation risk with a lot of general directional risk.  Did they not hedge the general direction risk?

I am not sure if I buy the whole story.  Still it is a very interesting hypothesis.

No comments: