The absurdity of the leveraged super senior trade
December 9, 2012
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The Financial Times has a couple of stories (behind a paywall) about the Leveraged Super Senior (LSS) trades of Deutsche Bank during the financial crisis. Grossly oversimplified, the story is roughly on the following lines:
- Let us say that in the heady days before the global financial crisis, a US bank seeks protection against catastrophic default losses on a portfolio of leading companies from around the world. Say on a portfolio of $125 million, it is willing to absorb the first $25 million of credit losses and wants protection only on losses above this threshold. This is like a catastrophe insurance in that losses on this scale would probably require a second great depression.
- The German bank provides this catastrophe insurance for a modest premium to many such banks on a truly colossal scale – apparently to the tune of $130 billion.
- The German bank then turns to a bunch of Canadian pension funds to offload this default risk, and the Canadians invest in massive amounts of Leveraged Super Senior (LSS) securities that embed this catastrophic default risk for a modest risk premium. At this point, it appears that the Germans have locked in a tiny spread and gotten rid of all the risk.
- There is a catch though. The Canadian fund that bought an LSS on say a billion dollar notional put in only $100 million of cash collateral. And no, we are not talking about counter party risk here. The Canadian fund did not assume a $ 1 billion obligation. They simply had an option to post more collateral and keep the security alive if losses threatened to eat away the original $100 million of cash collateral. But if they chose not to do so, the Canadians were perfectly within their rights to walk away, and the German bank will simply have to unwind the whole structure at prevailing market prices (assuming there is a market at that point).
- The German bank models the LSS on the assumption that the Canadians will keep posting more collateral. These models imply that the LSS is almost as good as an outright hedge of the entire $ 1 billion notional, and subtract a small amount (the “gap option”) to account for the risk that the Canadians will walk away.
- A proper analysis is provided by Gregory’s paper of 2008 which is also referenced in the Financial Times story. Figure 2 of this paper provides a succinct summary of the situation. Gregory says that instead of treating the (Canadian) LSS as a $1 billion hedge less a small correction for the gap option, we should actually treat it as only a $100 million hedge plus a small correction for the deleveraging option. Gregory also argues that under most situations, it would be suboptimal for the (Canadian) investors to post more collateral and therefore this positive correction is quite small. In other words, the gap option approach is really wrong. I strongly recommend reading Gregory’s paper in its entirety; it may appear mathematically forbidding, but it is a lot more readable than it looks.
- On top of all this, it is now being alleged that the German bank at one stage even stopped bothering to subtract the small gap option.
- During the global financial crisis, when the risk of a second great depression began to appear a little less remote, the German bank woke up to the fact that the Canadian LSS was denominated in Canadian dollars while the protection that it had provided to the US banks was denominated in US dollars. There was a currency mismatch and somebody had to worry about how the CAD/USD exchange rate would behave in an end of the world scenario.
- The only person that they could find willing to take a view on this fiendishly complex “quanto” risk (and put his money where his mouth is) was Warren Buffet. His Bershire Hathaway pocketed a $75 million premium for covering this risk, but very cleverly limited its risk to $3 billion. I suspect that Warren Buffet did not try to value this quanto derivative at all, but simply calculated that he was being paid a 2.5% premium to cover this risk. In comparison to most insurance deals, this must have appeared to be a very fat premium. To an insurer who is accustomed to working with physical probabilities rather than the risk neutral probabilities that are really relevant here, this must have looked like a bet that one could take blindfolded, and maybe that is what Berkshire did. Warren Buffet screams about weapons of mass destruction when he loses money on derivatives; he just keeps quiet and pockets the cash when he makes money on them.
- The German bank concluded that since losses in excess of $3 billion were extremely unlikely, the quanto risk was completely covered and they could stop worrying about it.
What I find interesting in this whole sequence of events is the sheer absurdity of almost every step in this.
- If you are worried that a large portfolio of top grade global corporations could experience default losses of 20-25%, whom would you buy insurance on this from? Most certainly not from a bank! The best run bank in the world would be broke long before this scale of default losses appears on a high quality corporate credit portfolio. This is worse than buying insurance on the Titanic from somebody who is himself on the Titanic. It is like buying insurance on a lifeboat (after the Titanic has sunk) from somebody who is swimming in the water without even a raft. There is only one situation where this hedge makes economic sense – if you are sure that you are dealing with a systemically important bank that would be bailed out if it fails. In this case, of course, you are buying insurance from the German taxpayer and that probably makes sense. The other reason for doing this is not economic at all – maybe the only reason for doing the trade was to save regulatory capital. In this case, of course, it does not matter whether you would ever collect on this insurance; maybe you would not be around to collect either.
- The Canadian pension fund which posts collateral upfront is obviously a far more credible seller of protection than a bank that is probably levered 30:1. The only problem is that the buyer now needs to model the “gap risk” and a large global bank obviously has a comparative advantage in browbeating its regulators into accepting a deeply flawed valuation of a complex hedge.
- I am not totally convinced that even Berkshire Hathaway is a credible seller of protection on a great depression risk particularly on a complex quanto risk.
All this reminds me of those fallacious mathematical proofs that use division by zero to prove that 1 equals 2. All these proofs work by creating a significant amount of needless complexity in the midst of which the audience does not notice that somewhere in the long chain of reasoning, you have actually divided by zero. The same thing is happening here; you need a significant amount of complexity to ensure that the regulators do not observe that some risks have slipped between the cracks unobserved waiting to be picked up by the unwary taxpayer.