Now Let Us Say Certain Things About DVA

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If you are in the business of selling derivatives you have to value them from time to time, because counterparties want to know what their thing is worth, and regulators want to know how deep in the hole you are. This is not always as easy as valuing a stock by just going out and getting a quote. But the principles can be stated sort of simply: you just take an integral of your net discounted cash flows over every possible future state of the world, appropriately probability weighted.*

Easy to say, but hard to do, because you have only so much direct access to possible future states of the world. Fortunately there are rules of thumb for this, of greater or lesser reliability, which exclude the unlikely and immaterial states of the world (your BAC warrants are worth zero if the world ends this Friday, but that’s unlikely; you’re perhaps equally likely to eat a bacon bowl or a salad for lunch tomorrow, but your choice will have only an immaterial effect on the value of your BAC warrants). All of these methods, however, provide only market-sanctioned guesses about the fair value of your derivatives; if the future world moves in ways not contemplated by the moving parts of your model your calculations are just wrong.

This is, I’ve always thought, a nice way to think of the world, and certainly more conceptually satisfying than "it's worth what people will pay for it" or "it's worth what the formula says." And once you get into thinking of things this way, you can have fun thinking of all the possible things that (1) are not trivially unlikely and (2) would have a not trivial effect on your stuff.

Like, it turns out, your own demise. It may seem sort of ghoulish to say "well, the nice thing about my horrible quarter is that I'm less likely to pay out on my debts, so I've made money on that" - but you have. There are states of the world where you're bankrupt. In those states, you get to collect on all your derivative assets and not pay out on your liabilities (subject to netting etc.). It's awesome! Not really. But it's true.

Or to put it another way, over-the-counter derivatives are a zero-sum bet between two parties. If your counterparty has to mark down the derivative on their books because your credit had an accident, then that counterparty "lost" "money," for some appropriate values of those words. If they lost money then you made money. No one else could have. (But wait, you say. No one else "lost" "money" - it's just a temporary markdown. Congratulations, you are a European bank.)

This is why the bellyachingaboutdebitvaluationadjustment (“DVA”)** seems a little overblown. You’re just valuing a derivative. It will move around in value for lots of reasons. You can say that some of those are "good" reasons, and some are "bad" reasons, but they're all reasons about the expected probability and size of future cash flows.

Also: it's not cheating. Or, sometimes it's not cheating. Under US accounting rules, what I said above is just what you do for derivatives. You value them at fair value, and if the fair value of your derivative liabilities goes down because you have gotten closer to death’s door, then them’s the breaks.

It is not, however, necessarily what you do for things that are not “derivatives,” particularly including your own bonds. There, you get to choose. Bond by bond. In practice, it appears that all the banks fair value at least some if not all of their structured notes, but wouldn't go so far down the ridiculous-hole as to fair value their vanilla debt.

Now. Sadly the disclosure from the banks who have reported is murky and I’ve been unable to find really clean numbers but consider:

"DV01," emphasis on the quotation marks, is (1) the dollar effect of 1bps of CDS spread change on DVA this quarter, divided by (2) total debt or derivatives liabilities, as the case may be, expressed in basis points. Total debt seems to me like the maximum pool of stuff that could be DVA adjusted (if you pretty much elect to fair value everything); derivatives liabilities is the minimum pool of stuff that could be DVA adjusted (if you fair value nothing but what you have to). This is not particularly science-y.

But it's interesting to think about what these numbers can mean. Directionally, having a higher pseudo-quasi-"DV01" here could mean one of two things:

- Good for you! You've convinced counterparties to trade with you without collateral, either by issuing tons of structured notes or just by sheer force of will or smartness or credit rating.

- Bad for you! You've failed to hedge your DVA and will have creepy earnings volatility. Or you're just fair-valuing everything in sight and/or cooking your books.

* It's best not to think too hard about the word "appropriately."

** I feel like I used to call it “CVA benefit,” but DVA seems to be winning the disclosures-and-press horse race so whatevs.

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