It Cost JPMorgan $1.5 Billion to Value Its Derivatives Right

This is a really long story about Libor, basically.

Last quarter, JPMorgan's financial results included a $1.5 billion loss due to implementing a funding valuation adjustment in its accounting for uncollateralized over-the-counter derivatives and -- wait, where are you going? Somewhere where people don't talk about accounting and derivative valuation? Oh, yeah, okay, that's fair, I cannot really argue with you. Go in peace.

If you want to stick around, though, we can talk about it, because I think it's pretty neat. Conceptually, derivatives are contracts that involve exchanging (normally uncertain) cash flows over time. So the way to value a derivative, loosely speaking, is to guess what those future cash flows are likely to be, and then discount them back to present value. But it turns out that banks mostly hedge derivatives by trading in the underlying stock or currency or commodity or whatever, or by trading offsetting derivatives in the interdealer market. What this means is that you should -- in theory! -- have no stock price or currency or whatever risk, and so you can guess those cash flows on a "risk-neutral basis." Similarly, since you have no risk, you can discount your cash flows on a risk-free basis.

That's the textbook, Black-Scholes-y way of valuing derivatives. But recent years have provided many reminders that people don't always pay what they owe on derivatives, so your risk-free cash flows can be risky, even if they have no risk to the underlying stock or interest rate or currency or whatever. There are two main ways of dealing with that fact, which are:

  1. Price it, or
  2. Collateralize it.

Both have their points. So there has been a big push to move derivatives onto exchanges, to increase collateralization requirements, etc., etc. If all your derivatives are perfectly collateralized -- with instantaneous movement of cash to cover all liabilities -- then your cash flows go back to being risk-free and you can live in a Black-Scholes world.

But some derivatives don't work well with collateral or on exchanges: Corporations like to get hedge accounting on their interest-rate swaps, for instance, and so don't like to collateralize. Sovereigns also have a thing about not collateralizing. So banks tend to have some big chunk of uncollateralized derivatives; for JPMorgan it's around $50-odd billion of uncollateralized receivables (that is, money that clients "owe" JPMorgan on derivatives, or the in-the-money value of its derivatives to JPMorgan). 1

So you price the fact that the cash flows aren't certain. The first thing you worry about is that someone who owes you money won't pay you, so you price that risk. This is called CVA -- "credit valuation adjustment" -- and simplistically speaking it's (1) the amount of uncollateralized derivatives receivables (that is, the expected value of what the client will owe you over the life of the derivative) you have with a client times (2) the duration of those receivables times (3) the client's credit spread to the risk-free rate. That gives you a number, and you subtract that from the price of the derivative: You'll pay someone less for cash flows from him that are uncertain. (And you might use the savings to hedge those cash flows, by buying credit default swaps on him or whatever.)

That's pretty sensible. The next one is quite creepy, and it's (usually) called DVA -- "debit valuation adjustment." This is, simplistically speaking, the risk that you'll owe someone money and won't pay them. If that happens, your bankruptcy estate will save some money, so it's worth something. This is ... sort of weird and hard to monetize, but accountants are really into it, and so a lot of banks have disclosed big DVA gains (when their credit gets worse) or losses (when it gets better), which are confusing and kind of non-economic, but which are nicely countercyclical so there's that.

Now there is FVA, funding valuation adjustment. Not a lot of banks have broken this out, but now JPMorgan has, so I guess it'll be a thing. FVA is about the fact that you have to fund the cash flows on your you-thought-it-was-risk-free trade: The Black-Scholes world assumes you can borrow limitlessly at the risk-free rate, but since 2008 that is no longer really true for banks. So if you have a trade that is in the money to you by $100 million (where in expectation the client will owe you $100 million), then there is a sense in which you are "lending" that client $100 million. If you actually loaned him $100 million, not only would you worry about his credit risk (CVA), you'd also have to go raise the money from somewhere -- wherever you normally raise money from, some combination of short-term debt and longer-term debt and a wee sliver of equity -- and that would cost you money. So you should apply a similar sort of charge on the derivative, because it costs you money to fund.

Loosely speaking your FVA is just your cost of funding -- call it your credit-default swap spread or whatever -- times the notional of the receivables. 2 JPMorgan chief financial officer Marianne Lake walked investors through some rough numbers on the earnings call:

To give you some context, if you start with derivative receivables net of cash and securities collateral of approximately $50 billion, apply an average duration of approximately five years and a spread of approximately 50 basis points, that accounts for about $1 billion plus or minus the adjustment.

If you don't do this, in some important sense you are pricing the derivative wrong. If you buy an option for $10 million, based on Black-Scholes pricing, then in theory you should make $10 million over the life of the option, plus maybe some reasonable bid/ask or profit margin. But if it actually costs you 1 percent more than the Black-Scholes risk-free rate to fund your option, then you'll lose $100,000 a year (give or take) on that option, which might well eat up your profit margin. So you really have to pay a bit less than $10 million if you want to make money trading options.

There are various oddities here, but let's start with one oddity-reducing effect: FVA offsets DVA. People get really mad at DVA because it is counterintuitive and uneconomic: When a bank's credit gets worse, its actual costs tend to go up. But DVA is an accounting ... trick? ... that says that its liabilities are worth less, so it's "made money." That's odd and annoying, or, if you like, an "abomination."

FVA, on the other hand, captures the fact that, when a bank's credit gets worse, its cost of funding its derivatives goes up. That's more intuitive (though: more procyclical). It's also sort of roughly offsetting: JPMorgan's uncollateralized derivative receivables and payables are within 10 percent or so of each other. 3 So as JPMorgan's credit gets worse, it will have roughly offsetting DVA gains on its payables and FVA losses on its receivables; as it gets better, it will have roughly offsetting DVA losses and FVA gains. And so JPMorgan's earnings deck says that "P&L volatility of combined FVA/DVA going forward is expected to be lower than in the past."

In other words, implementing FVA is a way to get rid of the weird unintuitive earnings volatility of DVA. It cuts down dramatically on how much time you need to spend explaining, "well we had a loss because our credit got better." (Something that Jamie Dimon particularly disliked doing.) That by itself is probably a good reason for banks to do it.

On the other hand, this has an important difference from DVA: DVA is an accounting concept that everyone gripes about because it isn't real. FVA is real: It doesn't just go into your accounting model; it goes into your pricing model for actual trades. You pay people less to enter into in-the-money derivatives with them (and, on the other hand, sell them out-of-the-money derivatives for cheaper 4 ).

But that's weird too, because not every bank has the same funding cost. It would be odd if, say, JPMorgan (5-year CDS in the 60s) was willing to pay more to do a derivative trade than Goldman Sachs (high 80s), just because it funds more cheaply. Presumably that sometimes happens, 5 but mostly people trade based on market prices, and in theory at least there should be one market price. How do you calculate that market price? Probably you can take your own credit spread into account, but presumably also there are some disconnects. So if "the market" charges 50 basis points of FVA, and your own funding costs blow out to be, say, 200 basis points, then the value of the derivative receivable to you is less than its market value.

That might affect your pricing model: You shouldn't do things that cost you more than they make you. 6 (That's presumably why banks with weaker credit get out of the over-the-counter derivatives business.) But it can't affect your accounting: You have to value things on your books at their market price, not your idiosyncratic private price. So there is, at least in theory, some gap between "my funding cost" and "FVA." It's unclear to me how much of JPMorgan's model is based on their own funding costs and how much is based on some "market" funding cost; the earnings deck talks about "market funding rates" and "the existence of funding costs in market clearing levels," so it seems that they're thinking more about a market price of funding than they are about their own cost of funding.

Oh one fun fact about that. That earnings deck says that FVA "represents a spread over Libor"; based on Marianne Lake's comments you can guess that that spread is around 50 basis points. That is, banks fund at around Libor plus 50 basis points.

Libor, you'll recall, is supposed to be the rate at which banks can fund themselves.

One reason that all of this is coming up now is that, in the olden days, you didn't distinguish between "the risk-free rate for discounting derivatives" and "the cost of funding for banks." Libor was the risk-free rate. Libor was the funding rate for banks. Plug it into the formula and you'll get the right price. But when everyone stopped trusting banks, two things happened. First, nobody could say that Libor -- a bank borrowing rate -- was risk-free. 7 And, second, nobody could say that it was the rate at which banks could fund themselves.

In some sense the FVA rate -- the market-clearing cost at which banks can fund themselves -- is a new Libor: It's not an individual bank's cost of borrowing, but a sort of market-based aggregation of banks' general cost of funding. And, unlike Libor, it's based not on a survey but on market transactions, albeit market transactions filtered through fairly complex models. The fact that the new Libor is, basically, "Libor plus 50 basis points" is not a great vote of confidence in the old Libor, though. 8

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  1. Page 87 of last quarter's 10Q shows $66.8 billion of net derivative receivables (already net of $63.1 billion of cash collateral, see page 136), with $12.5 billion of additional collateral against them, for about $54.3 billion of uncollateralized receivables. (Out of $1.2 trillion of gross derivatives receivables, ignoring any netting, or about $130 billion of net receivables before any collateral netting.) This quarter there's about $67.5 billion of net receivables (see page 20 of the earnings supplement), so figure the uncollateralized amount is still around $54 billion or maybe a bit more, though it's not yet disclosed I don't think.

    That sounds dumb when you say it like that. Two maybe better intuitions are:

    • If you have a $100 million derivative receivable and you sell it to a new bank, the new bank needs to raise money to pay for it. Raising that money will cost it something, so it won't be willing to pay the full $100 million.
    • The real way to think about it is a replicating portfolio. So imagine that day one you enter into an uncollateralized trade with a client that has a zero expected value. You hedge in the interdealer market with a trade that is offsetting and identical, except that (like interdealer trades generallly) it is collateralized. A year later, the client trade has moved in your favor by $100 million, so the client "owes" you $100 million, but posts no collateral. The hedge trade has moved against you by $100 million, so you post $100 million of collateral. So you are actually funding the $100 million, which costs you money. (I guess this looks like a cost of the hedge trade, not the client trade, but that's not quite right: The price of a derivative is the cost of hedging it, and here the cost of hedging it includes funding the hedge.)
  2. There's also FVA on uncollateralized derivative payables. But this is a lot like DVA, so it's kind of already picked up in DVA. You can argue about whether there's any difference -- that is, between your "own credit" and your "cost of funding" -- but the difference is relatively small. That's why JPMorgan had a big loss from implementing FVA: It was imposing the FVA cost on its derivatives receivables, but the FVA gain on its payables was already more or less incorporated into its accounting through DVA. JPMorgan chief financial officer Marianne Lake says, "there is a material overlap between DVA and FVA," but apparently not a perfect one.

  3. Again, page 87 of the 10Q: $54.3bn of receivables, $59.8 billion of payables. Of course the durations are not disclosed and may be different.

  4. Which is sort of DVA, whatever. There's some argument that DVA is economic.

  5. John Hull, in a presentation and a paper with Alan White, raises the prospect that clients might arbitrage this difference: Buy an option from Goldman (cheap! they like the funding) and sell it to JPMorgan (rich! they fund easily!) and pocket the difference in price. But this does not seem like a practical arbitrage because not many clients do uncollateralized derivatives trades, and those that do tend to be "natural" users -- corporates doing interest-rate swaps on their own loans -- rather than sharp arbitragey hedge funds.

  6. Hull has a finance-theory argument that you should discount all cash flows at their actual risk, not your own funding cost, because if you do more low-risk projects then your own funding costs will go down. Maybe?

  7. So risk-free discounting (for collateralized trades) moved to a series of more risk-free rates, Fed Funds, EONIA, and so forth. This is a good KPMG paper about FVA, which discusses those "CSA rates."

  8. I kid, a little: Libor is self-consciously a short-term borrowing rate, while FVA takes into account a bank's overall cost of funding. That cost, in turn, takes into account the fact that banks, for regulatory and risk reasons, have more equity, and more long-term funding, than they used to. Back in the day if you needed money you'd just go lever up and borrow all of it short-term at Libor. Now if you need money some of it needs to be equity and stuff.

To contact the author on this story:
Matthew S Levine at

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