Derivatives: A Catechism

Felix Salmon and Jesse Eisinger are having a little debate on whether we should worry about derivatives. Regular readers should be able to guess that, yes, I think we should worry. Regular readers should also write me with tips on dietary fiber.

“Derivative” is a vague term that covers everything from options and futures traded on public exchanges to interest-rate swaps and credit-quality bets negotiated in private. Two features unite all derivatives: 1) They are contracts that compel cash-flows between two parties based on changes in the price of some underlying security or asset; and 2) The theoretical justifications for their use have been far outpaced by developments in real-world markets. What follows is a catechism for the virtuous, that you may use to correct error in those who have been led astray, and to protect yourself when confronted by those who would deceive you into some state other than sheer panic.

Question: Do we need to worry that the “notional principal” of derivatives outstanding is several times the wealth of the entire world? Isn’t “notional principal” meaningless, since actual cash flows between parties are mere fractions of this principal?

It is true that, when everything goes right, most derivatives compel cash flows that are small fractions of notional principal per year. But some common and ever-more-popular derivatives (e.g. CDSs, forwards and futures) can provoke sharp cash flows whose magnitude approaches the notional liabilities. More importantly, even “balanced” derivatives like vanilla fixed/floating interest rate swaps can subject parties to liability for the full notional principal, should one party default and enter bankruptcy, if the lawyers haven’t been careful to write watertight “netting” agreements. Even where the legalese is solid, the credit-risk assumed by the “in-the-money” party to a derivative contract is proportional to notional principal. The hazard associated with a large notional principal is not primarily associated with the cash-flows that would be triggered by parties fulfilling their contractual obligations. Notional principal is a measure of the mayhem that would result should counterparties fail to meet their obligations in significant numbers.

Question: Isn’t much of the so-called notional principal is tied up in offsetting positions that cancel one another? Doesn’t that mitigate the risk?

No, not really. Offsetting increases credit risk, whereas genuinely closing positions diminishes it. Consider the following scenario: You and I enter into an interest rate swap with a notional principal of a billion dollars. I’m going to receive a fixed rate of interest for five years, and pay LIBOR to you, on that notional billion. After two years, the market has moved against me, the fixed rate I’m receiving is low compared to market rates, and I think it’s only going to get worse. I want out, and am willing to pay you the market value of your “in-the-money” position to escape. But you are a bastard. We had a five year deal, you say, and cackle evil-ly. So what do I do? I go to someone else, who agrees to pay me LIBOR on 1B, and I pay a (high) fixed rate, offseting the original contract and locking in my loss at a value equivalent to what I should have had to paid you to cancel the contract, if you hadn’t been a bastard. That is what offsetting means. The notional principal outstanding is now 2B, as there are two 1B swaps in play. But “really” there is only one swap between you and my new counterparty. I’m just a middle-man who passes funds along, but I no longer have any sensitivity to changes in interest rates. So, the 2B of notional principal is overstated, right? Well, let’s compare credit risk in the two scenarios. Originally, you were only exposed to my credit risk — I might go under, and be unable to make continued payments to you, depriving you of your gains. (Absent a netting agreement, I might even deprive you of the notional principal.) Now, you are exposed to my credit risk, and that of my new counterparty. That’s not true, you say. If my new friend goes under, that’s not your problem. It’s still me you have on the hook. Technically, that’s right. But in reality, since I’ve already booked a fixed loss and moved on, I may have taken on a lot of new leverage elsewhere. When my counteraparty defaults, and the “offset” contract comes at me like a ghost, it will hit you as well, my friend. Complicated networks of offsetting positions increase the likelihood that a credit event involving one market participant will cause cascading problems for other participants who may not have known they had such complicated exposure. An intelligent market would not have man-in-the-middle offsets, but would find ways to close out exposures. Public futures markets, designed so that contracts are written against a central clearing house, have this worthy feature. Those trillions and trillions in outstanding swaps do not, so offsetting positions contribute both to notional principal and systemic credit risk.

Question: Derivative markets are a zero-sum game, right? Somebody’s gain is somebody else’s loss, wealth is never destroyed, only moved around, right? Why should we care which “play-ah” wins or loses? In the aggregate, the markets and the public are whole. Right?

Wrong. When a party goes bankrupt and defaults, both parties lose. Absent the possibility of credit events, derivatives are a zero-sum game in terms of cash flow (leaving transaction costs aside). In the real world, where counterparties do sometimes default (and where transaction costs exist), derivatives are a negative sum game. Derivatives proponents are right that in real economic terms, derivatives can add wealth, by enabling economic activity through the sharing and mitigation of risk. But the expected negative value of credit losses and transaction costs must be weighed against the positive value of risk mitigation. When the notional principal of credit default swaps against some firm or issue far exceeds the value of actual bonds outstanding, it’s hard to claim that positive-sum risk mitigation is motivating the trade.

Question: Are derivatives bad?

No. Forwards and futures, options, various swaps and insurance contracts all have their uses, and represent very real innovations. But whatever their value to an individual market participant, their value to the economy in aggregate depends on the degree to which they hedge real economic risks, and is diminished by any credit, valuation, and liquidity risks they introduce. The financial community has done a good job at inventing useful contracts and describing the ways that they could indeed hedge real risks. The community has done a poor job, unfortunately, at cataloging the ways that they introduce new risk, and characterizing the conditions wherein derivative markets are likely to do more harm than good in the aggregate. As participants have focused on the well understood positive side of the ledger and neglected the poorly understood downside, it is unsurprising that these instruments have grown popular. But it should also not be surprising if the ill-defined costs we’ve not bothered to quantify someday turn out to be greater than we can easily afford.

The questions in this catechism are largely inspired by Felix’s defense of the trade. Credit, and clucking, where it is due…

Update: jck of the very excellent Alea takes me to task (in a comment here) for suggesting that vanilla fixed/floating swaps could provoke liability by a party for full notional principal if one party goes bankrupt, absent solid netting agreements. A swap can be viewed as a cross-sale of bonds, and if parties to a swap did write their contracts that way, it is true, as I claimed, that one party to the swap could be left holding the bag for the full notional principal should a counterparty gain bankruptcy protection. But swaps are not typically written like that. My claim is more uncontroversially true with respect to currency swaps, where the “notional principal” is not in fact notional, and must be delivered by the parties, unless some formula for netting is explicit. In any case, I had not intended to rest my argument on lawyers’ mistakes. Even when all i’s are dotted and the netting is good, notional principal matters, as it determines the size of the credit risk the winning side of a swap will be forced to bear. There is an unknown degree of legal risk out there. Despite the efforts of ISDA and others, swaps and many other derivative arrangements are private contracts with untested idiosyncracies. To the degree there is legal risk, it is proportional to notional principal. But even if legal risk turns out to be negligible, credit risk — the risk that parties will fail to meet even fully netted cash flows — is undeniable, and proportional to notional principal outstanding.

It’s also worth noting that in an essay about “derivatives” writ large, “notional principal” is a very imprecise term. For swap within a single currency, it’s fairly clear what “notional principal” means. In a currency swap, or a swap synthesized via offsetting bond agreements, the principal is not notional at all, but might still be referred to that way. With respect to forward contracts, futures, and options, notional principal is simply an incorrect term. One might talk about “open interest”. I use the term “notional principal” in this essay loosely to mean the value of the underlying assets upon which derivative cash flows are based.

Update History:
  • 18-Apr-2007, 1:20 p.m. EDT: Changed “I’m no longer have…” to “I no longer have…”
  • 19-Apr-2007, 1:31 a.m. EDT: Added an explanatory update, in response to comments by jck.
  • 19-Apr-2007, 8:46 a.m. EDT: Changed “single currency swap” to “swap within a single currency” in he update, for clarity.

5 Responses to “Derivatives: A Catechism”

  1. Mike writes:

    Interesting article and informative. Reminds me a lot of software development … where changes here and there might be great as “features” but usually cause side effects you don’t want. Another interesting parallel is leverage. In software you can use a lot of leverage, which can be a great strategy, but again … when things go wrong … they go very wrong.

  2. Mike, can you expand a bit on what you mean by leverage in software? I’d be interested. Thanks, and thanks for stopping by!

  3. Cassandra writes:

    Just as there are “get rich funds” and “stay-rich funds”, so too does the agent/principal dilemma rear its head in Derivatives markets particularly in the commercial banks &IBs. Though few today may recall Herstatt risk (except the esteemed jck), and even fewer care even if they did, it is worth noting that the first thing Warren Buffett did when he bought GenRe was to shutter its Financial Products group. Apparently (so the story goes) he went to visit their trading floor where the eager young bucaneers hoping to get rich described some of their trades (“….5 years of credit risk with WHO? for HOW MANY BASIS POINTS?…”). He left the room and immediately instructed a wind down of a complex and long-dated book. When you are in “stay-rich mode”, placing oneself intentionally in the midddle of the harms-way-web for a coupla bp’s is just not worth it. He’ll take risk where he’s getting paid for it and where the downside is a claim on assets, but it’s hard to argue the get-rich risk is worth it without saying something like “in a tail event, we’re buggered anyways….”

  4. Cassandra — The blogospheric word of the day is “trenchant”, and of course you always are. Two thoughts:

    1) “Herstatt risk” is such a delightful, quaint term for what we should all be worried about re derivatives. It’s what happens when the gentlemen in the casino begin to lose their shirts, and stop playing like gentlemen. Overlaid on the probability distributions all the quants in the world model, there is another distribution, on which there is nearly no data, that could only be pieced together by polling the subjective priors of lawyers and regulators the world over, and even that would result in a terribly loose approximation. Most people understand in ordinary commerce that the words of a contract define only a starting point, they bias but do not determine the outcome, should the parties enter into serious dispute. Derivatives are only contracts, and on a bad day, subject to as much legal maneuvering as a lease or insurance contract some party wants to squirm out of. But that’s hard to model in a financial mathematics course.

    2) One can understand then difference between the “get rich” and “stay rich” mindset just by understanding optionality. The already rich have much to lose, and face the full upside and downside of their choices. The “get-rich” have a very truncated lower tail, they have much to gain, and nothing to lose. Unfortunately, though Buffet may be above this sort of thing, the already rich have learned they can have their cake and eat it to by hiding their investments behind a limited-liability shell, and hiring a smart managers with nothing to lose.

    I’m flattered you drop by. I enjoy your thoughts and exploits in the land of the Rising Sun.

  5. PHYRON writes:

    JCK is dead on… reading your post was like going back to the 1980’s… the world just doesn’t look that way any more…

    I would posit this as a comparative framework…A Ten year Interest rate swap as cuurently structured and traded ever day in overwhelming size is on any rational basis less risky than trading in a Ten Year Note U.S. Treasury as they are currently traded.

    Recall that “nobody” really buys Treasuries on an outright basis, they are “leveraged” bets, financed through Repurchase agreements.

    Buying a Treasury has dramatically more risk than doing an interest rate swap…again the risk is not the US Treasury… but your O/N risk on the couterparty, and the Repo risk.

    In both these the risk is dramatically higher in the US Treasury.. as you have to full principal at risk if the counterparty defaults, where as in the swap, and particularly in these low volatility times for interest rates.. all you have is the PV of the interest rate differential from one day to the next.. late almost di minimus as interest rates have become a step function of central bank policy measures..

    So if it makes you feel any better substitute US Treasuries every where you mention a Swap.

    It’s simpler to think of these swaps as series of futures contracts… daily margined and collateralized… Roughly speaking original margin under the universal Span methodology is mean to describe the largest “likely” 5 day move…