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.