How Banks Hedge Counterparty Risk

Here's the long post I promised yesterday on hedging counterparty risk. It's by someone who wishes to remain anonymous, but who used to do this for a living at a very large bank. It's also incredibly wonky, even without a section on correlations and netting agreements.

If you want to cut to the chase (the what, rather than the how), here's a couple of excerpts.

A firm that wants to know how much money it would make or lose if a credit spread widens -- or defaults -- will aggregate the effect on credit derivatives that were explicitly written on that credit with the effect on counterparty risk due to derivatives with that counterparty. If you buy a CDS with a risky counterparty, your exposure to the credit of the reference credit goes down; your exposure to the credit of the counterparty goes up. If you accumulate a lot of risk on a single credit because you buy a lot of credit protection from it, that will show up in the risk reports, and you will hedge it just as you would if you had a lot of risk because you had sold a lot of protection to a client.

Ultimately, you try to hedge what you can hedge; what you can't hedge, you try to quantify; what you can't quantify, you try to understand; and what you can't understand, you keep small enough not to sink the firm.

In the real world, what would all this have meant if AIG went bankrupt? If it did so in a vacuum, then there's a good chance that the banks who bought credit protection from AIG would indeed have been hedged against such an event. But I don't know whether all hedge funds have the kind of risk controls which are outlined in this post. And when markets simply seize up without prices, as they're doing right now, hedging becomes effectively impossible. But to answer the narrow question of whether Goldman Sachs was justified in saying it was hedged against an AIG bankrupcy, I do believe the answer is yes.

Anyway, here's the whole thing. From here on in, "I" means the former risk manager, not Felix:

I'd like to start with a general background note: in pricing any risk, where market prices are available, we take those as "correct". If there is a liquid market for the coin flip in the upcoming Super Bowl that places the odds of heads at 40% -- we can take either side of a bet that pays off 3:2 -- then the price of a contract in which our counterparty delivers a barrel of oil in February only if the coin comes up heads is 0.4 times the forward price for a barrel of oil, not 0.5 times. We will probably want to take a significant stake on that coin flip (supposing it is clean -- there's no counterparty risk or other complication associated with it), but we can do that directly, and for purposes of pricing anything else, the market tells us how much it costs us to increase or decrease our risk. This is the basic relationship between hedging and pricing: the price of an instrument is equal to the cost of hedging all of its risks. Conversely, if we know how the price of an instrument varies with respect to some market variable -- interest rates, for example, or the implied probability of a coin flip -- then we can hedge our risks by making trades with the opposite risks.

If we wish to price a corporate bond from a particular company, then, where the bond is less liquid than the associated credit default swap, we can get the price of the default swap from the market; this tells us how much risk there is. The price of the CDS tells us what the default risk is, and that default risk and risk-free interest rates imply a bond price. If we charge a customer that price for the bond, and then buy the associated default swap, we should have a portfolio that is risk free and produces a risk-free rate of return.

The temptation of technicians, especially those of an academic orientation, is to be overly concerned about making statements that aren't quite true -- we complicate things by over-explaining. Well, the last sentence of the preceding paragraph isn't quite true; forgive me for the moment if I note: 1) I have assumed that the CDS itself does not have counterparty risk; if the reference credit defaults, we *will* be able to sell the bond at par; 2) I'm ignoring bid-offer spreads; we use a CDS price that reflects what we have to pay to lay off the risk, not necessarily the price at which the swap last traded in the market, and we will charge a customer something for our troubles; 3) I'm assuming the existence of an appropriate risk-free interest rate that I'm presuming is the correct amount to charge 4) a CDS+bond portfolio is actually not a perfect hedge, because if interest rates generally go up, the bond would be worth less than par even if it were risk-free; the credit risk is overhedged if interest rates are high (i.e. we make money if the counterparty defaults), while it is underhedged if interest rates are low (we only get par for the bond, rather than the higher price that a risk-free bond would offer). I'll try to suppress the need to get this wonky in the future, but items 1, 3, and 4 happen to be things I want to touch on directly anyway.

Starting with 4, what one would prefer here would be a contract to buy back the bond not at par but at some value reflecting interest rates. In fact, this sort of thing could solve our problem for any contract; if we pay for an option on a stock, we just go to a risk-free counterparty and buy a contract from them that will buy the option from us (or pay us for its lost value) if the counterparty on the option goes bankrupt. This is a contingent credit default swap, CCDS, and a market for these things has developed, particularly in commodities, in the past few years. If one has a price for a derivative with a risk-free counterparty, and a price for the associated CCDS with a risk-free counterparty, the appropriate price of the derivative with a risky counterparty is the risk-free price minus the cost of insuring against the risk. The CCDS is not, generally, terribly liquid, so its price is derived from ordinary CDS prices and the prices of the associated derivative. One of the main tasks of derivatives desks at the big sell-side institutions is to buy complicated derivatives from clients and hedge unwanted risks in more liquid markets; it will use the same tools to hedge unwanted counterparty risk the same way it would hedge the risk if it sold a CCDS to a client.

Back to item 1: a CDS has counterparty risk. If you bought a CDS to protect you on AIG, but you bought it from Lehman Brothers, you're not protected. If you were responsible, and had a lot of credit derivatives from Lehman Brothers, you probably then went and bought a CDS on them. In a simpler world, you could go around in a circle, buying insurance from a big set of counterparties on each other. In practice, because multiple counterparties can go bankrupt, you can't hedge your risks perfectly; the best you can hope for is to minimize them and to understand them.

One of the big advantages to the development of the credit derivatives market is that it is now easier to view counterparty risk as a market risk. A firm that wants to know how much money it would make or lose if interest rates go up by one basis point can aggregate the effect on the value of all the derivatives the firm has. Similarly, now, a firm that wants to know how much money it would make or lose if a credit spread widens -- or defaults -- will aggregate the effect on credit derivatives that were explicitly written on that credit with the effect on counterparty risk due to derivatives with that counterparty. If you buy a CDS with a risky counterparty, your exposure to the credit of the reference credit goes down; your exposure to the credit of the counterparty goes up. If you accumulate a lot of risk on a single credit because you buy a lot of credit protection from it, that will show up in the risk reports, and you will hedge it just as you would if you had a lot of risk because you had sold a lot of protection to a client.

Everything I've mentioned up to this point involves pricing or hedging counterparty risk that has been incurred. Pricing involves passing along to the client the cost of protecting yourself against its credit; if you buy an option, you pay less for it from a risky counterparty than from a risk-free counterparty. This makes selling the option less attractive to the counterparty; for long-dated contracts, this can be a big effect. On the other hand -- this was item 3 above -- your actual cost of funds is going to be higher than a "risk-free" rate of interest, and if you're putting up money up front, you need to make at least your own cost of funds on that. Accordingly, you end up charging the counterparty for your credit risk, too. Because of this, it is attractive to try to reduce the counterparty risk inherent in the contract. The simplest, first thing to do is to try to structure it as a swap; instead of my paying you for an option, I enter a contract with you in which I will pay you a fixed amount on the day the option expires. If you go bankrupt before then, I haven't paid the money up front, and stand to lose a lot less. On the other hand, if I go bankrupt before then, and the option has lost value, you will lose value due to my failure to make good on the deal. Still, for certain kinds of contracts, the aggregate counterparty risk can be diminished considerably.

A more obvious solution is to require collateral; every time the value of the deal changes by more than some threshold amount -- say the option has gained value, and I now stand to lose $5M if you go bankrupt tomorrow -- you will post collateral that I can sieze if you go bankrupt, applying it to your debt. This has its complications. For one thing, if the derivative is illiquid, you might not agree that you now owe me $5M; you think the option is worth less than I do, and refuse to post the collateral. These things will typically be subject to arbitration clauses. For another thing, it will typically take time for you to post collateral. Even if we have a deal that is supposed to be fully collateralized -- anytime the option is worth more than you have posted, you have to post more collateral -- I can still lose money if the market moves against me between the last margin call you actually meet and the point at which I figure out that you've definitively defaulted. We can try to calculate the size of this risk, too.

All of this can, to varying degrees, go wrong, which is why there is still a point at which risk controllers will say "no more". It can be very difficult to hedge against several big market moves happening at the same time, which, when counterparties are going bankrupt, is usually happening. Some corners of bankruptcy law haven't been tested, and, particularly in developing countries, the big foreign bank may find that laws that appear to be on its side aren't seen that way by a local judge. Ultimately, you try to hedge what you can hedge; what you can't hedge, you try to quantify; what you can't quantify, you try to understand; and what you can't understand, you keep small enough not to sink the firm.

Posted by Felix at 11:44 EST

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