Yet another story describing derivatives as “complex”. Having now read a rather large amount in this area, I realize that we’ve been deceived: they’re not especially complex.
Take the term “sliced and diced,” for instance, which always gets applied to mortgage-backed securities. “Slicing and dicing,” I now realize, is a term used by people who don’t understand how mortgage-backed securities were packaged; it’s a substitute for actual thought. Much better to believe that mortgage-backed securities are beyond human comprehension, and that anyone who handled them was just fiddling with the levers on a machine he didn’t understand. I myself have used such terms on this here blog, and I freely admit that it was based on ignorance.
The best explanation of “slicing and dicing” that I’ve read is in “The Economics of Structured Finance”. The big question people seem to have is: how did subprime mortgages become AAA-rated securities? The answer is straightforward, and reasonable. In a word, it’s “tranching.” That is, no matter how bad a credit risk the mortgages are, you can assign them to securities that get hit first or last when a mortgage defaults. If I own a security in the lowest-rated tranche, I’ll get cleaned out more quickly than someone who owns a security from the highest-rated tranche. In a very real, non-mysterious sense, then, the lower tranche carries higher risk than the highest tranche. As such, the highest-rated tranche should carry a lower return than the lowest-rated one.
What is tricky is how to estimate these various risks, hence how to determine the returns they should carry. In turn, how risky a given mortgage is, and therefore how risky a given tranche is, depends on how correlated defaults are. If either all mortgages default, or none do, then the correlation is perfect and it doesn’t matter which tranche you’re in: you’re going to get cleaned out exactly when everyone else does. If they’re uncorrelated, then you can treat default risk like any other insurable risk. Finance has constructed some reasonable models over the last 40 years of what to do with correlations less than 1.
The trick is that you need data to estimate correlations. Since mortgage default was rare before this recent debacle, data for correlations was hard to come by. This is where we get the now-infamous Gaussian copula, which estimated correlations seemingly out of thin air. And as the “Structured Finance” paper explains, the risk that you’ll be cleaned out in a certain instrument (CDO-Squared) is highly sensitive to the correlation between mortgages.
The term “derivative” generally means “a security whose value changes when the value of an underlying asset changes”; the derivative derives its value from the other asset. A mortgage-backed security derives its value from an underlying mortgage. A security which gives you the right — but not the obligation — to buy a given security at a given time, is a derivative of that security, and is called an “option.” (An option that entitles you to buy is called a “call option.” An option which entitled you to sell is called a “put option.”)
There’s a set of results, by now classical, on how much you should be willing to pay right now in order to buy that security later on. How much, for instance, should you be willing to pay to buy a share of General Motors stock one hour from now at $100? Given that GM is, at this moment, trading for $1.59, your answer should be “not very much at all.” The reason is clear: GM stock is extraordinarily unlikely to reach $100 within an hour. Suppose you paid $1 for the right — but, crucially, not the obligation — to buy GM at $100 in an hour. You would not exercise that right, of course, because you’d be drastically overpaying. You are nearly certain to lose $1.
The lesson here is that the price you should pay for an option depends on how rapidly the stock price moves. If GM routinely swung between $150 and $1.50 in the course of a day, you might be more willing to pay for the right to buy at $100. So a lot depends, then, on knowing how much GM stock moves. What you want is the probability distribution of GM’s stock-price movements. A lot of the theory makes assumptions about the general shape of this probability distribution. It typically assumes that stock-price movements look like a bell curve, or “Gaussian distribution.” You can weaken this assumption in various ways. When all is said and done, though, you need to take some sort of guess about how rapidly the stock price will change between now and when the option is exercised.
But note in all of this that there’s nothing really complex happening. The pricing of options depends on various assumptions about stock-price movements which may or may not be true. The construction of a mortgage-backed security is not difficult, at least in outline: pool mortgage payments, then divide them into tranches that have lower or higher exposure to default risk. At least in hindsight, it turns out that assets were more correlated than people expected. That doesn’t make the securities “mysterious” or “complex”; it means people made mistakes. The worst that can be said is that they used the wrong models, which in turn means they made the wrong assumptions. Underlying all of this might be the assumption that home prices would rise forever. That’s it, so far as I can tell. A bad assumption leads to a bad model, which fails catastrophically in the real world. Therein lies your “complexity.”
I blame the use of this term on people who don’t understand a little bit of statistics. “Complex” is also one of those terms that allows people to avoid clarifying their thoughts. Ze Frank talked about this:
The cool thing is, anyone can do that. Just say, “Well, it’s a little more complicated than that,” and the amazing thing is, no matter what you’re talking about, you’re probably right!
You see it everywhere. Describing a food’s taste as “complex” gives you the appearance of erudition without your needing to actually say anything; most any food, except maybe pure sugar and pure vinegar, is complex, inasmuch as it’s not reducible to a single note. Describing your emotions in a particular situation as “complex” makes you sound like a deep person. (Stephen King somewhere describes an interaction with an undergraduate English major: she tells him that something “is, like, hard to put into words,” to which he replies that she “ought to, like, pick a different fucking major.”)
The point of any interesting discipline is to actually solve problems, not to stand in awe of their staggering complexity. That goes double when it’s something like the economy, whose functioning it is everyone’s job to understand, at least at some level. Treating economics and statistics as strange incantations from a rarefied priesthood is, we now know, a recipe for suicide.