The "complexity" of derivatives

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.

10 thoughts on “The "complexity" of derivatives

  1. mrz

    Treating economics and statistics as strange incantations from a rarefied priesthood is, we now know, a recipe for suicide.

    But that’s the American way!

    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.

    I guess what people are wondering is was this notion that house prices would rise forever a greedy self-fulfilling prophesy or just bad forecasting. Nefarious or foolish?

    Reply
  2. slaniel Post author

    I’d be inclined to vote ‘foolish.’ It’s a classic bubble pattern: assume that something will rise until it doesn’t anymore; assume that even if it’s overvalued, there will always be another fool after you to pick it up. We saw it in the dot-com era, and we’ll see it again. Who knows what the bubble will be next time.

    I’ll be writing a review of Dean Baker’s “Plunder and Blunder” soon, but one of the really excellent tools inside of it is a guide to identifying bubbles. It’s a two-page arithmetic exercise on how you know when a price-to-earnings ratio is unsustainably high — in particular, when P/Es are far outside of historical norms.

    For the housing bubble in particular, you could look at the Case-Shiller Index. You can visually identify the housing bubble in there if you graph, say, Miami’s housing prices over time. Somewhere in “Plunder and Blunder,” Baker notes that housing prices, adjusted for inflation, hadn’t risen for 100 years. (That’s questionable to me, so I’d need to look at the data. I mean, aren’t homes supposed to be an investment? So wouldn’t they appreciate at least somewhat?)

    It’s all too easy to be condescending about this stuff, and to scoff at people who flipped houses during the boom. I’m not that guy. I wasn’t exactly standing on streetcorners shouting, “This boom is unsustainable! You all are crazy!” So please don’t misunderstand me on all of this. Another boom will come, and I will surely be caught just as unawares as (most of) the rest of the world.

    Reply
  3. mrz

    Well, I guess the thing is, you obviously want sustained growth rather than a “boom”. And it seems that people get into these foolish cycles because of greed and over optimism “Look! It’s going up! And it’s STILL going up! I need to get in on this! Everybody needs to get in on this!”.

    I guess the question is: Is it possible to construct a system of incentives so that you get good sustained growth without booms and without putting a damper on everything…and can you do that without destroying freedoms?

    Also, is it possible that a little bit of a boom is good? That is, rather than have a continuously rising line with shallow inclination, does it make sense to have a low ampitude sine wave that follows that line? In other words, if you just had a line that went ever upward, would it be too boring and stunt advances? It seems to me that booms seem to make cash flow and big advances can be made because people are freer with their money. Would a steady line cause people to be too stingy and hamper growth? Etc. Etc.

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  4. slaniel Post author

    On the “destroying freedoms” part: there’s a reasonable argument that just raising interest rates at the first sight of a boom would be a smart way to go. Interest rates seem to me like a very wide hammer. And it seems to me also that a wide hammer is exactly what we want; we don’t want government getting involved in the details of individual industries.

    The question whether we need booms for innovation is an empirical one that could probably be answered pretty clearly. I’d be surprised if there weren’t already papers on this. One quick answer that comes to mind is that if booms spur innovation, then busts hinder it. So I wonder whether boom-then-bust leads to just as much innovation as smooth-upward-growth, over the full course of the cycle.

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  5. mrz

    Yeah, i guess, do busts consume all that booms create or does a residual remain, and is that residual “large” enough vs. steady growth.

    As far as raising interest rates, I think the problem there is that it requires somebody to “take the punch bowl away when the party’s getting good”. There’s a strong social disincentive against this. I guess what I’m wondering is, can we setup a web of incentives/disincentives that keep pushing things in the right direction or is a fixed system always going to be gamed, or always require some guy on who’s shoulders rests the question of “Do I want to be hated for putting the brakes on now, especially when it’s so good?”

    Reply
  6. slaniel Post author

    Well, the Fed is supposed to be independent of the rest of the government. Its head is nominated by the president, confirmed by Congress, and appointed to a fixed term, exactly so that he can administer the economy apolitically.

    If even an independent Fed is necessarily political, and refuses to take away the punch bowl, then I can’t see much hope that we’ll ever take away the punch bowl.

    Reply
  7. slaniel Post author

    Society needs a debate about issues, Mike! Don’t you see?

    May or may not be related to a thought I had recently. Everyone likes to say that Americans are stupid. Everyone likes to say that. Everyone else is stupid. Just not us. Kind of like how everyone likes his Congressman, but Congress in general is corrupt.

    There must be some good studies of what Americans actually know about their society and government. Yes, I know that in many ways it is quite bad: lots of Americans can’t identify their country on a map; probably a sizable fraction can’t name their senators; and so forth. Only 24% of Americans can identify what “cap and trade” means. So these are all bad. And maybe the full story is bad. But it gives me pause that basically everyone thinks that everyone else is dumb.

    (Naturally, there’s the other question: of those who do know what they’re talking about, what fraction are Democrats? … Damn: when I put it that way, I very much do want to see some data.)

    Reply
  8. mrz

    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!

    On a similar note I keep recently hearing “We need to have an open debate about…” used in a similar manner. “Look at me! Aren’t I all equinanimous! We should have a debate. Oh, not right now and maybe not even us, but the metaphorical we should have a vigorous debate!”

    Reply
  9. Jamie

    I’m reading The Big Short by Michael Lewis (which I highly recommend for you), and it reminded me of this post. Certainly the media liked to call these financial instruments complex because they were being lazy and not taking the time to understand them (except maybe for the Planet Money folks at NPR).

    In The Big Short, however, many of the traders who were trying to short mortgage-backed securities described them as being “complex.” Many of them didn’t know what these things were when they first encountered them but they took the time and had the smarts to research them and figure them out. However, even after that effort, they still called them “complex.” Not because the concepts were difficult to understand, but because no matter how much they researched them, they could never really determine the quality of the underlying raw materials (mortgages) in any given security.

    The Wall St. firms that created and sold the CDOs deliberately made them obtuse so that it was difficult to determine the actual risk contained within. Part of the reason the firms loved selling CDOs was because they were able to take low-rated mortgage bonds they couldn’t otherwise sell and package them into higher-rated derivatives that they could sell. On a “first generation” mortgage bond, it might have been clear what the risk of investing in the product would be, as the firms did publish stats about them such as average FICO score or % of no-doc loans. But the firms sliced and packaged these bonds many times over to make the CDOs, such that it became very difficult for investors to get a real sense of the quality of the underlying raw materials in them. So everyone then just trusted the rating agencies.

    It’s like trying to determine the quality of mass-produced ground beef. You may know that one particular cattle farmer’s practices are sustainable and humane, but once you grind up his meat and combine it with the meats from thousands of different farms and feed lots, and then portion that ground meat into little hamburger-sized patties, it becomes almost impossible to determine the quality of any individual hamburger.

    Reply
  10. Pingback: Are Derivatives Really That Complicated? — Jamie Forrest

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