Felix Salmon makes rather more out of his own Gaussian copula article than he has any right to. In brief, what he showed in that article was that we never had any right to assume that the market knew how to estimate mortgage-default correlations properly. When mortgage was a rare event, we didn’t have the data.
It doesn’t follow that estimating correlations on assets generally is a fool’s errand. It is true, though I think largely vacuous, to assert as Salmon does that
correlation measures, by their very nature, are always backwards-looking, and that you can be pretty sure future correlation will be very different from past correlation.
The question for Salmon is: what’s the alternative to being “backwards-looking”?
I’ve seen a lot of financial handwaving about this financial crisis by now; it’s getting frustrating. There are at least two constituencies who get no value out of this handwaving, namely investors and bankers. Let’s consider them in turn.
The practical question for investors is: where do I put my money? Various theorems in finance began from the premise that it’s impossible to systematically beat the market, and that people should diversify across all available asset classes: stocks, bonds, real estate, venture capital, etc., etc. The theorems say to find asset classes whose risks were uncorrelated and invest in them, or at least to estimate correlations and balance your portfolio on the basis of the correlations. Yes, Salmon is right that estimating correlations is hard. But is there any better alternative for those who need to put their money somewhere?
Perhaps we should be overestimating correlations. This idea comes to me after reading Mike Rorty’s interview with economics professor Perry Mehrling (via Ezra Klein), in which Mehrling advises,
If you insure an earthquake, you are not making earthquakes more likely. The insurance contract is a purely derivative contract, it isn’t influencing earthquakes. That is not true of insurance of financial risk. When AIG is selling you systemic risk insurance for 15 basis points, that price is too low. People said: “If I can get rid of the whole tail risk that cheaply, I should load up. I should take more systemic risk.” So the prices were wrong. So the important thing for government intervention here is to get that price closer to a reasonable rate to prevent people from creating earthquakes.
The claim built into this is that the market hasn’t been properly setting the premiums on derivative insurance, and that maybe the government can do it better. This idea obviously needs to be defended: we typically expect that government pricing will be arbitrary and that markets will do a better job. Markets may have failed here, again possibly because they had limited data on which to base their correlation estimates. I say that they only “may” have failed because: what’s the alternative? Would someone else have done it better? Market failure can’t be judged in a vacuum.
In any case, maybe by now it doesn’t matter whether we price insurance exactly right; maybe it’s better than we charge too much for insurance, because the downside has much greater magnitude than the upside.
Which is to say: Salmon may be right that figuring out correlations (among certain securities) is difficult, but maybe it’s not impossible to set a lower bound on them: we may not know the exact correlation between Tampa mortgage defaults and Boston mortgage defaults, but we know that it’s at least 0.5. Can we estimate lower bounds in such a way that we could get useful insurance premiums?
Again, the point is to be useful, not to be wringing our hands about the metaphysical impossibility of estimating correlations. This is why I’ve been avoiding Taleb’s Black Swan book, which one of these days I will have to read: its public gloss suggests that it’s an extended claim for the impossibility of estimating real-world probabilities. More charitably, it may be that Taleb is discussing the distinction between risk and ambiguity, that is, the distinction between known probabilities and probabilities that cannot even be estimated. Again: yes, sure, fine, but: eventually someone has to figure out the appropriate price to assign to a mortgage-backed security. Do we not want to allow insurance against mortgage default? Last I checked, it was considered a good thing to allow banks to hedge against mortgage default. Do we forbid banks to hedge their mortgage risk, just because it’s “impossible” to estimate the correlation? Of course not. We need to estimate that risk. This may be difficult, but does anyone dispute that it’s necessary?
The practical question for central bankers is: how much do I tell my banks to hold in their reserves? Basel I told banks to hold a fixed fraction based on the quality of their assets. As Baseline Scenario put it,
Under Basel I, banks have to hold capital equivalent to 8% of their risk-weighted assets. Each type of asset has a risk weight that reflects its riskiness. For example, OECD government bonds have a zero risk weight – theoretically, they have zero risk, and hence require zero capital; home mortgages have a 50% risk weight; and uncollateralized commercial loans have a 100% risk weight. So if a bank held $100 in Treasuries, $100 in home mortgages, and $100 in commercial loans, it would have $300 in assets, but only $150 in risk-weighted assets (0% * $100 + 50% * $100 + 100% * $100); therefore would have to hold $12 in capital (8% * $150). Looked at another way, the capital requirements are 0% on government bonds, 4% on home mortgages, and 8% on commercial loans.
Basel II changed this to a more complicated value-at-risk process that depended upon (inter alia) the historical default probability of mortgages. So again we return to the difficulty of estimating that probability. Central banks need to tell their bankers how much money to hold onto. How should they do this?
Salmon’s much-puffed article focused on one particular tool for estimating probabilities. That tool relied upon assuming the Gaussian (“normal” or “bell-curve”) distribution in certain places. The Gaussian distribution appears in various places throughout finance, most notably in the Efficient Markets Hypothesis, where it’s an approximation to the shape of stock-price movements: lots of moderate movements and very few large movements. If stock-price movements actually were Gaussian, stock-market crashes on the order of the 1987 crash would happen far less frequently than they actually do. It’s been known for a very long time that stock-price movements are “heavier-tailed” — that is, feature more extreme movements — than the Gaussian would predict. There are statistical techniques to deal with heavier-tailed distributions, but they are far more complicated to handle than Gaussians.
Which is to say that the failure of the Gaussian copula says very little about the failure of finance or the failure of statistics or an inability to measure correlation generally. What it says is that using the Gaussian willy-nilly is a bad idea. What it may say is that we can expect financiers to reach for and misuse the easiest tool around. We see misuses of linear models all the time, because they happen to be easiest; we see users of statistical tools not checking that those models’ assumptions are satisfied. This emphatically does not mean that using statistical methods is a fool’s errand.
What’s the alternative to using statistical tools? Even the most evenhanded commentators on the recent financial crisis either don’t answer this, or wave their hands vaguely in the direction of “using your gut.” Even Justin Fox, in his fantastic Myth of the Rational Market, does this: Warren Buffett is supposed to be the paragon of “using his judgment” rather than using statistics. I obviously don’t doubt Buffett’s investing acumen, but Buffett is the rarest of rare cases; almost by definition, not everyone can be as good as Buffett. And even Buffett used quantitative methods early in his career: he followed his teacher Benjamin Graham’s advice and looked for those companies whose market value was less than the value of their physical assets; called these “cigar-butt companies”. Such companies could sell off their physical plant and yield more money than the market ascribed to them.
This approach of looking for cigar-butt companies eventually stopped working, because the rest of the market caught on. Salmon is, of course, correct here: any technique that systematically beats the market will eventually stop being useful. Eventually people will catch on and replicate your clever idea. This may not always be true, but it’s true enough that people shouldn’t expect to make money systematically by outsmarting the market. This is a toned-down version of the Efficient Markets Hypothesis, and it seems hard to dispute.
Again, though, Salmon takes this too far, and it’s not clear what pragmatic value to give to his assertion that ‘I suspect that any investment strategy more sophisticated than “buy low, sell high” is doomed to fail eventually.’ (“Buy low, sell high” isn’t even an investment strategy, which is surely the point here: you have to know that you’re buying low, and know that you’re selling high, and no one can know that.) Read a book like Dean Baker’s Plunder and Blunder and you’ll find at least a lot of little guidelines to let you know whether your investment strategy makes sense. Baker lays a quick back-of-the-envelope method for determining whether stocks or housing are in a bubble. It’s not a grand method for investing your money, but it’s a tool to add to the toolkit.
Tools in the toolkit are substantially more useful than metaphysical agonizing over the impossibility of smart investing, which is all that we seem to be getting nowadays from the likes of Salmon and Taleb.