Tag Archives: suprise

Economist on fat tails and finance

A special report on the future of finance in The Economist Fallible mathematical models: In Plato’s cave:

… although the normal distribution closely matches the real world in the middle of the curve, where most of the gains or losses lie, it does not work well at the extreme edges, or “tails”. In markets extreme events are surprisingly common—their tails are “fat”. Benoît Mandelbrot, the mathematician who invented fractal theory, calculated that if the Dow Jones Industrial Average followed a normal distribution, it should have moved by more than 3.4% on 58 days between 1916 and 2003; in fact it did so 1,001 times. It should have moved by more than 4.5% on six days; it did so on 366. It should have moved by more than 7% only once in every 300,000 years; in the 20th century it did so 48 times.

In Mr Mandelbrot’s terms the market should have been “mildly” unstable. Instead it was “wildly” unstable. Financial markets are plagued not by “black swans”—seemingly inconceivable events that come up very occasionally—but by vicious snow-white swans that come along a lot more often than expected.

This puts VAR in a quandary. On the one hand, you cannot observe the tails of the VAR curve by studying extreme events, because extreme events are rare by definition. On the other you cannot deduce very much about the frequency of rare extreme events from the shape of the curve in the middle. Mathematically, the two are almost decoupled.

The drawback of failing to measure the tail beyond 99% is that it could leave out some reasonably common but devastating losses. VAR, in other words, is good at predicting small day-to-day losses in the heart of the distribution, but hopeless at predicting severe losses that are much rarer—arguably those that should worry you most.

When David Viniar, chief financial officer of Goldman Sachs, told the Financial Times in 2007 that the bank had seen “25-standard-deviation moves several days in a row”, he was saying that the markets were at the extreme tail of their distribution. The centre of their models did not begin to predict that the tails would move so violently. He meant to show how unstable the markets were. But he also showed how wrong the models were.

Modern finance may well be making the tails fatter, says Daron Acemoglu, an economist at MIT. When you trade away all sorts of specific risk, in foreign exchange, interest rates and so forth, you make your portfolio seem safer. But you are in fact swapping everyday risk for the exceptional risk that the worst will happen and your insurer will fail—as AIG did. Even as the predictable centre of the distribution appears less risky, the unobserved tail risk has grown. Your traders and managers will look as if they are earning good returns on lower risk when part of the true risk is hidden. They will want to be paid for their skill when in fact their risk-weighted returns may have fallen.

Don Ludwig on the Black Swan

The applied mathematician and scholar of uncertainty Don Ludwig reflects on the financial crisis, resilience, and The Black Swan:

This is a sort of book review. By now you may have heard of The Black Swan: the impact of the highly inprobable by Nassim Nicholas Taleb published by Random House (2007).

Taleb is from Lebanon, but he prefers to be called a Levantine. He worked as a trader in currencies, and maybe also derivatives. He claims that nothing of importance in finance can be predicted, except its unpredictability. His book will undoubtedly attract attention for its claim of an inevitable financial collapse, like the one we are experiencing.

He writes on p. 225:
I spoke about globalization in Chapter 3; it is here, but it is not all for the good: it creates interlocking fragility, while reducing volatility and giving the appearance of stability. In other words, it creates devastating Black Swans [events that are extremely rare and important]. We have never lived before under the threat of a global collapse. Financial institutions have been merging into a smaller number of very large banks. Almost all banks are now interrelated. So the financial ecology is swelling into gigantic, incestuous, bureaucratic banks (often Gaussianized [assuming normal deviations] in their risk measurement) — when one falls, they all fall. [lengthy footnote here, which includes the statement that "Fannie Mae, when I look at their risks, seems to be sitting on a barrel of dynamite"] The increased concentration among banks seems to have the effect of making financial crisis less likely, but when they happen they are more global in scale and hit us very hard. We have moved from a diversified ecology of small banks with varied lending policies, to a more homogeneous framework of firms that all resemble one another. True, we have fewer failures, but when they occur … [no deletion here] I shiver at  the thought. I rephrase here: we will have fewer but more severe crises. The rarer the event, the less we know about its odds. It mean[s] that we know less and less about the possibility of a crisis.

Taleb goes on to mention the power blackout of 2003 as an example of what happens when things are tied too closely together.  Taleb points out that all the experts use Gaussian assumptions for risk analysis, which delivers precisely the wrong answer. Hence I think that it is extremely likely that the favored solution to the world financial crisis will be to tie the financial system even more tightly together, thus ensuring an even bigger collapse next time. It seems to be happening already. There is no sign that Obama has twigged to the hazards of greater financial integration. There is no sign that the experts can learn from collapses: they don’t seem to have learned from past collapses, as Taleb points out.

I think we can learn from Taleb: he writes very forcefully, but exaggerates his points too much. It may be that if we confine ourselves to financial situations, then his statements are valid, even though they are extreme. Taleb seems to have been treated very nastily by the financial establishment: Scholes, Merton & Co. He seems to be both hurt and angry. Perhaps this causes his arrogance as well. I had to grit my teeth to get through to the later chapters, which have most of the substance.

Taleb offers some financial advice:
1. Above all try to protect yourself from the big drops that are coming (have already come). This implies investing a very high percentage in lower risk securities such as government bonds.

2. Try to participate in the big booms that are also sure to come. Taleb advises spreading some stuff in venture capital. In view of the behavior of the Vancouver stock exchange, I should think that it would be necessary to try to avoid scams. See David Baines in the Vancouver Sun for details (e.g.).

What has this to do with ecology?

Buzz Holling has been talking for years about “surprise”, which is just another name for Black Swans. Anyone who has ever looked at ecological data knows that deviations are not Gaussian. Of course, if we drop the Gaussian or some similar assumption, we lose most of statistics, and we lose all of “risk analysis”. So we lose just about all theory. Experts can’t function without theory, so they make unrealistic assumptions, and come up with the wrong answers in Black Swan situations.

Since Black Swans are rare, ordinary experience doesn’t show any, and the experts are confirmed in their misleading assumptions, until the next time.

We can use analogies instead of theory. I recall the raft analogy we used years ago to illustrate resilience: in order to survive on rough seas, we use loose coupling rather than strong coupling. Likewise, we guard against overconfidence: another of Buzz’ favorite themes. Managing for resilience involves guarding against collapses, even though they might be rare: it implies a precautionary principle. In light of the recent financial collapse, this latter point might finally be accepted for ecological management.