Fat Tails

From a WSJ column:

To be fair, the Orszags and Mr. Stiglitz acknowledged that “the extremely rare events located in the tail of a distribution are often quite difficult to analyze accurately.” Even so, they noted that White House budget gnomes had tested Fan and Fred’s capital against “the financial and economic conditions of the Great Depression.” The result: “[G]iven 1990 levels of capital, both Fannie Mae and Freddie Mac had sufficient capital to survive.”
The crucial point is that assessing systemic risk is difficult to impossible—and the likelihood of coming to a reliable consensus about it is even lower. Both Orszags and Mr. Stiglitz were officials in the Clinton Administration and saw the debates about Fan and Fred that the Clinton Treasury began in the late 1990s, only to get clobbered by the companies’ lobbying machine. Yet the three amigos still saw fit to put their names to a paper dismissing any risk of failure.
Why should anyone think that regulators—or economists—will predict the next systemic debacle any better? We only know better about the past. When the next problem erupts, as in 2002, smart people will be on both sides of the argument. And when large, systemically important companies are threatened with curbs on their business, they will pay Nobel laureates to write studies that explain away the dangers, and hire lobbyists to block any reform. A future Treasury secretary may also dismiss critics of a future Fannie Mae, or Goldman Sachs, as “ideologues,” as Hank Paulson did in 2007-2008.
The very existence of a systemic risk regulator, or council of regulators, will assist the largest and riskiest firms by creating an illusion of stability in a world made less stable by the implicit guarantee that this regulator would convey. It would be an accident waiting to happen, and one made inevitable by the institution created to prevent it.

Clever people rationalizing away risk destroyed Long Term Capital Management and countless other leveraged financial businesses. (As the column suggests, the incentives facing bureaucrats and politicians make this problem even more acute for government-managed enterprises.) The idea is generally: we’ve looked at all the angles and done simulations and the odds of a ruinous meltdown are so small we’re not going to worry about it. The problem is that the models used to estimate risk are sensitive to errors in the assumptions. That’s what “extremely rare events located in the tail of a distribution are often quite difficult to analyze accurately” means. If the distribution is statistically abnormal the tails of the distribution might be fatter than you think, in which case those extremely rare events might not be so rare. For businesses that deal with statistically normal returns distributions, such as casinos and life-insurance companies, the risks are relatively easy to determine. Those are well understood businesses with almost no risk of failure as long as they are well capitalized and well managed. By comparison, the risks for a highly leveraged negative-gamma financial scheme are much more difficult to pin down. Fannie Mae was essentially a colossal short-put position on the mortgage industry. Was the risk of ruin 1 in 1,000,000 or one in a hundred? Who knows. A cursory look at the history of financial debacles suggests that such events happen much more frequently than many models have predicted. A reasonable person with extensive private-sector financial experience as a trader or fund manager would know better than to bet the ranch on the accuracy of a model whose worst-case outcomes involve unknown probability of unbounded loss. More likely he would want to be on the other side of that trade. Yet Congress jumped right in and kept doubling down when it should have been cutting its losses, and is now repeating the error with the FHA. Orszag and Stiglitz apparently didn’t understand this back in the day. Do they understand it now?

When people like these are in business and miscalculate they go out of business. If they’re lucky they then get to go to work for someone who has a better understanding of risk than they did. But when they’re in government and miscalculate they may pay no penalty or even be promoted, and the risks they rationalize may be ignored until institutions fail. I don’t mean to single out Orszag and Stiglitz, who probably meant well and were not responsible for Fannie Mae (Congress was). But the public sector is full of such people, and as the government expands they become more influential and their mistakes become more costly.

8 thoughts on “Fat Tails”

  1. It boils down to the essential fact that predicting the future is darn hard to do!

    In the nuclear power industry we have an analogous task of predicting failures in nuclear power systems. We call our methods “probablistic risk assessment” or PRA. Fortunately, we have less to worry about in external interferences. We still try and quantify our risk of reactor core damage to meet government safety goals.

    However, the biggest use is in the identification of vulnerablities – where are the components or procedures that are risk “hot spots.” We can then focus our efforts on reducing the risks at those points.

    It doesn’t sound like these financial models are used for REDUCING actual risk so much as wishing it away.

  2. Jonathan, I couldn’t agree more with your post.

    And correct me if I am wrong, but I understand the moral of your story will be something like: “Everyone should exercise some reserve of pragmatism when working with financial models, especially when a Nobel Prize winner and any of his pupils are behind those models”.

    Apparently, Mr. Stiglitz has now become the new darling of the European left:


  3. Once again, it is about feelings. Black swans happen and failure is the punishment for not anticipating them. You don’t have to be right every time; just to realize you could be wrong. In her book, After the Fall, Nicole Gelinas points out that, unlike most other investment banks, Brown Brothers Harriman remained a partnership and has not suffered the catastrophic losses that took down Lehman and others. She suggests that they were using their own money and that was enough to induce caution. I expect their profits were less but they are still there.

  4. I love math and equations. Equations are a model that can guide thinking and eliminate ridiculous propositions. But, people believe the “Fallacy of the Equation”.

    In special situations, usually in physics, equations match reality to .01% . This gives equations and mathematical models a false aura of authoritiy when used elsewhwere.

    In almost all cases, statistics and equations are only a guide to further thought. For example, I could calculate the breaking strength of a car axle as a guide to design. I would never ride in that car until that axle was tested in all conceivable ways, and I would watch out for rust in the coming years. If equations were trustworthy, no product would ever be recalled. It is dangerous to think that “the equations are correct, it is reality that is wrong”.

    Equations only capture what you know, or think about at the time. I would never trust everything to a mathematical prediction. Buildings and bridges are well understood and have been built for centuries. Still, some fail, and all are built to be 2-3 times as strong as “necessary”. If engineers really trusted their equations, they would build much lighter and cheaper. They don’t want to kill people, so they far exceed what the equations say, and they build physical models to see what happens.

    It is laughable to put much trust in predictions based on complex models. The model is complex only because reality is even more complex. Mathematical models assume such things as smoothly-changing equilibrium, and known distributions. Reality changes abruptly, is never in equilibrium, and the statistical distribution is unknown and changing.

  5. When you can’t estimate odds you go with capabilities, i.e., you prepare for the worst case. That’s what police officers mean when they say that they assume everyone is armed. It’s one of the reasons why we invaded Iraq in 2003. In finance it means that you always spread off your risk, so that if your longs go to zero and your shorts go to infinity your maximum loss is capped at an amount that you can afford. If you can’t spread off your risk you liquidate your position when your loss hits whatever level you decided beforehand is your limit. If liquidation is difficult due to market conditions then you trade a smaller position. If despite these measures you are still unable to control your risk you don’t do the trade.

    Businesspeople tend to learn these and similar lessons about risk through hard experience. In this regard the fact that only a small fraction of our current cohort of high government officials has significant business experience is worrisome.

  6. Too many people think that the argument for a strictly limited government is only concerned with liberty vs tyranny, and then get all confused when dealing with various state functions that seem innocuous, even necessary, because “somebody has to do it”.

    Many of the state expansions that have repeatedly caused economic or social damage are, naturally, proposed in bills that are labelled as, and promised to be, helpful or protective or compassionate. Those who support them are lauded as being “concerned”, while opponents are described as uncaring or cruel.

    What you have described in this post is a good example of this phenomenon. Bills are passed and agencies set up to “protect the public interest” or “contain the greed of the cold-hearted capitalists”. Actions by the agency are often trumpeted in the media, crusading lawyers or scrupulous regulators going after the latest villians as identified by the conventional wisdom of the day.

    The recent financial collapse, which was actually a political collapse with economic consequences, as is usually the case, is a perfect example. The greedy Wall Street villians were quickly spotlighted, and the crusading political types who were determined to chastise them, like Barney Frank and Chris Dodd, were praised and often quoted. (Sarcasm definitely intended)

    Meanwhile, the years of public policy and political pressure, including numerous court cases by “advocacy” groups such as ACORN, demanding that loans be made to unqualified recipients was conveniently ignored. The incestuous relationships between various political and financial actors never seemed important enough for the front pages or network news, even when some of the high profile wheeler-dealers ended up in court or prison.

    The danger of state power is the anonimity it gives to the corrupt and abusive, and the lack of consequences that can be arranged if the right scapegoat can be found to take the fall.

    If you are the owner and manager of a drug store, and your pharmacy keeps giving out prescriptions that make people sick because they’re filled with the wrong medicine, you will soon be bankrupt and out of business, or worse.

    If you are the pol whose compassion has resulted in a string of well intentioned but utterly counter-productive acts of legislation, or one of the “in crowd” of experts who rotate between academia to business to government post, you can leave a trail of destruction behind you that would shame Bernie Madoff, and if you can convince enough people that it was someone else’s fault, you will still get re-elected or re-appointed the next time around.

    The choice between public vs private control is more than liberty vs tyranny, although that is always a factor to be considered, it is also between responsiblility and irresponsibility.

    In any organization, as it grows, it becomes more and more difficult to figure out who does what, and who’s responsible for this success or that failure. When that organization is the state, filled with obscure boards and arcane commissions, complex regulations and conflicting rules, faceless cadres and influential, well connected “appointees”, reality fades away, and all that’s left is the spin.

    The state should be limited and restricted because, as its authority and power grows, the ability of the citizenry to accurately assign responsibility for mistakes and mismanagement declines. In our society, in which the citizen is alleged to be the source of authority and final arbiter of important questions, the byzantine nature of the endlessly expanding state defeats any attempt to make informed judgements and rational decisions.

  7. This kind of thing happens particularly when the person who *initiates* an activity is completely distinct from the person who *executes* the activity, and, hence, person #1 can disclaim any failures as a result of poor execution by person #2.

    An example often occurs in business, where the decision to do a merger/acquisition is pushed by a Business Development person, whose resume is improved by the doing of large deals. After the deal closes, it is rare for the BD person to be given the primary role in actually making the merger/acquisition actually *work*. Thus, there is a systemic bias toward doing rather than not-doing of deals…what has been called “deal heat” or “the corporate mating instinct.”

    I agree that the problem is much worse in government: in business, absent government intervention, failures are self-limiting.

  8. “For businesses that deal with statistically normal returns distributions, such as casinos and life-insurance companies, the risks are relatively easy to determine.”

    Tableb, in the “Black Swan” tells the story of a Las Vegas casino that discovered its real risk. The casino’s star entertainment act was Siegfried and Roy, and then Roy’s tiger went tiger on him. The loss to the casino far exceeded any gaming loss.

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