Markets and Black Swans
I began studying complexity theory as a consequence of my involvement with Long-Term Capital Management, LTCM, the hedge fund that collapsed in 1998 after derivatives trading strategies went catastrophically wrong.
After the collapse and subsequent rescue, I chatted with one of the LTCM partners who ran the firm about what went wrong. I was familiar with markets and trading strategies, but I was not expert in the highly technical applied mathematics that the management committee used to devise its strategies.
The partner I was chatting with was a true quant with advanced degrees in mathematics. I asked him how all of our trading strategies could have lost money at the same time, despite the fact that they had been uncorrelated in the past. He shook his head and said, “What happened was just incredible. It was a seven-standard deviation event.”
In statistics, a standard deviation is symbolized by the Greek letter sigma. Even non-statisticians would understand that a seven-sigma event sounds rare. But, I wanted to know how rare. I consulted some technical sources and discovered that for a daily occurrence, a seven-sigma event would happen less than once every billion years, or less than five times in the history of the planet Earth!
I knew that my quant partner had the math right. But it was obvious to me his model must be wrong. Extreme events had occurred in markets in 1987, 1994 and now 1998. They happened every four years or so.
Any model that tried to explain an event, as something that happened every billion years could not possibly be the right model for understanding the dynamics of something that occurred every four years.
From this encounter, I set out on a ten-year odyssey to discover the proper analytic method for understanding risk in capital markets. I studied, physics, network theory, graph theory, complexity theory, applied mathematics and many other fields that connected in various ways to the actual workings of capital markets.
In time, I saw that capital markets were complex systems and that complexity theory, a branch of physics, was the best way to understand and manage risk and to foresee market collapses. I began to lecture and write on the topic including several papers that were published in technical journals. I built systems with partners that used complexity theory and related disciplines to identify geopolitical events in capital markets before those events were known to the public.
Finally I received invitations to teach and consult at some of the leading universities and laboratories involved in complexity theory including The Johns Hopkins University, Northwestern University, The Los Alamos National Laboratory, and the Applied Physics Laboratory.
In these venues, I continually promoted the idea of inter-disciplinary efforts to solve the deepest mysteries of capital markets. I knew that no one field had all the answers, but a combination of expertise from various fields might produce insights and methods that could advance the art of financial risk management.
I proposed that a team consisting of physicists, computer modelers, applied mathematicians, lawyers, economists, sociologists and others could refine the theoretical models that I and others had developed, and could suggest a program of empirical research and experimentation to validate the theory.
These proposals were greeted warmly by the scientists with whom I worked, but were rejected and ignored by the economists. Invariably top economists took the view that they had nothing to learn from physics and that the standard economic and finance models were a good explanation of securities prices and capital markets dynamics.
Whenever prominent economists were confronted with a “seven-sigma” market event they dismissed it as an “outlier” and tweaked their models slightly without ever recognizing the fact that their models didn’t work at all.
Physicists had a different problem. They wanted to collaborate on economic problems, but were not financial markets experts themselves. They had spent their careers learning theoretical physics and did not necessarily know more about capital markets than the everyday investor worried about her 401(k) plan.
I was an unusual participant in the field. Most of my collaborators were physicists trying to learn capital markets. I was a capital markets expert who had taken the time to learn physics. One of the team leaders at Los Alamos, an MIT-educated computer science engineer named David Izraelevitz, told me in 2009 that I was the only person he knew of with a deep working knowledge of finance and physics combined in a way that might unlock the mysteries of what caused financial markets to collapse.
I took this as a great compliment. I knew that a fully-developed and tested theory of financial complexity would take decades to create with contributions from many researchers, but I was gratified to know that I was making a contribution to the field with one foot in the physics lab and one foot planted firmly on Wall Street. My work on this project, and that of others, continues to this day.
I think it’s important to know that no two crises are ever exactly the same. But we can learn a lot from history, and there are some elements today that do resemble prior crises. Right now today, as we sit here in 2016, the damage of 2008 is still fresh in a lot of people’s minds. It was eight years ago but there’s nothing like the experience of being wiped out and a lot of people saw their 401(k)s erased.
It wasn’t just stock prices but real estate, housing, unemployment and students graduating with loans that were not being able to get jobs. There was a lot of trauma and distress.
That’s still clear in people’s minds, even though it was, as I say, eight years ago. But what’s going on right now, in my view, more closely resembles that 1997–1998 crisis than it does the one in 2007–2008.
Let’s skip over the dotcom bubble in 2000 because that was clearly a bubble with an associated market crash but not a severe recession. We had a mild recession around that time, and then of course that played into the volatility due to 9/11. It was painful if you were in some of those dotcom stocks, but that wasn’t a real global financial crisis of the kind we saw in 1998 and again in 2008.
What was interesting about that time was that the crisis had started over a year earlier — July 1997 in Thailand. It ended up in my lap at LTCM in September 1998 in Greenwich, Connecticut. That was fifteen months later and about halfway around the world.
How did a little problem that started in 1997 in Thailand end up in Greenwich, Connecticut fifteen months later as ground zero?
The answer is because of contagion. Distress in one area of financial markets spread to other seemingly unrelated areas of financial markets.
It’s also a good example of how crises take time to play out. I think that’s very important because with financial news, the Internet, the web, and Twitter, Instagram, Facebook, chat and email, there’s a tendency for people to focus on the instantaneous and ignore trends.
In fact, the mathematics of financial contagion are exactly like the mathematics of disease or virus contagion. That’s why they call it contagion. One resembles the other in terms of how it’s spread.
An equilibrium model like Fed uses in its economic forecasting basically says that the world runs like a clock. Every now and then, according to the model, there’s some perturbation, and the system gets knocked out of equilibrium. Then, all you do is you apply policy and push it back into equilibrium. It’s like winding up the clock again. That’s a shorthand way of describing what an equilibrium model is.
Unfortunately, that is not the way the world works. Complexity theory and complex dynamics tell us that a system can go into a critical state.
I’ve met any number of governors and senior staff at the Federal Reserve. They’re not dopes. A lot of people like to ridicule them and say they’re idiots. They’re not idiots, though. They’ve got the 160 IQs and the PhDs.
Every year, however, the Fed makes a one-year forward forecast. In 2009 they made a forecast for 2010. In 2010 they made a forecast for 2011 and so on. The Fed has been wrong seven years in a row by orders of magnitude.
I just laugh. How many years in a row can you be wrong and still have any credibility?
But they’re not dopes — they are really smart people. I don’t believe they’re evil geniuses trying to destroy the world. I think they’re dealing in good faith. If they’re so smart and they’re dealing in good faith, though, how can they be so wrong for so long?
The answer is they’ve got the wrong model. If you’ve got the wrong model you’re going to get the wrong result every single time. The Federal Reserve, policymakers, finance ministers and professors around the world use equilibrium models. But the world is a complex system.
What are examples of the complexity? Well, there are lots of them.
One of my favorites is what I call the avalanche and the snowflake. It’s a metaphor for the way the science actually works but I should be clear, they’re not just metaphors. The science, the mathematics and the dynamics are actually the same as those that exist in financial markets.
Imagine you’re on a mountainside. You can see a snowpack building up on the ridgeline while it continues snowing. You can tell just by looking at the scene that there’s danger of an avalanche. It’s windswept… it’s unstable… and if you’re an expert, you know it’s going to collapse and kill skiers and wipe out the village below.
You see a snowflake fall from the sky onto the snowpack. It disturbs a few other snowflakes that lay there. Then, the snow starts to spread… then it starts to slide… then it gains momentum until, finally, it comes loose and the whole mountain comes down and buries the village.
Question: Whom do you blame? Do you blame the snowflake, or do you blame the unstable pack of snow?
I say the snowflake’s irrelevant. If it wasn’t one snowflake that caused the avalanche, it could have been the one before or the one after or the one tomorrow.
The instability of the system as a whole was a problem. So when I think about the risks in the financial system, I don’t focus on the “snowflake” that will cause problems. The trigger doesn’t matter.
Once a chain reaction begins it expands exponentially, can “go critical” (as in an atomic bomb) and release enough energy to destroy a city. However, most neutrons do not start nuclear chain reactions just as most snowflakes do not start avalanches.
In the end, it’s not about the snowflakes or neutrons, it’s about the initial critical state conditions that allow the possibility of a chain reaction or avalanche. These can be hypothesized and observed at large scale but the exact moment the chain reaction begins cannot be observed. That’s because it happens at a minute scale relative to the system.
This is why some people refer to these snowflakes as “black swans”, because they are unexpected and come by surprise. But they’re actually not a surprise if you understand the system’s dynamics and can estimate the system scale.
It’s a metaphor but really the mathematics behind it are the same. Financial markets today are huge, unstable mountains of snow waiting to collapse. You see it in the gross notional value derivatives.
There are $700 trillion worth of swaps. These are derivatives off balance sheets, hidden liabilities in the banking system of the world. These numbers are not made up. Just go to the Bank of International Settlements (BIS) annual report and it’s right there in the footnote.
Well, how do you put $700 trillion into perspective? It’s ten times global GDP. Take all the goods and services in the entire world for an entire year. That’s about $70 trillion when you add it all up. Well, take ten times that and that’s how big the snow pile is.
That’s the avalanche that’s waiting to come down.
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