Stock returns have a fat-tailed distribution; this means that large shocks are far more likely than one might expect. A few examples illustrate why this matters to investors. The stock price of Tesla Motors Inc. has an annualized volatility of 45% but has risen 1,250% in four years. Assuming log-normality, Tesla's four-year return would have had a probability of 10^43. Yet examples like this are not uncommon. Indeed, even the stock market crashes of 1929 and 1987 were to be expected, given the observed tail exponent. There is nothing surprising or abnormal about such events: as long as market returns continue to have a fat-tailed distribution, we will have crises such as these. As we'll explain below, market automation has made pricing far more precise than it was in human-dominated markets, but has not removed the root cause of fat tails in asset returns.
Why should the distribution of price shocks have a fat tail? The magnitude of crises like the Great Depression may be explained by unique circumstances in credit markets and monetary policy. But the tail exponent itself is a universal property that can be observed at all scales and in very different macroeconomic environments. If fat tails are a universal property of markets and make major crises inevitable, it seems worthwhile to try to understand what might cause them.
One explanation of huge price shocks can be found in an analogy between asset pricing and complex systems in physics. Trading models rely on historical data to estimate the parameters in models or earnings and/or relationships between asset prices. The same applies to analysts and portfolio managers: we all learn from historical analogues. Models interact with one another through the markets: a long-term model's buy decision will spawn orders that push the price up when executed; a mean reversion trading model may respond by deciding to supply liquidity. Trading models interact in the same way as species in an ecology: each model exploits a niche but also shapes the fitness landscape of other models. Capital allocation to one type of trading model increases its market impact and thereby creates opportunities for others. There are symbiotic species, parasites, prey and predators. Copying successful modeling ideas is an example of herding by machines. A successful herd increases aggregate leverage and a benign environment promotes specialization (better training, new drivers, etc.).
In good times, traders need to evolve models to compete in an increasingly crowded niche. But increased specialization and leverage make the ecology more vulnerable to a change in the environment, increasing the risk of a major crisis. Simple ecological models have demonstrated the emergence of self-organized criticality. In a world where quantitative models dominate asset pricing, the models in aggregate are the system and their designs and parameters are its degrees of freedom … prices themselves are merely gauges we can use to diagnose the condition of the patient. Fat-tailed event-size distributions are a generic property of self-organized critical systems. Are major financial crises in essence extinction events in the population dynamics of asset pricing models?
At first glance this seems a bit strange: how do asset pricing models, a technical aspect of the function of markets, lead to macroeconomic crises? Do financial markets solely reflect the state of the real world or can the endogenous dynamics of a market trigger events in the economy? Asset prices drive capital flows and economic activity, so erroneous pricing can lead to misallocation of capital, sometimes on a massive scale. The 2005 credit crisis provides a good illustrative example: a systematic underpricing of risk in asset-backed securities led to the aggressive marketing of mortgage-related products and an unsustainable growth of the aggregate debt burden of consumers. In an economy highly dependent on consumption, this could not end well.
This example illustrates how herding in model space causes systemic fragility (in this case, the failure of the Gaussian copula model), and also how it relates to criticality in the credit market. Another example is the occurrence of self-organized criticality in margin debt: the success of momentum strategies and low trailing volatility measures draws aggregate margin debt towards criticality.
Trading models are in effect asset pricing models — so criticality in this ecology translates to criticality in asset pricing. A mass extinction is not only an extermination of certain classes of trading models, more importantly it reflects on asset prices and through these on economic activity. This is clear in the case of market crashes, but price shocks occur at all scales and in both directions. In the example of Tesla's stock at the top of this article, there is little doubt that Tesla's stock price story has affected investment decisions at competing auto manufacturers and impacts economic activity in the real world.
In recent empirical and theoretical work we showed that the markets are performing a remarkably efficient task of solving two problems simultaneously for each market-traded asset. First, market-makers enforce the Martingale property: the current price is equal to the expected future price given what has been revealed in market data and other public sources. Second, portfolio managers feed the market private information from research and quant models. Portfolio managers receive information signals and create buy or sell orders. The aggregate response to a signal is called a “metaorder.” Our work shows that metaorder sizes are related to the value of the information in a precise manner: the implementation shortfall of a metaorder is equal to its permanent impact, a property we called “fair pricing.” In contrast, uninformed cash flow trades have no permanent impact, regardless of their size — this shows that markets are accurately measuring the information conveyed by metaorders. Markets coordinate the work of many computers and individuals by processing signals (orders) and producing outputs (prices) which in turn feed back into pricing models. Viewed as a single computing machine, the global markets have the architecture of a type of recursive neural network called a Jordan network. The aggregate computing capacity of this network makes it the most powerful computing machine ever created. At approximately 1 exaflop (10^18 operations per second), the global markets are processing information at a rate that is 100 times faster than the computing capacity of the human brain, as illustrated in Ray Kurzweil's popular book “The Singularity is Near.”
Fair pricing implies that the market is informative in the sense that metaorders correct any mispricing. Its information-processing capacity has vastly improved since 1929 and 1987. Unfortunately, this does not do away with criticality in the market ecology. The fair price is only the collective opinion of models that participate in price formation. If these models are using parameters that are no longer in line with reality, the fair price they will agree to could well be wrong by a wide margin. The global financial market may act as an extremely intelligent artificial organism accomplishing a difficult prediction task, far superior to the human brain in its ability to process statistical data. But as long as models are trained predominantly on recent historical data, this artificial organism will not be immune from the bias that impairs our own judgment. The forces of competition will continue to drive over-specialization and herding in the market ecology, asset returns will continue to exhibit fat tails and there will continue to be opportunities for those with a longer-term view.
Henri Waelbroeck, Ph.D., serves as global head of research at Portware LLC, a developer of trading execution software. He leads Portware's Alpha Vision research, applying machine learning to optimize execution management.
