Fat Tail and the Bail Out 

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”  Mark Twain

Risk management is the difference between success and ruin in the financial markets.  As Nassim Taleb so succinctly stated, “risk is what can really hurt you.”  It is arguably the single most important consideration for any participant, from the single independent trader to the juggernaut of a Goldman Sachs in the financial markets.

But what is risk?  There are many discussions of what constitutes risk in the financial markets but not surprisingly, there is no one definition.  Typically, discussions of risk revolve around the concepts of Value at Risk (VAR), beta, delta, the capital asset pricing model (CAPM) and the Black-Scholes options pricing model (BSM).  All these ways of quantifying risk are based on inarguably faulty assumptions.  The recent credit crisis and mortgage meltdown is another example of how Wall Street’s methods of modeling market behavior and accounting for risk, are fundamentally flawed.

Do you know what a Gaussian Bell Curve is?  Most MBA types who go on to work at and eventually run investment banks do.  There are really only two things you need to know about a Gaussian Bell Curve.  A Gaussian Bell Curve assumes events occur in a normal distribution.  What this means is that in a Gaussian Bell Curve, if events or occurrences were plotted, they would occur in the largest numbers at or towards the very center of the bell curve.  All these events, plotted on a chart would take the shape of a bell curve, hence the name.  Events which occur less frequently would occur towards the edges of the curve.  The further the event was from the center of the bell curve, the more improbable it is to occur.  This is called a normal distribution.  The second thing one should know about the Gaussian Bell Curve is that it does not predict market events very well at all.  In fact, knowing what it is, you may disregard it completely.

Analysts at investment banks make models of reality with predictive capability.   It is true.  How one may ask, can you make a model of realty that is able to predict market movements and price, without having God-like prescience?  Do not be skeptical, it is not that difficult and it happens all the time-you can be an analyst at an investment bank. It is called modeling.  J. P. Morgan invented Risk Metrics in 1994 as a set of financial models that were to be used by investors to measure portfolio risk.  Risk Metrics like financial modeling in general, attempts to take a certain set of variables or causes and isolate them as being the very variables that account for change in financial markets.  This is a bit simplistic but nonetheless true.  Financial models seek to replicate financial reality much like economic models and models of human behavior that have become extremely popular in the social sciences writ large.

Humans do not like indeterminacy.  We do not like to make decisions or look back in hindsight and think we made decisions by tossing a coin.  On the contrary, we like to find reasons for why we made decisions and why events occurred.  We tend to think we can.  We have at times an irrational belief in the rational.  But as Pascal once stated, nothing is more rational than the abdication of reason itself.  The ability of social scientists or investment bankers to explain events through the actions of rational human actors appeals to our psyche.  It is appealing to think we can.

Models of the financial markets like models of the human behavior in the social sciences have serious limitations.  To start, they have to simplify reality.  One of the ways that modeling simplifies and in a sense, falsifies reality is by making assumptions about human beings, which are not true.  For example, modeling tends to assume that humans, whether in a marketplace or in a poker game are rational and that they act at all times in accordance with their best interests.  This is not borne out by reality.   Any cursory historical account of human behavior belies that humans act rationally.  Human beings are emotional actors as much as they are rational actors.

The supremacy of emotions to the human story is only matched by our social scientists willful neglect of them.  However, given a choice, time and again, we often act on our emotions and against our rational interests.  Our strongest emotions keep us awake at night, they cause us physical pain, they have helped our race to achieve beyond all expectation when at other times they have left us paralyzed.  We think wishfully when we rationally should not.  The markets are replete with examples of irrational exuberance, traders who act out of hope, fear and greed as much as they act out of a consistent rational interest in maximizing their profits.  Markets historically at tops and bottoms have betrayed the irrational mob mentally of the masses of its participants.

If humans were truly rational, we simply would not have addictive behaviors like gambling, drug addiction, drinking or any self-destructive behavior.  We may not even have much ill-health, skin cancer, road-rage, or obesity because knowing we should take care of ourselves, we would-this is rational.  We may never purchase luxury items or clothes.  We may not care so much about how our neighbors live because we would not feel envy, jealousy, sympathy or pity.  The pursuit of leisure and charitable activities may well be quite different.  So many of Tocqueville’s observations about American life would not hold water.

But in reality, half of our brains are devoted to pure emotion.  And this half has expressed itself as the stuff of life.  We cannot seem to choose our emotions one at a time either.  If we were, we would want to be able to love with being vulnerable to grief, to experience the wings of hope without putting ourselves in danger of experiencing disappointment or the failure of our hoped-for event.  As a race, we have spent most of our time acting on our emotions and being in their grip as is borne out in our history, our mythologies, culture, our wars and literature. It is in every sense human to be irrational or at least to experience emotion.  To argue that humans are rational actors is at a minimum to simplify things, but really it is not a valid assumption.

Modeling also suffers from faulty assumptions about the ability of human participants to gather, assimilate and react to information.  Most models are sensitive to information.  Information causes the rational actor in a model to act a certain way, presumably in a way that will maximize that actor’s interests.  In the real world, information is not perfect.  There is misinformation.  Rumors, false tips, erroneous analyst reports are example of misinformation.  Some information that is available to a rational actor is false information.  Even if we assumed that all the information available to market participants was correct and no false or misinformation was available, market participants would process and assimilate the information differently and at different rates.  One example of misinformation and information assimilated at different times is the discovery of a report in 2008 on the internet that United Airlines was facing bankruptcy.  This report was over a year old but it caused the price of the stock to drop by over 40% in a single day, before it was discovered that the report was old.  In the real world, individually and collectively, we have different intellectual and ideological frameworks, we also have different levels of intelligence, among other factors that allow us to reach very different conclusions when faced with the same information.  My neighbor may react to rising gasoline prices years faster than I would by immediately cutting down on his driving or purchasing a hybrid vehicle.  Market participants react to identical information at various rates.    One person may react quickly to too little information and another may wait much longer accumulating much more information.  Sometimes waiting to act while accumulating and digesting information is not a good thing like waiting to liquidate a losing position before your losses wipe you out when acting sooner would have allowed you to cut your loss without going broke.

Another problem with financial models is that they do not account for insider information.  One of the inherent conflicts in investment banks has been the Chinese wall that is supposed to separate the investment banking and sales functions of the investment house from the research and analysis side.  Some have argued that this Chinese wall did not always exist.  There is an inherent conflict between the need to sell the investment banking services of a bank to the same customer who is being covered by the bank’s analysts.  If the analysts were too harsh in their coverage, then the ability of the bank to sell its investment banking services may suffer.  What about the potentially insider information that the analysts obtained in covering a company and the danger that this information would travel across the room to the trading floor of the investment bank?  Another conflict of interest certainly, but it is also an example of a market participant having insider information or simply information that other market participants do not have, before they have it.

Another fallacy with financial modeling is that models are required to isolate a fixed amount of causal variables.  In other words, a financial model that was designed to predict the risk of an investment portfolio would be comprised of say twenty factors or variables, each of which or a certain number of which would affect a change in measure of risk to the investment portfolio.  What if in reality, it was one hundred or ten thousand different variables or things that would change the riskiness of the portfolio?

The financial models of investment bank analysts assign likelihood to the possibility of certain events occurring.  Financial models assume a normal distribution (a bell curve) of asset returns or risk.  The belief that most market events occur in a normal distribution is the single key assumption made by many financial models, including the capital asset pricing model (CAPM) and the Black-Scholes option pricing model (BSM) and VAR.  Using a normal distribution, events that diverge from the mean or center of the bell curve, by five or more standard deviations, known as a five-sigma event, are very rare and ten-sigma events are nearly impossible. However, the 1987 market crash represents a change of 22 standard deviations. The odds of such a 22 standard deviation event occurring are so low as to deemed impossible.

In the real financial markets, events considered nearly impossible by financial models assuming normal distributions of events, not only are possible, they are occurring frequently. There have been multiple fluctuations greater than five standard deviations in our most recent past.

Events that according to a Gaussian Bell Curve are supposed to occur only once every one hundred thousand years, if at all, are occurring in certain cases, several times in a decade.  Plotting out these events, like our current credit crisis, the market crashes of 1987 and 2000, Long-Term Capital Management, the collapse of Bear Stearns, the Savings and Loan Crisis, the crash of 1929, the collapse of Northern Rock, the Russian Debt crisis, the 1997 Asian financial crisis, the 1990 Japanese asset bubble crisis, the 1973 oil crisis and 1978 energy crisis, etc.  would lead to an unseemly looking bell curve-really it would hardly resemble a bell curve at all.

These impossibly unlikely events if plotted on chart would give an ordinarily symmetrical tidy looking Gaussian Bell Curve a very fat tail.  Hence improbable or impossible crisis like our present credit crisis are called fat tails.  A fat tail is an occurrence that is considered to be well outside the range of what is considered normal or possible.

Think of a fat tail happening in your own life as described by the writer Chevelle in Models and Agents as the occurrence of the following,

“It’s 10am, your rottweiler has just chewed your Italian leather boots, your wife has burnt your pancakes and your mistress is on the phone proclaiming that ‘it’s over because, really, you’re pretty lousy in bed.’ Oh yeah, and while you’re at it, your broker is leaving you a message that the stock market is crashing and you’ve lost a third of your savings. A bad hair day? No, my friend. You’re likely living in a fat tail!… It all began with what we call a probability distribution. Think of each day of your life as a dot under a bell-shaped curve: Most of the dots are concentrated around the middle, in the bulge of the bell: Days of medium pain and medium pleasure; boots are shiny, pancakes edible and mistress satisfied (at least that’s what you think!).”

Dramatic market events or fat tails do occur in a greater frequency than is possible assuming normal distributions suggesting distributions are not normal.  Since the 1998 Russian debt crisis, the global financial markets have experienced at least 10 fat tails, none of which were supposed to occur more than once every few billion years.

Our models of the financial markets cannot anticipate the occurrence of fat tails and according to our present models, they are statistically so unlikely to occur as to be deemed essentially impossible.  Where does this leave us?  Why are we using them at all?

It may arguably be simple arrogance to believe a mathematical model can predict future history.  Or as John Maynard Keynes wrote in his concluding paragraph on General Theory,

“Too large a proportion of mathematical economics are a mere concoction, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.”

Alternatively, the answer may be that the financial services industry is full of at least two generations of analysts, investment bankers and statisticians, who have been indoctrinated through college and their MBA programs to believe in the bell curve and normal distributions.

Do we disregard the occurrence of catastrophic market events like the many we have experienced over the past twenty years alone, or should we critically examine the way we model risk and financial behavior?  Perhaps the latter.*

R. Tamara de Silva