Tandon in the Media

How To Protect Investments From Cataclysmic 'Fat Tails'

"And get the bits together, the fat tail, every good part." Ezekiel 24:4

If you traveled back in time thousands of years to tell Abraham, Moses or Ezekiel that you had some fat tails, they would have been delighted. In ancient times, the fat tails of certain Middle Eastern sheep were considered a delicacy. Today, they're more often associated with investment cataclysms.

Simply put, a financial fat tail describes a rare and extreme event. The term is derived from the inverted U-shaped bell curve that statisticians draw to describe the probability of events happening. Near the middle of such diagrams are "thin tail" events that happen all the time. As you move toward the edges, events become increasingly unlikely but can be highly significant on the rare occasions when they do occur.

Fat tails have been in the spotlight recently because we've been living inside of one--the global financial crisis--for the past two years. The current focus on financial fat tails aside, if you look at data going back to 1950, you may be surprised how full of fat tails, or non-normal events, stock market returns have been.

A prime example: Oct. 19, 1987, when the S&P 500 fell 20% in a single day. The average move up or down over the past half century is 0.65%. By that measure, Black Monday was what is referred to as a 25-sigma event, meaning it was 25 standard deviations away from the mean. If you were to plot a normal statistical distribution, a 25-sigma event would happen ... well ... never. It would be less likely than winning the Powerball a trillion times a day every day for a trillion trillion trillion lifetimes.

Even ignoring Black Monday, if returns were "normal," statisticians would expect the S&P 500 to move up or down by 3.5% or more only once every 10,000 years.

In contrast, we've experienced 118 such occurrences since 1950--nearly half of them in the past two years. Over the past two years, the average daily move up or down has been 1.3%. With that as a baseline, a normal distribution would see a fat-tailed move of 6.4% once every 100 years. In fact, it has already happened 11 times in the past two years. Therefore, we have not simply entered an era with a "new normal," when volatility will regularly stray outside the previous boundaries. We truly live in a non-normal world of fat tails. That raises the obvious question: What is causing the fat tails? Could we ourselves be behind them?

Is Investor Behavior Causing Fatter Tails?

One possible explanation for fatter tails is that business has simply become increasingly risky, and market jumps reflect that. Another is that our trading behavior itself is creating, or exacerbating, fat tails.

If the latter is the culprit, irrationality is the likely cause. Behavioral finance has unearthed numerous psychological biases that prompt investors to act in peculiar, and not particularly rational, ways. One of the strongest is loss aversion, or the tendency for potential losses to loom larger in investors' minds than do potential gains.

Would you bet on the toss of a coin if you stood to win $150 if it comes up heads and lose $100 if it's tails? People often reject such statistically sound bets because they feel that losing $100 will cause twice as much pain as winning $150 will bring in pleasure. Likewise, loss aversion prompts many investors to hold onto losers in the hope that they will bounce back and prevent them from suffering the anguish of realizing loss.

Mental accounting is another important psychological bias. It describes investors' tendency to divide wealth into separate buckets with no fungibility between them. We spend windfall gains differently than we do permanent increases in salary--even if they have the same effect on lifetime wealth. This tendency also explains why people with low-interest savings accounts often carry high-cost credit card debt.

Recent research suggests that in certain cases, investors subject to these two biases--loss aversion and mental accounting--will generate fat tails via their trading activity. In trying to avoid losses and compartmentalize investment decisions, they can exacerbate moves upward and down. For example, when earnings randomly rise, investors buy more; and when earnings fall, they sell. This is not very logical, but it is very human.

How to Plan for Fat Tails

Whatever the relative causes, it's important to put fat tails in perspective. If, for example, an investor faces 20 possible independent fat-tail events, each with a 5% probability, there's a 64% chance that at least one of them will occur.

What might these fat tails look like to an individual investor? How about a major stock market crash (we've had two in the past decade already), or the chance that you achieve your savings goals but then get hit with a half-million dollars of unforeseen medical expenses?

One "quick fix" is to continue using a normal distribution to predict fat tails but hike volatility assumptions. That is, you don't assume fat-tail events are going to be any more common than in the past, but you do assume that more normal events will be more disruptive. This is better than nothing, but even if you triple the average S&P 500 daily move to around 2%, you would expect to see an 8% up or down move only about once every 100 years. We have seen eight such moves in the past 25 years. The reason that this approach doesn't go far enough is that a higher standard deviation expands the middle of the probability distribution but fails to extend out far enough the tails of unlikely, but still possible, eventualities.

How Fat Tails Can Help You

One possible response to fat tails is to avoid them at all costs. The problem here is that the purpose of investing is not to limit your risk but to reap the rewards derived from investing patience and capital.

It's also important to keep in mind that not all fat tails are "left tail" events that put us in the red. There can be upside too. Winning the lottery would seem the fattest of right-tail events. Less spectacular, but still important, "plump" tail events can be meaningful as well for investors who stay the course through turbulent times. The stock crash last fall and following rally since March is a prime example.

In fact, risk and return have always been intertwined. Investors daring enough to be in micro-cap stocks at the nadir of the Great Depression earned a whopping 567% in the 12 months through June 1933. More recently, eight of the 10 biggest up days in the history of the S&P 500 all took place in the last year and a half. If you were not in the market on those days, you would have missed out on a 60% return.

The primary reason so many investors end up suffering through the bad days while missing the good ones: self-destructive behavior. We herd like sheep, bidding up stocks simply by buying them to levels beyond what is justified by fundamentals. Then when sentiment turns, the media, blogs and soccer field conversations accelerate the sell-off.

How to avoid buying high and selling low? First, it's important to view extreme events as more likely to occur than is the norm when planning your financial life. Those extreme events can take the form of merely expecting more fat tails, or of more qualitative assessment of life's risks, like losing one's health insurance the same year you need open-heart surgery. Rather than relying solely on historical risks and returns to plan, reflect on possible risks and returns as well.

Once you accept the notion that fat tails are likely to affect you personally, strategies for insulating your portfolio can range from sophisticated tools, like using options that protect against downturns, to the more mundane strategies, like saving more and incurring less debt--precisely the sort of practices that many individuals are belatedly adopting.

In this respect, loss aversion and mental accounting can actually help investors by encouraging them to over-save relative to rosy scenarios and maintain rainy day funds. This is a different sort of emotional engagement than chasing winners and shunning losers.

It is even possible to profit directly from the emotion-driven behavior of other market participants by "surfing the fat tails." Such momentum investing, however, requires catching waves early, riding them until they turn a profit and then getting out before the market turns--a feat few individuals have the discipline to pull off successfully.

Bottom line, investors can respond to fat tails by becoming more conservative, incorporating defensive strategies or embracing them outright. In all cases, facing up to fat tails should increase your odds of meeting your financial goals, with a lot less stress along the way.

Gregg S. Fisher, CFA, CFP, is president and chief investment officer of Gerstein Fisher. Philip Z. Maymin, Ph.D., is an assistant professor of finance and risk engineering at the Polytechnic Institute of New York University and the program director of alternative finance at the Gerstein Fisher Research Center for Finance and Risk Engineering at NYU-Poly.



More to Read