Can You Plan for a Black Swan?

By Michael Finke

November 30, 2015 at 07:00 PM

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In the July 20, 2015 issue of The New Yorker magazine, Kathryn Schulz laid out evidence that the Pacific Northwest United States has experienced a series of 41 devastating earthquakes that have occurred with surprisingly regularity over the past 10,000 years. That's roughly one every 243 years. The last one hit in 1700, meaning that we're past due for an earthquake on the so-called Cascadia subduction zone. Such a quake will bring commerce essentially to a halt in cities including Seattle and Portland.

Like many rare and important events, a devastating earthquake is a possibility someone has discussed. If the earthquake occurs next year, many will point to Schulz's article and other research to say that the event is not, in hindsight, a surprise. And if the earthquake hits, what impact would this have on the U.S. economy? The costs of rebuilding would surely be in the trillions of dollars. Where would the money come from when the government debt has grown to over 100% of gross domestic product? What would happen to bond prices if other countries started to lose confidence in our ability to pay back our debt?

Is it beyond the realm of possibility that the United States could go bankrupt as a result of a black swan?

Nassim Nicholas Taleb's book "The Black Swan" spent 36 weeks as a surprising best seller in 2007. The timing of its publication was impeccable, since Taleb argued in the book that traditional financial models that promised an ability to better predict and control financial risk were flawed. These models created an illusion of technical sophistication, but relied too much on observable historical data and not enough on the unseen, rare and dramatic events that could blow up the models and change the world.

Trading on Extremes

To academic statisticians, the argument that Taleb makes is not a new one. In a distribution of possible random events, there are always going to be observations that fall at the tails. These rare and significant events are built into conventional statistics in the sense that we know that big and nasty things can happen, but they are highly unlikely.

Financial economists have long been aware that financial asset returns exhibit extreme events. Stock returns exhibit a larger number of outliers than a normal distribution would predict. This is what's known as "fat tails." When we look at historical international asset return data, we see evidence of a larger than expected number of extreme return events. In other words, there are more big positive and negative returns than we would expect. Financial economists can even build these fat tails into their models to account for the possibility of extreme events.

That didn't stop Universa Investments, a hedge fund where Taleb serves as principal/senior scientific advisor, from earning over $1 billion this summer by betting that the market underestimated the probability of an extreme correction. In 2008, Universa doubled (instead of halving) its investors' money during the financial crisis. The same financial crisis that was arguably caused by mathematical modelers at financial institutions who underestimated what would happen to asset prices when their employers accepted risks that seemed acceptable until the market fell apart.

The market anomaly that Universa exploits is the tendency to misprice options that pay out when markets crash. Put options give investors the right to sell shares at a given price. If you believe that extreme negative returns happen more frequently than the market expects, then you can profit from buying put options when the market sees smooth sailing in the future. When a hurricane comes out of nowhere, traders will look for any safe port that provides insurance against a crash in asset values. Enter the hedge fund that's been stockpiling put options.

An easy way to see how the market feels about the likelihood of an extreme event is to look at the pricing of put and call options on the market. The VIX index, created in 1993 by the Chicago Board Options Exchange (CBOE), calculates how the market is pricing options that expire in a 30 day time period. When prices are high, the market expects a lot of volatility. One can simply back out the expected volatility from the prices of the options. Higher prices mean there's a lot of uncertainty or anxiety about the market.

A look at historical VIX reveals that the market seems to do a really terrible job of predicting when stock prices are going to go crazy. When the ocean is calm, people forget that risk exists. When the wind starts picking up, people start to get worried. This is a bit of a mystery, because the chance of a storm always exists and so the pricing of risk should always reflect this possibility. One could simply buy up options when the market isn't worried very much about risk and wait for the storms to come. They always do.

Black Swan Blind

The Goodfellow Rebecca Ingrams Pearson brokerage in England has reportedly sold over 30,000 insurance policies that will pay just over $150,000 to policyholders who are able to provide evidence that they were abducted by aliens. They get double if they became impregnated during the abduction (even men, because — who knows?).

It's tough to estimate the likelihood of alien abduction because our data set on past abductions is limited. Those of us who build models that project how financial strategies will pan out in the future rely on data from the past. Why? Because that's all we've got. We can't project things in the future that haven't happened in the past.

This is where Taleb takes up his critique of conventional statistics. Anyone living in Seaside, Oregon, will rely on past experience to judge the risk of building a retirement home in the coastal town. Has there been an earthquake or a tsunami in the last 100 years? No. In fact, since recorded history (of European Americans at least), the Oregon coast wouldn't seem like a particularly risky place to live.

Yet that doesn't prevent an astute observer from looking beyond recent history to imagine potential future risks. This is one of the most important points of the black swan concept. Taleb doesn't say that we should all insure ourselves against alien abduction because the risk is a remote possibility. He's saying that extreme events will occur with some regularity, they will have a big impact on our life, and they're often hidden in plain sight.

In hindsight, many dramatic events make sense. But few protected themselves against the event. It's not hard to imagine a scenario in which it might be nice to have locks on cockpit doors of an airplane, and after 9/11 the risk seemed obvious. The fearful pessimist continually crying wolf over all the potential disasters is always ignored because we tend to get lulled into believing that tomorrow will look like today and most wildly pessimistic projections are wrong.

When the disasters inevitably occur, instead of waking us up to the power of extreme events, we tend to create a narrative in which we believe the risk was perfectly obvious in retrospect. In a famous academic study from the 1970s, participants were asked how likely Richard Nixon's visit to China was to yield various outcomes. After the visit, the same participants were asked to recall the probabilities they had placed on each of the outcomes. Of course, they recalled that they had placed a much higher likelihood on the outcome that actually happened.

Think of how often we look back and say "I knew that was going to happen." In reality, we probably didn't or we could have either prevented or profited from a lot of bad events. Hindsight bias gives us the confidence to believe that we can project all the negative events that are going to occur in the future. This also gives us the misplaced confidence to ignore the doomsayers in the present (since of course our ability to project the future is better than theirs).

One of my favorite examples is of a spirited debate at a Federal Reserve conference in 2005 between the esteemed financial economists Larry Summers and Raghuram Rajan. Presenting a paper titled "Has Financial Development Made the World Riskier?" Rajan convincingly laid out the dangers posed by the increasing ability of financial intermediaries to accept risk for a price.

Since shareholders had limited liability and intermediary managers could profit personally from accepting ever greater risk on behalf of institutions, intermediaries might take on more risk than the institutions could manage — posing danger to global markets. "Not only can these intermediaries accentuate real fluctuations," noted Rajan in the paper, "they can also leave themselves exposed to certain small probability risks that their own collective behavior makes more likely." He actually warned of a "catastrophic meltdown" of asset prices.

After the presentation, Summers criticized Rajan for holding a "slightly Luddite" view of financial derivatives and dismissed the need for alarm or additional regulation. Of course, the financial crisis caused a catastrophic meltdown of world markets that led to far more additional market regulation than Rajan recommended.

Did Summers recognize his own unwillingness to acknowledge a reality that didn't jibe with his personal beliefs? In a 2015 editorial, Summers warned that "policymakers who ignore adverse market signals because they are inconsistent with their preconceptions risk serious error. This is one of the most important lessons of the onset of the financial crisis in 2008." A fair point to make in hindsight.

Advisory Implications

When we create an optimal investment portfolio or project a safe withdrawal rate from retirement savings, we often rely on historical data to estimate how much risk a client will bear. Using historical data on asset returns from the U.S. is a bit like estimating earthquake risk in Oregon based on seismic activity from the last 100 years.

The risk of using a small sample to predict the future is that we often don't have enough observations to recognize how bad these tail observations can be. One of my favorite new data sets on asset returns was collected by Elroy Dimson, Paul Marsh and Mike Staunton (available through Morningstar) that includes 115 years of asset return data from 20 different countries. It's hard to dispute that Russian, Japanese, and German investors have seen some black swans over the 20th century.

In our own analyses using international data, we come up with a much less sanguine view of the safety of strategies that involve taking greater investment risk. It's good to remember that risk is real, and if it wasn't real we wouldn't get rewarded for taking it.

Economist Zvi Bodie has become notorious for his frequent admonishments of financial advisors who encourage clients to take greater risks in order to meet goals that would otherwise be out of reach using safe assets. In financial markets, risk should be transferred from those who can't cut back on spending to those who can. Bodie thinks that most retirees don't look like the kind of folks who should bear the risk of a market crash or runaway inflation.

Should we be constantly on guard against the possibility of a market crash? Should advisors be encouraging clients to hold less risk or even to consider entering the market for financial derivatives and hedge funds that protect against tail risk?

Not all statisticians are on board with the notion that black swans represent the greatest source of danger to investors. According to Berkeley statistics professor David Aldous, many of the most important social changes in the U.S. didn't come about after an extreme event. He points out that our cognitive biases will often place too much importance on extreme events while ignoring gradual changes that may be far more important.

Aldous asks us to think about all the changes that have gradually occurred in the U.S. over the last 50 years. What if you had gone to sleep in 1965 and awakened in 2015 with a supercomputer in your hands and a black president? Each was the result of gradual changes in technology and racial attitudes that in sum had greater effect than 9/11 or the financial crisis.

Taleb terms a world riven by significant shocks as "Extremistan," and warns that statisticians too often perceive "Mediocristan," a world governed by inertia.

Mediocristan possesses its own dangers. One significant risk these days is the gradual decline in real asset returns. Throughout the world, real returns on safe government bonds are hovering near zero. Stock prices are 70% above their historical average. The gradual shifts in asset returns that have been around for well over a decade may have an even greater impact on clients' ability to meet future goals than would a black swan like the financial crisis.

What will the future hold? Taleb's fundamental message is to remain wary and informed. Don't place too much faith in the recent past. Don't get complacent when markets are calm. Above all, prepare for the possibility that the future is going to be a lot different than you expect. And if you live in Kansas City, you might want to hold off on that move to Portland.

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