Tag Archives: black swans

The VIX is too low!

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September 30, 2017 —   During most of this year, the VIX — the Volatility Index on The Chicago Board Options Exchange — has been at the lowest levels of the last ten years.  It recently dipped below 9, even lower than March 2007, just before the sub-prime mortgage crisis. It looks as though, once again, investors do not sufficiently appreciate how risky the world is today.

Known colloquially as the “fear index,” the VIX measures financial markets’ sensitivity to uncertainty, in the form of the perceived probability of large changes in the stock market.  It is inferred from the prices of option on the stock exchange (which pay off only when stock prices rise or fall a lot).   The low VIX in 2017 signals that we are in another “risk on” environment, when investors move out of treasury bills and other safe haven assets and instead “reach for yield” by moving into riskier assets like stocks, corporate bonds, real estate, and carry-trade currencies.

Figure 1: The VIX is at its lowest since 2007


One need not rely exclusively on the VIX to see that the markets are treating the current period more as a risk-on opportunity than risk-off.  The returns on safe-haven assets were generally lower than the returns among risk-on assets in the first half of the year.  On the one hand, the Swiss franc depreciated.  On the other hand, the Australian dollar and Chinese yuan appreciated.  And the stock market has hit record highs.

True risk is currently high

Why do I presume to second-guess the judgment of the VIX that true risk is low?   One can think of an unusually long list of major possible risks. Each of them individually may have a low probability of happening in a given month, but cumulatively they imply a worrisome probability that at least one will happen sometime over the next few years:

* Bursting of stock market bubble.   Major stock market indices hit new record highs this month (September 12), both in the United States and worldwide.   Equity prices are even elevated relative to such benchmarks as earnings or dividends.  Robert Shiller’s  Cyclically Adjusted Price Earnings ratio is now above 30.  The only times it has been this high were the peaks of 1929 and 2000, both of which were followed by stock market crashes.

Figure 2: Shiller’s adjusted P/E shows stocks at their 3rd-highest valuations since 1880.

* Bursting of bond market bubble.  Alan Greenspan has suggested recently that the bond market is even more overvalued (by “irrational exuberance”) than the stock market.   After all, yields on corporate or government bonds were on a downward trend from 1981 to 2016 and the market has grown accustomed to it.  But, of course, interest rates can’t go much lower and it is to be expected that they will eventually rise.

* What might be the catalyst to precipitate a crash in the stock market or bond market? One possible trigger could be an increase in inflation, causing an anticipation that the Fed will raise interest rates more aggressively than previously thought. The ECB and other major central banks also appear to be entering a tightening cycle.

* Geopolitical risks have rarely been higher, and faith in the stabilizing influence of America’s global leadership has rarely been lower.  The gravest risk lies in relations with North Korea, which Trump’s response has been exceedingly erratic.  But there are also substantial risks in the Mideast and elsewhere.  For example Trump threatens to abrogate the agreement with the Iranians that is keeping them from building nuclear weapons.

* In many policy areas it is hard to predict what Trump will say or do next, but easy to predict that it will be something unprecedented.  So far, the ill effects on the ground have been limited, in large part because most of the wild swings in rhetoric have not translated into corresponding legislation.  (If he really had stuck with his decision to kick 800,000 young DACA workers and students out of the country it could have caused a recession.)  But this is a time of policy uncertainty if there ever was one.

* US Congressional showdowns over the debt ceiling and government shutdown were successfully avoided in September, but only by kicking the can down the road to the end of the year, when the stakes could well be higher and the stalemate worse.

* A constitutional crisis could arise, if for example Special Counsel Robert Mueller were to find that contact between the Trump campaign and the Russian government was illegal.

Black swans are not unforecastable

The current risk-on situation is reminiscent of 2006 and early 2007, the last time the VIX was so low. Then too it wasn’t hard to draw up a list of possible sources of crises.  One of the obvious risks on the list was a fall in housing prices in the US and UK, given that they were at record highs and were also very high relative to benchmarks such as rent.  And yet the markets acted as if risk was low, driving the VIX and US treasury bill rates down, and stocks, junk bonds, and EM securities up.

When the housing market indeed crashed, it was declared an event that lay outside any standard probability distribution that could have been estimated from past data, supposedly an example of what was variously declared to be Knightian uncertainty, radical uncertainty, unknown unknowns, fat tails, or black swans.  After all, “housing prices had never fallen in nominal terms,” by which was meant they had not fallen in the US in the last 70 years.  But they had fallen in Japan in the 1990s and in the US in the 1930s.  This was not Knightian uncertainty, but classical uncertainty with the data set unnecessarily limited to a few decades of purely domestic data.

In fact the “black swan” analogy fits better than those who use the term realize.  Nineteenth-century British philosophers cited black swans as the quintessential example of something whose existence could not be inferred by inductive reasoning from observed data.  But that was because they did not consider data from enough countries or centuries.  (The black swan is an Australian species that in fact had been identified by ornithologists in the 18th century.)  If I had my way, “black swan” would be used only to denote a tail-event that could have been assigned a positive probability ex ante, by any statistician who took the care to cast the data net widely enough, but that is declared “unpredictable” ex post by those who did not have a sufficiently broad perspective to do so.

The risk-on risk-off cycle

Why do investors periodically under-estimate risk?  There are specific mechanisms that capture how market analysts fail to cast the net widely enough.  The formulas for pricing options require a statistical estimate of the variance.  The formula for pricing mortgage-backed securities requires a statistical estimate of the frequency distribution of defaults.   In practice, analysts estimate these parameters by plugging in the last few years of data, instead of going back to previous decades, say the 1930s, or looking at other countries, say Japan.  More generally, there is a cycle described by Minsky whereby a period of low volatility lulls investors into a false sense of security which in turn leads them to become over-leveraged, leading ultimately to the crash.

Perhaps investors will re-evaluate the risks in the current environment, and the VIX will adjust.  If history is a guide, this will not happen until the negative shock – whatever it is – actually hits and securities markets fall from their heights.

[A shorter version of this post appeared at Project Syndicate.  Comments can be posted there or at Econbrowser.]

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Black Swans of August

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       Throughout history, big economic and political shocks have often occurred in August, when leaders had gone on vacation in the belief that world affairs were quiet.   Examples of geopolitical jolts that came in August include the outbreak of World War I, the Nazi-Soviet pact of 1939 and the Berlin Wall in 1961.  Subsequent examples of economic and other surprises in August have included the Nixon shock of 1971 (when the American president enacted wage-price controls, took the dollar off gold, and imposed trade controls), 1982 eruption in Mexico of the international debt crisis, Iraq’s invasion of Kuwait in 1990, the 1991 Soviet coup, 1992 crisis in the European Exchange Rate Mechanism, Hurricane Katrina in 2005, and US subprime mortgage crisis of 2007.   Many of these shocks constituted events that had previously not even appeared on most radar screens. They were considered unthinkable. 

The phrase “black swans” has come to be used to mean a very unlikely event of this sort.  Managers of Long Term Capital Management in 1998 or of most major banks in 2008 have suggested that they could not be expected to have allowed for a financial collapse such as the one that followed the default of Russia or the one that followed the bursting of the US housing bubble, because it was a “7-standard deviation event,” that is, an event of inconceivably tiny probability…in the realm of the probability that two major meteors hit the earth at the same time.   This is nonsense.  If the statistical model says the probability of a financial crisis is that low, it is the model that is wrong.  This is like the case when “hundred-year floods” turn up every few years.

A bit more enlightened are people who talk about Knightian uncertainty or “unknown unknowns.” Ignorance with humility is better than ignorance without it.    A still better interpretation is that statistical distributions have “fat tails,” in technical terms.  But it would be nice to get beyond the Jurassic Park lesson (“don’t be surprised if things go wrong”), to be able to say intelligent things about what causes tail events. 

       What does “black swan” really mean?   In my view, it should refer to an event that is considered virtually impossible by those whose frame of reference is limited in time span and geographical area, but that is well within the probability distribution for those whose data set includes other countries besides their own and other decades or centuries. 

      Consider five examples of mistakes made by those whose memory did not extend beyond a few years or decades of personal experience in a small number of countries.

1. “All swans are white.”  The origin of the black swan metaphor was the belief that all swans were white, a conclusion that might have been reached by a 19th century Englishman based on a lifetime of personal observation and David Hume’s principle of induction.   But ornithologists already knew that there in fact existed black swans in Australia, having discovered them in 1697.  A 19th-century Englishman encountering a black swan for the first time might have considered it an event of unthinkably low probability, even though the relevant information to the contrary had already been available in ornithology books.  It seems a waste of an excellent metaphor to use the term just to mean a highly unexpected event.  A better use of “black swan” would be to mean an event that would not have been quite so unexpected ex ante if forecasters had cast their data net over a broader set of countries and a longer time perspective.

 2. “Terrorists don’t blow up big office buildings.”   Before September 11, 2001, some terrorist experts warned that foreign terrorists might try to blow up tall American office buildings.   These warnings were not taken seriously by those in power at the time.   Many Americans did not know the history of terrorist events taking place in other countries and in other decades.  

 3. “Housing prices don’t fall.” Many Americans up to 2006 based their behavior on the assumption that nominal housing prices, even if they slowed down, would not fall.   After all, “they never had before,” which meant that they had not fallen in living memory in the United States.   They may not have been aware that housing prices had often fallen in other countries, and in the US before the 1940s.  Needless to say, many a decision would have been made very differently, whether by indebted homeowners or leveraged bank executives, if they had thought there was a non-negligible chance of an outright decline in prices.

 4. “Volatilities are low.”   During the years 2004-06, financial markets perceived market risk as very low.  This was most nakedly visible in the implicit volatilities in options prices such as the VIX.  But it was also manifest in junk bond spreads, sovereign spreads, and many other financial prices.  One of the reasons for this historic mis-pricing of risk is that traders were plugging into their Black-Scholes formulas estimates of variances that went back only a few years, or at most a few decades (the period of the late “Great Moderation”).  They should have gone back much farther – or better yet, formed judgments based on a more comprehensive assessment of what risks might lie in wait for the world economy.

 5. “Big banks don’t fail.”   “Governments of advanced countries don’t default.”   “European governments don’t default.”  Enough saidGreece‘s debt troubles, in particular, should not have caught anyone by surprise, least of all northern Europeans.   The perception was that euro countries were fundamentally different from emerging markets, that like Germany they were free of default risk.  Suddenly, in 2010, the Greek sovereign spread shot up, exceeding 800% by June. But even when the Greek crisis erupted, leaders in Brussels and Frankfurt seemed to view it as a black swan, instead of recognizing it as a close cousin of the Argentine crisis of ten years earlier, the Mexican crisis of 1994, and many others in history, including among European countries.

      My next blog post will list some of the shocks that, even though low-probability, have high enough probability that they should be treated as thinkable rather than unthinkable, they would have great consequences, and they therefore warrant some advance preparation.

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