Heresies of Finance — Benoit Mandelbrot on Volatile Volatility

The score of market misbehavior

Every lay person and their dog knows that financial markets are risky. One cannot be certain that an investment in stocks, housing, or commodities will yield an attractive rate of return. But in the Misbehavior of Markets, Benoit Mandelbrot says that markets are not just risky. They are “more risky than the standard theories imagine.”

The equity premium puzzle, for example, says that stocks have earned a larger than expected premium over the course of history. As Jeremey Siegel and Richard Thaler point out, the result is unusual because it is not easily explained by conventional economic models or theories of risk aversion. They suggest instead that some irrationality and biases are at hand.

Perhaps so. But “the [puzzle] also assumes wrongly that the bell curve is a realistic yardstick for measuring risk”, Mandelbrot writes. “Real prices gyrate much more wildly than the Gaussian standards assume. In this light, there is no puzzle to the equity premium.” Naturally, risk-averse investors seek compensation for the fat tails that modern finance ignores.

“Wall Street likes to keep score. When it comes to measuring risk, however, the industry’s toolkit is surprisingly bare. The two most common tools… [are] volatility, and beta, or the degree to which a stock’s price changes correlate to those of the market overall. Both numbers only have meaning if prices vary mildly by the bell curve, which they certainly do not.”
Benoit Mandelbrot and Richard Hudson. (2004). The Misbehavior of Markets. A Fractal View of Risk, Ruin, and Reward.

Embedded turbulence and phantom motions

Indeed, markets are sometimes turbulent because the macroeconomy and natural world on which it depends is forever in flux. Mandelbrot himself likes to imagine “the world economy [as] a chamber of mirrors.” Here, “each company relays, distorts, and attenuates the economic signals that flash around the globe.”

While attractors and equilibria may exist, “markets are inherently uncertain.” They are sensitive to initial conditions and human anticipation. Mandelbrot suggests that bubbles and crashes are not outliers but embedded features of our system. Rallies and panics come and go. Hyman Minksy presents a similar view in his financial instability hypothesis. He describes the market as a system that transitions between stable, speculative, and Ponzi-like regimes.

Volatile volatility and uncertain uncertainty

Financial markets are doubly deceptive because people confuse streaks for order and stability for safety. We should remember that “even the record of a Brownian motion—accumulation of a coin-toss game—can appear deliberate and ordered”, writes Mandelbrot.

One line of defense against statistical illusions involves looking for invariances, asymmetries and concentrations. Mandelbrot notes, for example, that a “study of tornado damage in Texas, Louisiana, and Mississippi found [that] 90 percent of the claims came from just 5 percent of the insured land area.” In finance, volatility clusters too. That is, “large price changes tend to be followed by more large changes”, while “small changes tend to be followed by more small changes.” George Soros experienced this firsthand during the subprime meltdown. As Soros recounts in a 2009 lecture, while he had anticipated the crash, he had underestimated the change in volatility and “took on positions that were too big to withstand the swings.” He “learned the hard way that the range of uncertainty is also uncertain.”

“Of course, you cannot predict anything with precision. Forecasting volatility is like forecasting the weather. You can measure the intensity and path of a hurricane, and you can calculate the odds of its landing; but… you cannot predict with confidence exactly where it will land and how much damage it will do.”
Benoit Mandelbrot and Richard Hudson. (2004). The Misbehavior of Markets. A Fractal View of Risk, Ruin, and Reward.

History, memory, and path dependency

Changes in prices, likewise, do not follow a random walk. Variations are not independently and identically distributed as is commonly assumed. Price changes can exhibit inertia and memory, both in the short and long-term, Mandelbroit argues.

Put another way, when it comes to price determination, it is not enough to say that “all that matters is today’s news and the expectation of tomorrow’s news.” What is gained and lost in the culture and memories of the collective affects how people perceive, believe, and behave. And this is difficult to describe without reference to economic, financial, and social history. Economic theories that ignore history and path dependencies are therefore partially deficient.

“In the 1960s, some old-timers on Wall Street—the men who remembered the trauma of the 1929 Crash and the Great Depression—gave me a warning: “When we fade from this business, something will be lost. That is the memory of 1929.” Because of that personal recollection, they said, they acted with more caution than they otherwise might. Collectively, their generation provided an in-built brake on the wildest forms of speculation.”
Benoit Mandelbrot and Richard Hudson. (2004). The Misbehavior of Markets. A Fractal View of Risk, Ruin, and Reward.

Shipbuilders and the Hippocratic Oath

Each of these heresies have practical consequences. For one, options pricing and value-at-risk models that treat risk as a static, bell-curve may misperceive reality. Likewise, financial institutions that operate as if disasters are normally and independently spread may find themselves under-protected and overexposed when clusters of fat-tailed calamities arrive.

If you want to build a high enough dam, it is “not just the size of the floods” that matters, “but also their precise sequence”, Mandelbrot reminds. “A bank that weathers one crisis may not survive a second or a third.” One can only imagine what might be if finance was more akin to medicine, aviation and shipbuilding than to the modern-day peddler on Wall Street.

“Pragmatism is needed in financial theory. It is the Hippocratic Oath to “do no harm.” In finance, I believe the conventional models and their more recent “fixes” violate that oath. They are not merely wrong; they are dangerously wrong. They are like a shipbuilder who assumes that gales are rare and hurricanes myth; so he builds his vessel for speed, capacity, and comfort—giving little thought to stability and strength. To launch such a ship across the ocean in typhoon season is to do serious harm. Like the weather, markets are turbulent. We must learn to recognize that, and better cope”.
Benoit Mandelbrot and Richard Hudson. (2004). The Misbehavior of Markets. A Fractal View of Risk, Ruin, and Reward.

The value of value

Finally, Mandelbrot adds that “the idea of ‘value’ has limited value” in finance. While he does not deny the existence of intrinsic value, he says its “usefulness is vastly overrated” in practice given the wild and unpredictable nature of financial markets.

Fundamental analysts believe, by contrast, that the economics of some businesses are predictable. They expect prices to move towards their fuzzy estimate of value. This assumes, of course, that their thesis is right, and that the invisible hand, while imperfect, works reasonably well over the long run.

But if you agree with Mandelbrot’s assessment, then legions of analysts are perhaps speculating about things they cannot really know. He suggests instead that “the price mover in a financial market is not value or price, but price differences; not averaging, but arbitraging.” The latter, after all, does not rely on arbitrary estimates of intrinsic value.

However, as Andrei Shleifer reminds, real world arbitrage can be limited too. For starters, close substitutes may not always exist. What’s more, during a mass panic, investors may withdraw funds just when arbitrageurs need to be active. And if prices and financing move unfavorably in tandem for long enough, it can put even the best traders and investors underwater.

I’d argue then that the real mover of financial markets is not arbitrage per se, but the health of the real economy, quality of underlying investments, and the expectations of the collective. Price dynamics in turn gyrate around this invisible attractor that is constantly evolving. And it is amplified or dissipated in part by feedback mechanisms like the confidence multiplier and credit cycle.

The heresies of finance

Today, Mandelbrot’s “heresies of finance” are not all that controversial. The deficiencies of modern finance are clear as day, and the financial system is more unpredictable than industry cares to admit. In the end, we must remember that “there is something in the human condition that abhors uncertainty, unevenness, unpredictability”, Mandelbrot says. When it comes to finance, people will continue to pursue all sorts of beliefs and mental maps. No matter how outlandish or spurious they may seem, “people like the comfort of such thinking.” As George Akerlof and Robert Shiller write in Animal Spirits: “Capitalism fills the supermarkets with thousands of items that meet our fancy. But if our fancy is for snake oil, it will produce that too.”

Sources and further reading

Mandelbrot, Benoit., and Hudson, Richard. (2004). The Misbehavior of Markets. A Fractal View of Risk, Ruin, and Reward.
Shleifer, Andrei. (2000). Inefficient Markets: An Introduction to Behavioral Finance.
Soros, George. (2009). Financial Markets. The Soros Lecture at the Central European University. Open Society Foundations.
Soros, George. (2009). General Theory of Reflexivity. The Soros Lectures at the Central European University. Open Society Foundations.
Akerlof, George., & Shiller, Robert. (2009). Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism.
Bernanke, Ben., Paulson, Henry., & Geithner, Timothy. (2019). Firefighting: The Financial Crisis and Its Lessons.

Heresies of Finance — Benoit Mandelbrot on Volatile Volatility and Valueless Value