Now, let’s change the game. Heads, you lose £200. Tails, you lose nothing. Or you can skip the toss and pay £100 right now. What’s your move?
Suddenly, most people want to gamble. They’d rather risk losing £200 than definitely lose £100.
Logically, thse choices should be mirror images. But they’re not. This was a research experiment. People who participated, gambled. The sound option is to pay the £100, but people feel differently about gain than they do about loss. Humans are not the rational beings that economic theories assume. Humans are often irrational, and hence, so are markets.
Mandelbrot, Fractals and Finance
Benoit Mandelbrot entered this world when he turned his brilliant mind to finance. Born in Warsaw in 1924, Mandelbrot was a renegade mathematician. He was best known for his work on fractals, a word he coined. Fractals are shapes that have repeating patterns. These patterns appear similar, or exactly the same, regardless of how close or far away the observer is.
Nature is made of fractals, and they’re visible from the smallest viruses to the largest mountain ranges. Snowflakes are fractals, and so are tree branches. Coastlines, with their jagged edges, look similar when viewed up close or from a distance. Looking at ferns, we can see smaller and smaller components, each looking the same as the entire plant.
An animation of a triangle made up of multiple triangles, an example of fractal geometry. It looks the same at any perspective.
Mandelbrot was the first to point out that the mathematics of fractals could be a tool in applied mathematics: “My whole life,” he said, “has been a study of risk.” In his groundbreaking book ‘The (Mis)behavior of Markets’, he used mathematics to challenge traditional financial theories. He showed how markets, like nature and humans, are irregular and hard to predict. The book revolutionised the modern understanding of financial markets.
There are innumerable takeaways from The (Mis)behavior of Markets. The work has countless insights. There are too many to list here. Five will, for this article, ideally suffice. If you apply them, they’ll maintain your company and help it thrive.
1. The Chaos of Markets
What does this mean for businesses? Be prepared for sudden changes. Do not plan for gradual shifts but for disasters. A useful method derived from Mandelbrot’s writings: list, for instance, three scenarios that might harm your firm.
A key supplier goes bust overnight. A key product’s price suddenly halves. A new technology makes your service obsolete. Plan how you’d react to these events. As Mandelbrot described the world, the unexpected isn’t possible but inevitable. The question is not whether surprises will come but when and how well your company is prepared to handle them.
2. The Past is Not a Crystal Ball
Mandelbrot was deeply sceptical of financial models that claimed to predict the future based on past performance. He knew the limitations of human knowledge and the complexity of economic systems. The natural world, he said, was erratic, its workings obscure. “If,” he wrote, “the physical world is so uncertain […] then how much more uncertain and unknowable must be the world of money? Finance is a black box covered by a veil. Not only are the inner workings hidden, but the inputs are also obscured, by bad economic data, conflicting news reports, or outright deception.”
Mandelbrot warned about anyone claiming they could predict future market behaviour based solely on historical data. The lesson for business owners is to build an organisation that is adaptable and responsive to change. To do that, add flexibility and redundancy into your operations so you can pivot when circumstances change. Use a variety of sources of information, from people to publications. Use Companies House. Use trade publications. Use industry conferences. Maintain contact with your suppliers and your customers, and be as familiar with them, and how their businesses are operating as you can. You should try to form a business robust enough to thrive in an uncertain world.
3. Turbulence is the Norm, Not the Exception
Mandelbrot was fascinated by turbulence. Volatility and unpredictability were, he said, inherent features of markets, not aberrations. These insights came from his work on fractals. When viewed at different time scales (every hour, every day, every month), he noticed that price charts showed similar volatility patterns. “The flight of a bird, like the whims of a horse, cannot be predicted or controlled,” he wrote. “We can think of financial prices in much the same way: not predictable, not controllable.”
The FTSE 250 Index from 1990 until 2024 showing daily closes as a line chart.
The same FTSE 250 daily index prices, but plotted as a logarithmic scale. The volatility and fluctuations from day to day are far clearer. This is a method Mandelbrot used to the unpredictability of markets.
It is a matter of prudence to embrace volatility as a normal part of business life. Volatility is not a deviation. Develop a surge capacity in your operations, the ability to rapidly scale up or down in response to market shifts. Create modular products or services that can be adapted to changing market conditions. Use dynamic pricing strategies that can adjust to market fluctuations. It is futile to try and predict or control market turbulence. The sagacious option is to be ready to adapt to any situation.
4. Beware the False Comfort of Models
On September 29, 2008, the Dow Jones plunged 777 points. In hours, $1.6 trillion vanished from American industry. There were many culprits, but much of the blame can be attributed to over-optimism, fuelled by supposedly advanced modelling tools. Banks bet billions on these models. Regulators trusted them to keep markets safe. Both were wrong. Quoting Mandelbrot, “The credit crisis was magnified by a phenomenon new to our generation: an over-confidence in our understanding of markets, as reflected in the industry’s increasingly sophisticated computer models.” He knew models couldn’t capture the true complexity of markets. Models are, at best, approximations of what they represent. They are not replicas. Predictive models are especially dangerous and made more so when they aim to forecast events in which humans are involved. It is human nature to want to predict the future. It gives comfort. But it is a false comfort, and when the model fails, the results can be, and have been catastrophic.
Models can never predict the future. That is beyond the capacity of any human, or any thing.
Don’t trust any model that claims certainty. The future is always unclear. Plan for multiple scenarios. What if sales double? What if they halve? Be ready for both. Never let a model blind you to reality. A model is not reality. It’s a simplification, sometimes expedient, but always limited. In business, as in markets, the unexpected is typical. Don’t try to predict it. Arrange for it. Cultivate multiple revenue streams. Maintain a strong community relationship. Reach out to people in your industry, other sectors, and different fields. Connect your business with academics, researchers, and business groups. Be pliant. Map and stress-test your supply chain. Magnify it. Speak with business consultants. Speak with brokers. Above all, ignore models and predictions. Disregard anyone, whether in the newspapers, on television, online or elsewhere, who claims they know what will happen in the future. It’s all fantasy, or as Mandelbrot said, “a fun-house mirror”. Anticipation, he wrote, “is the stuff of dreams and vapors.”
5. Focus on ‘How’, Not ‘Why’
For most of us, chance, risk and uncertainty are, as Mandelbrot says, unexamined ideas. For financiers, it is different. For some people outside that field, it is different too. It seems common sense to look at causes and, from those causes, derive simple explanations for the prices of financial instruments or other commodities. Wars are chaotic and so cause disruptions in oil access or transport. The pound falls. Wheat prices rise because of heat waves. “Would it were so simple,” Mandelbrot warned. “In the real world, causes are usually obscure. Critical information is often unknown or unknowable.” There are a variety of factors that cause prices to rise or fall. Oil companies, knowing people assume that a lack of access to oil can cause the prices to rise, charge more. Other big companies do the same. Important information, Mandelbrot wrote, is often “concealed, or misrepresented, as during the Internet bubble” or the Enron scandal. During the latter, Enron compelled power companies to shut off electricity. So, the price of electricity, which they were selling as an asset, grew higher.
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Enron concealed their illegal practices from customers, suppliers, regulators, shareholders and almost everybody else. The result: blackouts, high energy prices and political fallout. Nobody knew the cause until after Enron’s role in market manipulation was revealed. (Image courtesy of Investopedia.)
The reasons why world events occur are not worth pondering because of these misrepresentations. What merits consideration is your business, the immediate impact of prices on that business, and how you can navigate those impacts. The trap of concerning oneself with why global developments occur is a trap worth escaping. Mandelbrot said that for centuries, shipbuilders learned to put care into the design of their vessels. The sea may be moderate, but typhoons and storms may arise. According to Mandelbrot, “shipbuilders don’t just plan for good weather. They build for storms. The financiers and investors of the world are,” he said, “like mariners who heed no weather warnings.”
To look beyond one’s industry is beneficial. Considering how events in unrelated industries and how those could, in practical terms, influence your firm is vital. So, too, is curiosity. Preparation, and not prediction, is the advice Mandelbrot gave. It is rewarding advice. Be aware of risk. Be aware of how it can be curtailed. Know that the world is uncertain. As the novelist Toni Morrison wrote, “why is difficult to handle,” and so, “one must take refuge in how.”
Mandelbrot’s insights are a reminder that the business world, like the natural world, is complex and unpredictable. By embracing uncertainty, preparing for volatility, and focusing on adaptability, businesses can operate in a commercial environment replete with risk. Firms can understand uncertainty and function well, confidently and steadfastly.
