The financial theories you learn about in school are coherent, neat, convenient – and wrong. In fact, they’re so wrong that they might also be dangerous: in underestimating the risk of markets, we inadvertently set ourselves up for catastrophe. The Misbehavior of Markets lays out the flaws of economic orthodoxy, and offers a novel alternative: fractal geometry

Benoit Mandelbrot insists that…

• Current risk models are incapable of capturing the inherently irregular forces of capital markets – 2008 financial crisis reminded investors of this fact!
• Modern investment theory is built upon the premise of “rational” investor behaviour
• Mainstream theories of finance contend that each individual will make the most profitable, obvious rational choice
• In reality, our irrational behaviour is due to our entirely human tendency to mis-interpret information and misjudge probabilities

Behavioural Experiment:

Participants in the study were given the choice to either collect $100 immediately or flip a coin and win $200 for heads and nothing for tails. Unsurprisingly, most people opted to collect the free $100.

Then, the rules were altered: now, people had to choose between paying $100 or flipping a coin and losing $200 for heads and nothing for tails. This time, most people decided to gamble.

Objectively, the potential wins and losses were the same, so any rational person should make the same choice under both conditions.

Key Point: People are irrational, and so most of the participants acted as if the odds for both games were different

Critique of the assumptions embedded in orthodox economic theories

• All Investors follow the same strategies
• All Investors will act in essentially the same way if they are in comparable situations
• All Investors have the same investment time horizons

The authors reflect on whether this type of simplification creates poor predictions about market behaviour and consequently, bad investment decisions?

The fallacy of Normal Distribution

• According to modern financial theory, prices don’t jump – rather, they glide
• They glide and are bounded by a normal distribution which infers extremely low probability to extreme risk events
• Male heights in the US follow a normal distribution. Most men, on average have a height of 70 inches with 95% of American men between 66 and 75 inches tall
• But stock prices do jump! Thus, changes and price can’t be considered normally distributed

The authors point to several empirical studies which have demonstrated that price movements aren’t actually independent from one another. Trend is a phenomenon ignored by orthodox financial theory.

Is there a better approach?

• Theories that embrace the markets granularity and roughness would be more accurate and helpful
• The authors draw inspiration from a kind of math called “fractal geometry”
• “Fractals” – tracing their roots back to the Latin word fractus, meaning “broken” – exhibit a unique kind of regularity
• Volatile stock markets mirror the air movement in wind tunnels – undulating forward and backwards between periods of smooth flow and turbulence, with sudden gusts and complex swirls
• A “smooth” framework for understanding financial markets just does not hold water

 Lessons from “The Misbehavior of Markets”

• Classic financial theory still dominates our understanding of market behaviour
• However, these rigid models fail to adequately capture the inherent risks and market volatility
• Fractal geometry [among other methods] offers a revolutionary re-evaluation of the tools and models of modern financial theory.
• Benoit Mandelbrot is recognised as the father of “chaos theory”, a moniker that may better capture the true nature of asset prices over the shorter term.