Causality, Chaos and Risk in Markets | by Todd Moses | January 2024

Mathematician Benoit Mandelbrot’s work in finance is a fascinating contrast to what is taught in most business schools. From cotton prices in the 19th century to modern stock markets, Mandelbrot found that both exhibited similar behavior (Mandelbrot & Hudson 2009). He concludes: “But it is clear that the global economy is an unimaginably complicated machine.”

Most notable is Mandelbrot’s discovery that “real markets are wild. Their price swings can be far-fetched—much larger and more damaging than the modest variations of orthodox finance.” Much of the work that came out of this discovery helped shape chaos theory, which we discuss later.

Spearman correlation measures the monotonic relationship between two variables (Ramzai 2020). This means that when one changes, so does the other. It means more than coincidence, but less than a causal relationship. A change in one variable will most likely cause a non-linear change in the other.

When there is no constant change between two correlated variables, it points to a third unknown variable that holds the causal relationship. For example, when shares of Apple (NASDAQ: AAPL ) move, shares of Amazon (NASDAQ: AMZN ) often move in the same direction. However, a change in the value of Apple’s stock will not cause a change in the value of Amazon. Instead, there is something else that causes both stocks to change.

The only way to prove causation is through an experiment. Researchers calculate the probability of a potential causal relationship with a variable as P(O|C) minus the probability of it occurring in its absence, P(O|¬C) (Matute et al. 2015). They do this through a series of tests:

Δp=P(O|C)−P(O|¬C)

Psychologists Allan and Jenkins explain: “When the probability of an outcome occurring in the presence of a cause is greater than the probability without a cause, Δp is positive.” This result means that the potential cause contributes to the result. Similarly, when Δp is negative, the probability of an outcome without a cause is more significant. However, the cause prevents the result (Matute et al. 2015).

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