“ Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.”

G.K. Chesterton

Risk means different things to different people; its essence is embedded in the eye of the beholder.

While the concept of fate has long been established, our understanding of risk is still quite new in historic terms. The gradual removal of religious shackles and superstitions during the Renaissance helped shed the belief that destiny is mapped out and unchangeable.

Curiosity, freedom of thought and experimentation meant that it was only a matter of time before a greater understanding of risk was sought out in the early modern era. While the initial impetus was provided by Italian thinkers, it was the French, with their love of mathematics, who got their teeth into the subject.

French mathematicians Blaise Pascal and Pierre de Fermat founded decision theory, an impressive advance in understanding. Pascal took probability theory and linked it together with decision making under certain conditions. Pascal’s Wager is classic probability insight here. Faced with the decision as to whether to believe in God or not, the rational choice is to live as though God exists. The downside to taking this approach only to find out he doesn’t is finite, sacrificing some short term earthly pleasures, whereas the flipside is to face an eternity in hell.

Risk is uncertainty

Risk, ultimately, is about the future, and the inherent uncertainty built in to what lies ahead. In that sense, it cannot be about the past – unless of course you believe the past can predict the future. Yet we have devised methods that exploit numbers to analyse what happened in the past.

Extrapolating from the past can help inform the probability of future events; however, it can only go so far in the real world. Uncertainty cannot be eliminated as the limits to our knowledge and understanding are huge. Measuring risk is therefore fraught with danger. Scientific proxies like volatility and standard deviation metrics are helpful, but they are just that, proxies.

The financial world is not easy model because it is constantly in flux, and goes through both cyclical and structural changes. This dynamism occurs because it is constructed and driven by humans. Yet the mathematics behind our understanding of it is, for the most part, both backward looking and static. The financial crisis provided a more dramatic, practical reminder of these limitations.

The sheer scale of the task in understanding dynamic systems, like the weather, helps explain why no revolutionary changes have been made. Yet encouraging progress is being made in certain areas. Physics professor Didier Sornette has led us into the realm of big data. One approach to dealing with the problem of vastness, intelligibility and uncertainties is, to some degree, to ignore it and to focus on what you believe to be really important. As data visualisation techniques improve, contextualising and sorting such large swathes of data should become far easier.

Portfolio risk

The core types of risk that permeate the world of investment are risks that revolve, within and around credit, liquidity, markets, compliance, regulation, politics, legal, catastrophes, and reputation.

Making the distinction between more introspective portfolio risk and the broader risks that affect the financial and economic system is important because, while they are inextricably linked, what really matters to a client is whether or not their investment portfolio performs as expected and allows them to enjoy the benefits that those expected returns offer to their lives.

The evolution of the investment industry is relatively recent and has occurred with the “efficient market hypothesis” at its core. Intellectual giants such as Eugene Fama and Harry Markowitz put forward the notion that equities are always correctly priced because every market participant has all relevant and available information at their fingertips. This is plain wrong. Yet that didn’t stop others building out the concept further with more mathematical modeling, such as Black Scholes. As is so often the case, the great minds who create such complex and sophisticated tools know full well their limitations – it is the lesser minds that follow, trailing behind who fail to grasp the fallacies and plough on as if the outputs are gospel.


Risk is always going to maintain an air of mystery. Its elusive tendencies will unlikely ever be fully conquered. However, by thinking more intelligently about it, accepting our cognitive limitations when trying to tame it, we can make progress, by making better policy decisions at the macro-economic level and better investment decisions at the portfolio level. And so as we wait for the academics and industry professionals is to invent the ‘mathematics of surprise’, we must adopt a practical and thoughtful approach to dealing with risk.



Against the Gods, the remarkable story of risk – Bernstein

Keynes: the return of the master – Robert Skidelsky

The General Theory of Money, Employment & Interest – John Maynard Keynes

Why stock markets crash – Didier Sornette

My life as a quant – Emmanuel Derman



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