Four traditions, one system

The Monte Carlo method was born not in finance but in physics. In 1946 the mathematician Stanisław Ulam, while recovering from an illness and playing solitaire, realised that the behaviour of complex systems could be studied not by solving equations analytically but by generating a large number of random trials and observing the distribution of the results (Eckhardt, 1987).

Not the solution of an equation but a distribution of results – this is the idea that finance would later take up.

1. 1946Ulam’s idea: random trials instead of equations
2. March 1947von Neumann’s letter: how to turn the idea into a computational procedure
3. 1947applied to neutron scattering calculations at the Los Alamos laboratory

The RAND Corporation in the post-war period: Herman Kahn applies the scenario method – structured thinking about alternative futures – not for forecasting but for the systematic exploration of the strategic possibilities of nuclear war.

The book On Thermonuclear War (Kahn, 1960) caused a public controversy but established scenario planning as a serious analytical discipline.

Kahn’s main contribution was epistemological: scenarios are not forecasts; they are structured hypothetical narratives, intended not to guess the future but to widen the thinking horizon of decision-makers (Kahn & Wiener, 1967).

In 1964 David B. Hertz published the article “Risk Analysis in Capital Investment” in the Harvard Business Review – the first systematic application of the Monte Carlo method to investment decisions (Hertz, 1964).

Hertz was the first to state clearly the idea that a single-figure assessment may look accurate, but it says nothing about uncertainty – the phenomenon of spurious precision discussed in Chapter 2.

For decades Hertz’s ideas remained more theoretical than practical, not because of conceptual shortcomings but because of technological limits: in 1964 Monte Carlo simulation required a mainframe computer.

Its practical application in business planning became possible only in the 1970s and 1980s, with the arrival of personal computers and spreadsheet add-ins such as @RISK.

Royal Dutch Shell, the late 1960s: Pierre Wack applies structured scenarios to the oil market. The dominant assumption: the price of oil would remain stable, because the countries of the Organization of the Petroleum Exporting Countries (OPEC) would have no motivation to change supply drastically.

At the same time the import needs of the consuming countries were due to grow much faster – this gap constituted OPEC’s future power. Shell’s management was prepared for the oil crisis of 1973, although not for its timing (Wack, 1985).

In finance, sensitivity analysis became an inseparable part of modelling along with the spreadsheet revolution: when VisiCalc and Excel made it possible to change assumptions interactively, “what if?” questions became part of an analyst’s everyday practice (Chapters 1 and 2).

In 1994 JP Morgan publicly released RiskMetrics – a standardised methodology for calculating Value at Risk (VaR), which for the first time turned a complex risk model into a publicly available standard (Chapter 3). In 1996 the Market Risk Amendment of the Basel Committee allowed banks to use internal models to calculate their capital requirements.

VaR’s major shortcoming was exposed on a wide scale by the financial crisis of 2008: VaR shows a loss threshold that under normal conditions is not exceeded with a stated probability, but it says nothing about what happens when those conditions are breached.

A theoretical answer to this shortcoming had been given already before the crisis by Artzner, Delbaen, Eber and Heath in the article “Coherent Measures of Risk” (Artzner et al., 1999): four axioms that a good risk measure must satisfy:

• monotonicity
• subadditivity
• positive homogeneity
• translation invariance

Conditional Value at Risk (CVaR), also called Expected Shortfall, satisfies the axioms – so in the Basel III reform, through the Fundamental Review of the Trading Book (FRTB), Expected Shortfall became the principal regulatory risk measure.