The bell-curve shape of Gaussian distributions is what banks’ risk models assume

Evidence

The second valuation method used in finance is probability-based statistics. Statistics were used in the 19th century by insurers to estimate the probabilities of accident or death based on observed past frequencies, but remained confined to the world of actuaries. It was only later that they arrived in the world of finance, through the work of researchers trying to predict stock exchange movements (Walter 1996, 1999). Fluctuations in prices on the markets, and the occasionally high volatility even within a single day, were incompatible with the idea that prices necessarily have some objective foundation, and can be predicted. One ”solution” to this problem has been to consider it possible to describe stock market prices using mathematical expectations and volatility (standard deviation). This hypothesis then became generalised and is now used to construct models assuming that value generally follows a probabilistic law that is principally describable by the mean and standard deviation (as in a Gaussian distribution). This conceptualisation was then introduced into all management and valuation models, and every financial valuation now assumes that the two criteria of risk and return will be taken into consideration. — Ève Chiapello, Financialisation of Valuation, 33 (#expands, via linked claim)

If one was dealing with stock or portfolio returns over periods as long as a month, Fama concluded, the tails became slim enough that “the normal distribution is a good working approximation.” The “costs of rejecting normality for securities returns in favor of [Levy] non-normal distributions are substantial,” Fama wrote. Although “most of the models of the theory of finance” could be reconstructed on the basis of Levy distributions, the “exposition” of those models became more complicated and “statistical tools for handling data from [Levy] non-normal … distributions are primitive relative to the tools that are available to handle data from normal distributions.” — Donald MacKenzie, An Engine, Not a Camera, 510 (#complicates, via linked claim)

The risks involved in LTCM’s positions were carefully calculated and controlled using the “value-at-risk” approach, a standard practice of the world’s leading banks (Meriwether interview). Value-at-risk is a measure of the exposure of a portfolio to adverse price movements. In the case of the dollar swap spread, for example, historical statistics and judgments of likely future values led LTCM to estimate that the spread had an “equilibrium value” of around 30 basis points, with a standard deviation of about 15 basis points per annum (Rosenfeld interview; a “basis point” is a hundredth of a percentage point). Using those estimates, it was then possible to work out the relationship between the magnitude of possible losses and their probabilities, and thus to work out the value-at-risk in the trade. — Donald MacKenzie, An Engine, Not a Camera, 995 (#exemplifies, via linked claim)

Categorization

• XREF: connects to: Under a Gaussian distribution extreme tail events become effectively impossible — Mark Blyth, Austerity: The History of a Dangerous…, 106; Probabilistic valuation methods migrated from actuarial science into financial markets via Gaussian risk models — Ève Chiapello, Financialisation of Valuation, 33; Value-at-risk quantifies portfolio exposure through estimated loss probabilities. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 995 (+7 more)

Broader Connections

• Probabilistic valuation methods migrated from actuarial science into financial markets via Gaussian risk models #expands (0.82) — Ève Chiapello, Financialisation of Valuation, 33
• Practical statistical convenience, not empirical fit, drove finance’s retention of the normal distribution #complicates (0.80) — Donald MacKenzie, An Engine, Not a Camera, 510
• Value-at-risk quantifies portfolio exposure through estimated loss probabilities. #exemplifies (0.78) — Donald MacKenzie, An Engine, Not a Camera, 995
• Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones #contradicts (0.75) — Donald MacKenzie, An Engine, Not a Camera, 138
• Banks’ risk models treat the past as the limit of what can happen #expands (0.74) — Mark Blyth, Austerity, 109
• The Levy distribution’s failure to survive time aggregation cooled academic interest in fat tails #complicates (0.72) — Donald MacKenzie, An Engine, Not a Camera, 509
• Financialization treats risk as probabilisable, displacing close knowledge of the object valued #expands (0.70) — Ève Chiapello, Financialisation of Valuation, 35