The sharp jump in spreads in credit markets in 1998 that brought an end to the hedge fund Long Term Capital Management, and near collapse of the financial system was characterized as a 10 sigma event. An event that would occur once in over a half of the age of our planet. The Black Monday crash of 1987 was considered a 20 sigma event, even more absurd, Goldman in the 2007 credit crunch blamed losses on a 25 sigma moves “several days in a row”.
Are we really living in such a unique time that, events of cosmological frequencies are all concentrating in a few decades? There is a simpler explanation; we are using the wrong yardstick to measure frequency of rare events. The tails in the bell shaped distribution of the Gaussian or ‘normal’ distribution used for these sigma estimations are thin, representing large moves as extraordinarily rare. More realistic non-Gaussian distributions exhibit ‘fat tails’ implying higher frequencies of large moves.
Extreme event or tail risk has become part of risk manager vocabulary as research by Eugene Fama, Benoit Mandelbrot and Nassim Taleb among others, have convincingly demonstrated the existence of fat tails in financial prices. Unfortunately, the rarer the price move the less available data, and the harder to model and manage. Risks at these extremes are unmeasurable or at least hard to estimate with a reasonable degree of confidence.
This has implication for assets represented in ledgers that require a token to operate such as Ripple or Bitcoin based ledgers, as cryptocurrency have no special immunity to these tail risks. On average, the value of the on-chain token embedded on an off-chain asset is disproportionately minuscule relative to the asset being represented in the ledger, but this has little relevance, what is of more critical importance, is that the value of this tokens is unbounded in dollar or fiat terms.
Taleb recommendation in dealing with tail risk is to ‘clip the tails’ e.g offsetting with instruments that benefit with extreme moves such as Out Of The Money (OTM) Options. This is not easy thing to do in the cryptocurrency world, as it requires a robust and mature derivatives market or some sort of centralized clearing that can offset tail risk among members.
For shared ledgers seeking to represent financial assets, the clip-the-tail solutions is trivial, avoid ledgers requiring tokens.
Fat tail risk is easy to dismiss in tokenized ledgers, since historically these ‘fees’ have ranged in the pennies or fractions of pennies, inducing a false sense of security. While historical data can give a hint of how many sigmas prices can move, it fails to reveal the bounds of the movements. A reminder of the boundless of financial price series, is the German mark exchange rate during the 1920s which sank from around 300 marks to a dollar to 4 trillion to a dollar.
Maybe, this is the more valuable insight that we can draw from historical data, that what never happened before, can happen.