(Bloomberg) -- Trump has been called the ultimate "tail-risk candidate," so it's perhaps unsurprising that his electoral success has been greeted with outsized market reactions.

Stocks, bonds and currencies were rattled by the vote, registering market moves that are supposed to be incredibly rare according to the normal distribution of probabilities that still form a bedrock of the financial models employed by large trading desks on Wall Street.

Statistical theory holds that 68% of all observations in a normal distribution lie within one standard deviation of the average of that sample. Events that lie on the fringes of this distribution are defined by a number of sigmas, which denote the decreasing likelihood of this outcome being realized.

(Bloomberg News)
Global markets were thrown into disarray as Donald Trump won the election. (Bloomberg News)

These multi-sigma moves tend to wreak havoc with so-called Value-at-Risk models, and can spawn waves of indiscriminate selling as market participants scramble to dial down their exposure. To be sure, big banks are well aware that financial markets don't, in practice, display such a normal distribution, and have adjusted their models appropriately in light of rare events turning out to be more common than anticipated. In addition, post-crisis regulation has mandated the use of adjusted, stressed VaR models.

Stocks, bonds and currencies registered market moves that are supposed to be incredibly rare.

At its trough, shortly after midnight in New York, the Mexican peso was down nearly 12%, to its lowest level on record, in what was a more than 15-sigma move.

Gold was up almost 5%, which as a closing price would have been the best showing for the precious metal since 2008, and a four-sigma move.

The three-sigma widening of the spread between two- and 30-year U.S. Treasury yields constituted the biggest basis-point move since the 2013 taper tantrum.

Front-month S&P 500 futures staged a comeback after President-Elect Trump's victory speech, but had been down 5% by midnight.

That poor showing would have constituted a daily drop of more than three standard deviations below its 10-year average.

Front-month Chicago Board Options Exchange Volatility Index futures retreated as Europe woke up.

But at their session highs, the 7.5-point jump in VIX futures was more than five standard deviations above its 10-year norm.

And while we've seen far worse than a 1.5% drop in the U.S. dollar relative to the Japanese yen at numerous times this year, that retreat still amounts to a two standard-deviation decline.

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