Explaining big events

The expression ‘this month’s once-in-a-million event’ has become a cliché in finance. From the sudden bankruptcy of investment-grade companies to 5% daily moves in foreign exchange markets, we’ve seen them all. Rare events – which for practitioners mean ‘big events’ – happen far more often than expected. And as the above phrase implies, naive use of statistics makes fools out of us because experience is wildly different from what the theory predicts.

The truth is more subtle. The sum total of the decisions of many unseen people, market events (large and small) have causes. However, a good starting point for modelling markets is to assume complete ignorance of these causes. Expressed mathematically, this implies that market events are random. The Gaussian probability distribution follows naturally as the simplest expression of such assumed