ForecastingStocks

Quantitative finance starts with a humbling admission: prices are random, or close enough that we model them probabilistically. A quant does not predict the next tick with certainty — a quant estimates the distribution of what might happen and acts on its shape.

The normal distribution and why it seduces

The normal (Gaussian) distribution is the workhorse of classical finance. It is fully described by two numbers — a mean (its centre) and a standard deviation (its spread) — and it makes the math tractable. Much of the early theory, from portfolio optimisation to option pricing, assumed returns were normally distributed.

The bell curve says extreme events are vanishingly rare. A move of five standard deviations should happen roughly once in millions of days.

Fat tails — where the money is lost

Real market returns are not normal. They have fat tails (excess kurtosis): extreme moves happen far more often than a bell curve predicts. The 1987 crash, 2008, and every flash crash since are events a Gaussian model rates as essentially impossible — yet they keep arriving.

This single fact has consequences:

Risk models built on normality systematically understate the chance of disaster.
Strategies that look smooth for years can be wiped out in a day the model said could not occur.

A serious quant reaches for distributions that allow fat tails — the Student-t, or empirical distributions estimated straight from data — and never forgets that the rare event is exactly the one that matters.

Returns, not prices

One more convention: quants almost always model returns (preferably log returns, the natural log of the price ratio) rather than raw prices. Returns are roughly comparable across assets and time, and log returns add cleanly across periods. Prices are not — a 100 dollar stock and a 10 dollar stock are not comparable, but their percentage moves are.