T Distribution vs S&P 500

98% of the last 65 year's daily stock returns are explained by one simple formula:

tinv ( dof ) * Stdev.s * [ ( dof - 2 ) / dof ] ^ 0.5

The t distribution is a wonderful thing.

Plus the original paper from 'Student' himself is an easy read!

Why is the t-distribution so good?

My hunch is it's due to the actual volatility continuously shifting under our feet.

With a constant volatility you'd soon end up with a normal distribution sooner or later.

Whenever volatility changes the new level's scent is quickly picked up again by the t distribution.