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.