Describing n-day returns with Student's t-distributions

►n-fold self-convolution of a truncated t-distribution with ν=3 is considered. ► A truncated t-distribution rapidly becomes normal-like under n-fold self-convolution. ► Results explain the development of n-day returns from t to normal as n increases. ► Mixture of normal and truncated variance yields a t-like pdf with exponential tails. ► This exponential development of the tails effectively truncates a t-distribution.