I wonder if multivariate normal distribution is the only class of distributions whose random vectors have distributions of the same class after linear transformations? How can one justify it?
Is there a name for such property of distributions? Bodie's Investment calls this "stable".
the normal distribution belongs to a special family of distributions characterized as "stable," because of the following property: When assets with normally distributed returns are mixed to construct a portfolio, the portfolio return also is normally distributed.
Thanks!