Some researchers have recently criticized using the normal distribution for modeling stock returns. While it’s true that the normal distribution is inappropriate and leads to the extreme outliers, known as the Black Swans problem, other elliptical distributions allow addressing this issue. The Student’s t-distribution with 3 to 4 degrees of freedom and the Laplace distribution both can be used to largely eliminate Black Swans in daily returns. Both distributions are compatible with the modern portfolio theory. We also show that no single distribution is clearly preferred when describing periodic returns, but the Black Swans problem is not so acute when considering returns over holding periods longer than one month.