The stationary-normality assumption is essential to many areas of financial analysis, from the most simple asset value-at-risk calculation to the stochastic pricing of a portfolio. Its outstanding influence on estimation techniques which are addressed to developing risk-return profiles has placed this assumption as a building block of the modern finance theory, from the outset. However, after the 2007-2008 financial crisis some authors have criticized its longstanding validity in financial analysis, especially because the real performance of the market variables is not regularly stationary-normal in presence of Black Swans. In particular, it is argued that any price forecasting technique which is based on normality it is doomed to failure. This paper aims at analyzing the points of views which seek to take this assumption out of the theoretical core by stressing the link between stationarynormality and the true nature of Black Swans. The main conclusions of the paper state that non-normality is not only a statistical matter but also a result of the way speculators, rating firms and regulators behave in financial markets when pricing assets in periods of crisis.