The role of the normal distribution in financial markets

The hypothesis that financial variables are normally distributed is often rejected in both theoretical studies and extremely specific cases. In the ''real'' world of financial investors -- where risk averse agents mainly hold government bonds, a few equities and do not hold derivatives -- the normal distribution still plays a lead role. To show this result, in this paper we focus on a number of efficient portfolios subject to several constraints which make them close to the portfolios held by most of financial agents. A multivariate approach is proposed, which refers to the case of a financial asset manager who cannot only pay attention to the average return of all of his portfolios, but must evaluate the risks associated to each of his portfolios jointly.