  Risk aversion plays a significant and central role in investors' decisions in
the process of developing a portfolio. In this framework of portfolio
optimization we determine the portfolio that possesses the minimal risk by
using a new geometrical method. For this purpose, we elaborate an algorithm
that enables us to compute any generalized Euclidean distance to a standard
simplex. With this new approach, we are able to treat the case of portfolio
optimization without short-selling in its entirety, and we also recover in
geometrical terms the well-known results on portfolio optimization with allowed
short-selling. Then, we apply our results in order to determine which convex
combination of the CAC 40 stocks possesses the lowest risk: not only we get a
very low risk compared to the index, but we also get a return rate that is
almost three times better than the one of the index.
