A new geometrical method for portfolio optimization

Risk aversion plays a significant and central role in investors’ decisions in the process of developing a portfolio.  In this portfolio optimization framework, 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 Euclidean distance to a standard simplex.  With this new approach, we can 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 to determine which convex combination of the CAC 40 stocks possesses the lowest risk.  Thus, we not only obtain a very low risk compared to the index, but we also get a rate of return that is almost three times better than the one of the index.

portfolio optimization
short-selling
Euclidean distance to a standard simplex
geometrical approach of portfolio optimization
geometrical algorithm
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