Cluster analysis for portfolio optimization
Rosario N. Mantegna
Physics - Physics and Society | Condensed Matter - Other Condensed Matter | Quantitative Finance - Statistical Finance
arxiv: Computer Science::Computational Engineering, Finance, and Science | Statistics::Other Statistics | Mathematics::Optimization and Control
We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.