Title: A good basis for projections in functional data analysis: Markowitz portfolio optimization
Authors: Lajos Horvath - University of Utah (USA)
Shanglin Lu - Renmin University of China (China) [presenting]
Zhenya Liu - Renmin University of China (China)
Abstract: A new basis for projections in functional data analysis is proposed and used to solve the minimum-variance portfolio optimization for large dimensional assets. We measure the large dimensional asset returns in the cross-section as Hilbert-space-valued random function. The proposed basis is formed by the eigenfunctions belonging to the d-largest eigenvalues of a bivariate function, which combines the covariance function and the mean function proportionally. A comprehensive simulation study shows better performance in terms of shrinking error when using the d-dimensional projections in dimension reduction. In the empirical application to the U.S. industry portfolios, Fama and French portfolios, and S\&P500 constituent stocks, the optimized portfolio also give better out-of-sample performance by employing the proposed basis.