Dimension Reduction in Optimal Portfolio Selection Problem Using Nonnegative Matrix Factorization and Nonnegative Principal Components Analysis

In multivariate time series, data reduction techniques allow for a fast and thorough analysis since features of the data with high dimensions are preserved at adequate and manageable levels. Reducing dimensionality in time series may require additional interpretation since negative values may be inherited from the transformation, as in the case with prices. This study explores the effects of nonnegative matrix factorization and nonnegative principal components analysis on Markowitz's mean-variance portfolio optimization model, by backtesting dimensionally reduced and unreduced portfolios.Optimal portfolio selection problem determines the amount of capital to invest in diversified securities by measuring risk and return. Markowitz's mean-variance model assigns equal importance to returns while measuring the risk using the returns' covariance matrix. However, it disregards the volatility within the investment horizon. The returns' covariance matrices are calculated after reducing time dimensions of the dataset - composed of 300 days of closing prices for 143 stocks of industrial corporations enlisted in Turkish Industrial Index