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


International Conference on Information Complexity and Statistical Modeling in High Dimensions with Applications (IC-SMHD-2016), Nevşehir, Turkey, 18 - 21 May 2016, pp.15

  • Publication Type: Conference Paper / Full Text
  • City: Nevşehir
  • Country: Turkey
  • Page Numbers: pp.15


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.