Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)2022-03-142022-03-14https://noesis.uis.edu.co/handle/20.500.14071/5497Selection of the securities for investment portfoliodesign is one of the most important optimizationproblems of the last century. For this, numerousstrategies and mathematical models have beenproposed. For instance, the passive investmentstrategy performs the tracking of market indices with theintention of reproducing its performance with anoptimized portfolio as described in [1]. This passive strategy is based on the advances shownby Palomar [2] who deals with the issue of designingsparse portfolios to efficiently reproduce the returns ofany index. Once the stocks have been selected, thefollowing step aims at dividing the investment capitalbetween these stocks in some efficient way. Thisstrategy has shown promising performance, however, itdoes not take into account the correlation between theselected stock returns, which is an important factor inthe efficient selection of the stocks, but a cointegrationbased approach. Therefore, the main objective of this work relies onformulating a mathematical model that allows to findhigh correlated stocks for the sparse portfolio design.Thus, it aims at modifying previous work to improve thequality results by taking into account the correlationbetween the stocks. In this manner, the proposed optimization problemincludes the nuclear norm over the market returnsmatrix multiplied by the desired variable weights, suchthat it is possible to apply some thresholding techniqueover the singular value decomposition of this resultingmatrix as presented in [3]. This allows to reduce its rankiteratively with the objective of obtaining its low-rankapproximation, which multiplied by the inverse returnsmatrix, results in the desired portfolio weightsapplication/pdfSparse Portfolio OptimizationIndex TrackingLow-Rank ApproximationCorrelated Stocksinfo:eu-repo/semantics/articlehttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)