@article{Chacón Suárez_2019, title={68- #1168 SPARSE PORTFOLIOS FOR HIGHDIMENSIONAL FINANCIAL INDEX TRACKING WITH LOW-RANK MATRIX CONSTRAINT FOR STOCKS}, volume={2}, url={https://revistas.uis.edu.co/index.php/memoriasuis/article/view/10477}, abstractNote={<p>Selection of the securities for investment portfolio<br>design is one of the most important optimization<br>problems of the last century. For this, numerous<br>strategies and mathematical models have been<br>proposed. For instance, the passive investment<br>strategy performs the tracking of market indices with the<br>intention of reproducing its performance with an<br>optimized portfolio as described in [1].</p> <p>This passive strategy is based on the advances shown<br>by Palomar [2] who deals with the issue of designing<br>sparse portfolios to efficiently reproduce the returns of<br>any index. Once the stocks have been selected, the<br>following step aims at dividing the investment capital<br>between these stocks in some efficient way. This<br>strategy has shown promising performance, however, it<br>does not take into account the correlation between the<br>selected stock returns, which is an important factor in<br>the efficient selection of the stocks, but a cointegration<br>based approach.</p> <p>Therefore, the main objective of this work relies on<br>formulating a mathematical model that allows to find<br>high correlated stocks for the sparse portfolio design.<br>Thus, it aims at modifying previous work to improve the<br>quality results by taking into account the correlation<br>between the stocks.</p> <p>In this manner, the proposed optimization problem<br>includes the nuclear norm over the market returns<br>matrix multiplied by the desired variable weights, such<br>that it is possible to apply some thresholding technique<br>over the singular value decomposition of this resulting<br>matrix as presented in [3]. This allows to reduce its rank<br>iteratively with the objective of obtaining its low-rank<br>approximation, which multiplied by the inverse returns<br>matrix, results in the desired portfolio weights</p>}, number={1}, journal={Memorias Institucionales UIS}, author={Chacón Suárez, Javier Alexi}, year={2019}, month={ene.} }