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Portfolio Optimization under Cardinality Constraints: A Comparative Study
Department of Applied Mathematics and Statistics, Laboratory of Big Data and Stochasticity, Waseda University, Tokyo, Japan
Department of Applied Mathematics, Laboratory SAMM (Statistics Analysis and Multidisciplinary Modeling), University of Paris 1, Pantheon Sorbonne, Paris, France
Department of Mathematics, Faculty of Science, University of Yaounde 1-ENS-Higher Training College, Yaounde, Cameroon
Department of Applied Mathematics and Statistics, Laboratory of Big Data and Stochasticity, Waseda University, Tokyo, Japan
Department of Mathematics, Faculty of Science, University of Yaounde 1-ENS-Higher Training College, Yaounde, Cameroon
- 1 Department of Applied Mathematics and Statistics, Laboratory of Big Data and Stochasticity, Waseda University, Tokyo, Japan
- 2 Department of Applied Mathematics, Laboratory SAMM (Statistics Analysis and Multidisciplinary Modeling), University of Paris 1, Pantheon Sorbonne, Paris, France
- 3 Department of Mathematics, Faculty of Science, University of Yaounde 1-ENS-Higher Training College, Yaounde, Cameroon
- 4 Department of Applied Mathematics and Statistics, Laboratory of Big Data and Stochasticity, Waseda University, Tokyo, Japan
- 5 Department of Mathematics, Faculty of Science, University of Yaounde 1-ENS-Higher Training College, Yaounde, Cameroon
Open Journal of Statistics·Volume 07 (2017)·Pages 731–742·Published 21 July 2017·DOI10.4236/ojs.2017.74051
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Abstract
The Cardinality Constraint-Based Optimization problem is investigated in this note. In portfolio optimization problem, the cardinality constraint allows one to invest in assets out of a universe of N assets for a prespecified value of K . It is generally agreed that choosing a “small” value of K forces the implementation of diversification in small portfolios. However , the question of how small must be K has remained unanswered. In the present work, using a comparative approach we show computationally that optimal portfolio selection with a relatively small or large number of assets, K , may produce similar results with differentiated reliabilities.
KeywordsCardinality ConstraintsDiversityPortfolio SelectionPortfolio ReliabilityParametric Statistics
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