Cardinality Constrained Mean-CVa R Portfolio Optimization

Due to the transaction cost and other market friction,investor usually holds only small number of stocks to cut cost and manage portfolio.This common phenomena motives us to study the cardinality constrained portfolio optimization model.Instead of using the traditional mean-variance criteria,we use the Conditional Value-at-Risk(CVa R)as the risk measure to build the cardinality constrained portfolio optimization model.This problem is a NP hard optimization problem,which can be reformulated as an mixed-integer programming problem.To evaluate the CVa R,it is necessary to generate a large number of scenario,which increases the size of this problem significantly.Thus,it is not practical to solve the resulted mixed-integer programming problem directly.With the development of the research on portfolio optimization,people have made some progress in dealing with cardinality constrained portfolio problems.However,it seems that non of them can balance the accuracy and efficiency desirably.Based on the former works,instead,we propose to use two algorithms to solve the NP-hard problem.We also introduce two-stage model to expand our algorithm.Our main works are as follows:· Instead of solve the cardinality constraint problem directly,we propose reweighednorm method to find the approximated solution of this problem.The flexibility of the choosing different weights enables us to achieve different degree of the sparse portfolio.The computational experiments show the prominent feature of this approach.· On the base of former works on clustering portfolio problem,we make a further study on the basic economic importance of clustering algorithm.We propose the improved clustering algorithm to further raise the computing power and explain the economic principle of our clustering portfolio reasonably.· As an expansion of reweighed-norm approximate method,we constructed the 2-stage reweighed-norm model to study the advantages and disadvantages of our reweighed-norm algorithm.· We carried out some simulation on each model to test and compare the efficiency and accuracy of these methods.