On cardinality constrained mean-CVaR portfolio optimization

Due to the transaction cost and other market friction, investor usually holds only small number of stocks to construct 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(CVaR) 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 CVaR, 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. Instead, we propose to use the reweighed l(1)-norm 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.