Sparse tangent portfolio selection via semi-definite relaxation

The high-cardinality of mean-variance portfolios is a concern in practice because it increases transaction costs and management fees. Therefore, we propose a method to resolve the cardinality problem by applying the semi-definite relaxation method to a cardinality constrained optimal tangent portfolio selection model. We find that the relaxed model becomes a semi-definite programming problem that is efficiently solved with existing optimization solvers. Numerical analyses with historical stock returns confirm that the proposed relaxed model effectively constructs sparse tangent portfolios.