Reducing Portfolio Quadratic Programming Problem into Regression Problem: Stepwise Algorithm

Abstract

Mathematical programming can be classified into linear and non linear programming. This study involved a literature knowledge of formal theory essential for understanding of optimization and investigation of algorithms used for solution of special case of non linear programming, namely quadratic programming. The solution of quadratic objective function has been found using numerical and statistical approaches. Numerical technique is based on Cholesky decomposition algorithm and statistical approach is based on Least squares technique. The selected model chosen for the purpose of solving quadratic programming problem is related to portfolio selection in presence of transaction costs. The objective is to minimize the sum of squares of error by estimating parameters. It was not the purpose of study to discuss all algorithms but an algorithm namely stepwise algorithm has been discussed in detail. Using stepwise technique, we have reduced quadratic programming problem into regression problem and found the values of estimated parameters. This approach has efficiently solved the quadratic programming problem and gave the optimum values of unknown parameters.