Pivoting Algorithm for Mean Lower Semi-Absolute Deviation Portfolio Optimization Model

Downside loss-averse preferences have seen resurgence in the portfolio management literature. Mean-lower semi absolute deviation (MLSAD) model is one of the most important mean-lower partial moment (MLPM) models. The MLSAD model is established and converted into a linear programming model. The pivoting algorithm for linear programming is presented to solve the model. The pivoting algorithm can deal with equality constraints, variables with lower and upper bounds, free variables directly and conveniently and need not add any auxiliary variables during the course of calculation. These excellent properties guarantee high computing efficiency of the algorithm. Based on the real trade data of Shanghai Security Exchange, the paper calculates the efficient frontier of the MLSAD model. The result shows that the algorithm has high computation efficiency.