l0- Norm Sparse Portfolio Optimisation using Proximal Spectral Gradient Method on Malaysian Stock Market

In this paper, we introduce a modified norm-constraint mean-variance portfolio selection method. First, we use the Augmented Lagrangian method (ALM) to convert the objective function to an unconstrained objective function. Then we apply the proximal spectral gradient method (PSG) onto the unconstrained objective function to find an optimal sparse portfolio. This novel sparse portfolio optimization procedure encourages sparsity in the entire portfolio using norm. The PSG utilizes a multiple damping gradient (MDG) method to solve the smooth terms of the function. The step size is computed using the Lipschitz constant. Also, PSG uses the iterative thresholding method (ITH) to solve norm and induce the sparsity of the portfolio. The performance of the PSG is illustrated by its application on the Malaysian stock market. It is found that PSG’s sparse portfolio outperforms the equal weightage portfolio when the initial portfolio size is around 100 stocks and is prefiltered using the Sharpe ratio or the coefficient of variation.