ianmadlenya / modeling-portfolio-optimization Goto Github PK

This repository contains modeling portfolio optimization using AMPL programing language.

Problem Formulation: Invest the entirety of capital K in an asset universe comprising N securities. No short-sell is allowed. Denote the proportion of the capital invested in asset i by W_i. The allocation policy is based on the variants of the mean-variance (Markowitz) portfolio optimization model. The problem is to minimize the variance of the portfolio's return given that an expected return will be at least or equal to a threshold value R.

a) Formulate portfolio optimization problem as a quadratic optimization.

b) Provide an equivalent second-order cone programming formulation of part a).

c) Provide an AMPL code for the formulation of parts a) and b). Add a constraint that stipulates that one can invest in at most 12 securities and set the minimal level of expected return to 5%.