High Speed Hill Climbing Algorithm for Portfolio Optimization

Abstract

Portfolio can be defined as a collection of investments. Portfolio optimization usually is about maximizing expected return and/or minimising risk of a portfolio. The mean-variance model makes simplifying assumptions to solve portfolio optimization problem. Presence of realistic constraints leads to a significant different and complex problem. Also, the optimal solution under realistic constraints cannot always be derived from the solution for the frictionless market. The heuristic algorithms are alternative approaches to solve the extended problem. In this research, a heuristic algorithm is presented and improved for higher efficiency and speed. It is a hill climbing algorithm to tackle the extended portfolio optimization problem. The improved algorithm is Hill Climbing Simple–with Reducing Thresh-hold Percentage, named HC-S-R. It is applied in standard portfolio optimization problem and benchmarked with the quadratic programing method and the Threshold Accepting algorithm, a well-known heuristic algorithm for portfolio optimization problem. The results are also compared with its original algorithm HC-S. HC-S-R proves to be a lot faster than HC-S and TA and more effective and efficient than TA.

Keywords: Portfolio optimization, Hill climbing algorithm, Threshold percentage, Reducing sequence, Threshold Acceptance algorithm.