Stock Portfolio Optimisation

Abstract

In the competitive business of algorithmic trading and capital management new methods for determining optimal investments are always needed to maintain competitive advantage. In this thesis project we design, implement and investigate an algorithm for stock portfolio composition based on Markowitz’s modern portfolio theory [1]. In it’s original formulation modern portfolio theory uses past share returns to find an optimal portfolio, in our model we have replaced this for company net profits. We hope that as this new input data carries direct information on the companies’ operations and profitability our model will have better grounds to compose a portfolio. The model is implemented with the CVXOPT library [2] as quadratic program solver and tested on a set of companies having shares listed on the Nasdaq Stockholm Stock exchange in the years 2010 to 2020. The results show that our model succeeds in composing stock portfolios. However, the portfolios do suffer from some issues where the main one is an imbalance problem, in general a very large portion of the capital is invested in the company with the smallest net profit variance. This problem derives from the fact that the correlation between companies’ net profit is small compared to the variance of net profit. The objective function to be minimised in modern portfolio theory is the portfolios’ variance, due to the variance-covariance size difference this function depends mainly on the companies’ variance. This issue is mitigated, but not completely resolved, by applying different conditions to the optimisation problem. The portfolio value development is also heavily influenced by the optimisation conditions. Some conditions on the company net profits results in portfolios that outperform a market cap weighted index during the time period 2015 to 2020. It is noteworthy that all generated portfolios lose more value than the comparison index during the 2020 corona virus economic crisis.