Portfolio optimisation is a process used in finance to select the best portfolio (collection of assets) from a suite of potential portfolios that meet certain criteria. To-date, the Markowitz mean-variance optimisation model stands out as the most widely accepted formula for portfolio optimization.

Since these approaches rely on several assumptions, they may not fully capture the complexities of real-world market dynamics. Most of these assumptions are made to ensure that the problems are solvable in polynomial time (P). However, quantum computing has enabled solving certain Non-deterministic Polynomial Time problems (NP hard and NP-complete).

Thus, we reformulated the Markowitz’s model to be solved using quantum annealing. In contrast to the traditional approach, where the output is a proportion of the budget to be allocated to each asset, the reformulated approach generates the number of units to be purchased in each asset. This ensures an investor will not get stuck at a fractional number of assets to be purchased, as in real-world applications, assets are traded in discrete units. However, the conversion will not propose a new model, instead it will bring in additional constraints that are more realistic to cap one of the unrealistic assumptions held by the base model - “assets are infinitely divisible”.

Using real-time quantum cloud service provided by D-wave, Leap, the formulated algorithm was fitted to the daily profit of 113 stocks obtained from Yahoo Finance from the beginning of 2000 until end-2023.

In conclusion, this white paper discusses the complete process of formulating the Markowitz model, the results and a comparison of the QC approach with the results from the vanilla model run on a classical computer.

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