Quantum Computing Enhances Stock Portfolio Optimization, Study Finds

A study by researchers from Deutsche Börse AG and Technische Hochschule Brandenburg explores the use of quantum computing in optimizing investment portfolios. The team focuses on the Markowitz portfolio theory, which assumes stocks can be bought in fractional increments, a challenge in real-world scenarios.

They propose a discrete Markowitz portfolio theory (DMPT) considering finite budgets and integer stock weights. The study also incorporates ESG ratings for EURO STOXX 50 index stocks, balancing risk, return, and ESG-friendliness. Quantum computing, particularly quantum annealers, offers a more efficient solution to DMPT problems, outperforming traditional rounding methods.

What is the Quantum Computing Approach to ESG-friendly Stock Portfolios?

The study by Francesco Catalano, Laura Nasello, and Daniel Guterding from Deutsche Börse AG and Technische Hochschule Brandenburg, Germany, explores the application of quantum computing in optimizing investment portfolios. The researchers focus on the Markowitz portfolio theory (MPT), a traditional portfolio optimization method that assumes stocks can be bought in fractional increments. However, this approach faces challenges when applied to real-world scenarios where stocks are typically not tradeable in fractional increments.

To address this issue, the researchers propose a discrete Markowitz portfolio theory (DMPT) that considers finite budgets and integer stock weights. However, solving DMPT problems is a non-polynomial (NP) hard problem. The researchers suggest that recent advancements in quantum processing units (QPUs), including quantum annealers, make solving DMPT problems feasible.

The study establishes a mapping between continuous and discrete Markowitz portfolio theories and finds that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. The DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods even for moderate budgets.

How Does Quantum Computing Enhance ESG-Friendly Investments?

The researchers also respond to the growing demand for environmentally and socially responsible investments. They enhance their discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks.

They introduce a utility function incorporating ESG ratings to balance risk, return, and ESG-friendliness. This approach could have significant implications for ESG-aware investors, providing them with a more effective and efficient method of optimizing their portfolios while also considering their ESG commitments.

What are the Challenges and Solutions in Portfolio Optimization?

Every investor’s primary goal is to find an optimal balance between risk and return. Markowitz formalized this problem by finding optimal weights for each security so that the portfolio maximizes the return and minimizes the risk.

However, this approach faces problems when implementing such portfolios in a realistic environment where traded contracts are discrete, and securities prices are finite. In practice, this challenge is easily overcome by rounding to the nearest multiple of the securities price. However, for small and intermediate portfolios, the rounding may affect the relative weighting significantly and create suboptimal implementations of originally optimal portfolios.

How Does Discrete Markowitz Portfolio Theory (DMPT) Work?

Discrete extensions of the Markowitz portfolio optimization, where the discreteness of securities contracts is considered from the start, have been studied for a long time. Such discrete portfolios also facilitate the inclusion of further realistic features such as transaction costs or Boolean constraints on stock selection.

However, the discrete Markowitz portfolio theory (DMPT) is a non-polynomial hard problem, even if the trajectory problem is only formulated for a single period. The main problem is that the number of possible portfolio compositions grows factorially with the number of assets in the investment universe and the allowed number of assets in the portfolio.

How Does Quantum Computing Address the Challenges in Portfolio Optimization?

In recent years, the rapid progress in manufacturing of quantum processing units (QPUs) and the development of hybrid quantum-classical workflows has reignited interest in this type of problem. Quantum computing, particularly quantum annealers, has shown potential in solving DMPT problems, which are not feasible on classical machines.

These problems have been approached using heuristic and approximate methods on classical computers, which do not guarantee an optimal solution. However, quantum computing offers a more efficient and potentially optimal solution to these problems, making it a promising tool for portfolio optimization.