Every investment involves some level of risk. Investors typically seek higher returns to compensate for increased investment risks. While higher risk may result in higher returns, an optimised portfolio will result in higher returns at a lower risk. However, the return on an investment is determined by both the risk and the investment strategy. Optimized investment strategy helps in making decisions about where and how to invest. Classical portfolio optimization techniques have been used for many years. However, these techniques rely on assumptions that the underlying data is normally distributed, which is not always the case in real-world scenarios. The goal of optimization is to maximise portfolio return for a given level of risk or decrease the risk for a given return (risk-return trade-off). This goal can be met by analysing historical performance, forecasting future prices, stock market bubbles, crashes, and a range of other parameters that can affect the portfolio's value. The computing time and complexity grow as the number of parameters increases. Quantum computing is a new technology that has the potential to revolutionise financial industries and offers a new approach to solving these problems.

Quantum Algorithms for Portfolio Optimization:

In quantum portfolio optimisation, three types of algorithms are commonly used.

1. Variational Quantum Eigen Solver
2. Quantum Approximate Optimisation Algorithm
3. Quantum Walk Optimization Algorithm

These algorithms can determine the optimal portfolio in polynomial time, which means they can handle significantly larger volumes of data much faster than classical algorithms.

Variational Quantum Eigen Solver (VQES):

VQES is a hybrid quantum-classical algorithm to find the minimum eigen value (factor by which asset price moved) associated with the lowest risk and the corresponding eigen vector (direction the stock value moved) representing the optimal asset allocation.  Eigen solvers explore different scenarios and parameters and analyse the impact of changes on portfolio performance. This capability allows investors to assess risk and return trade-offs under varying market conditions leading to more informed investment decisions.

Quantum Approximate Optimization Algorithm (QAOA):

QAOA is another hybrid quantum-classical algorithm that can provide better approximation results than any other classical algorithm now in use. Different portfolios with various probabilities are returned by the QAOA algorithm, along with corresponding average approximation ratios. Which means, the algorithm uses quantum mechanics to determine the most likely outcome of a given set of measurements. In the instance of portfolio optimisation, the algorithm calculates predicted returns and risk by identifying correlations between different assets based on the quantum state of the investment portfolio. This enables the algorithm quickly to determine the best combination of investments for maximising profits while minimising risk.

Quantum Walk Optimization Algorithm (QWOA):

QWOA is a newly developed quantum algorithm for finding solutions to the portfolio optimization problem. QWOA significantly reduces the search space, resulting in consistently better performance in configuring a high-quality portfolio using fewer iterations with a significantly lower standard deviation. QWOA significantly outperforms QAOA in terms of annual returns. Expected annual return and annual risk values ​​are obtained by multiplying the probability of each portfolio by the corresponding annual return and risk.

Gains from Quantum Portfolio Optimization

There are several benefits in using quantum portfolio optimization relative to classical computing-based methods.

1. Quantum computing can perform complex calculations much faster than classical computers. This enables investors to optimize large portfolios in near real-time, using models consuming wide range of variables and market conditions.
2. Non-normal distributions, which are common in real-world scenarios, can be accommodated effectively by quantum portfolio optimization. This means the algorithm can handle wide range of investment options and still deliver accurate results.
3. Quantum portfolio optimization can help investors manage risk more effectively. By calculating the expected risk of different investment combinations, the quantum algorithm can provide investors with a more accurate and insightful view of their portfolio's risk profile. This could help investors build more robust portfolios that are better able to withstand market volatility and economic shocks.
4. Finally, by using quantum computing, investors can identify investment opportunities that were previously unknown or too complex to analyse using classical algorithm. This could allow them to generate higher returns by making more informed investment decisions while taking advantage of market inefficiencies that may have been overlooked by other investors.

Developmental Challenges

While there are potential benefits to using quantum computing for portfolio optimization, there are some challenges to implementing quantum portfolio optimization that needs to be addressed. One of the biggest challenges facing the adoption of quantum computing in finance is the current limitations of hardware. While there has been significant progress in developing quantum hardware in recent days, it is still in development and are currently limited in terms of capacity and stability. This can make it difficult to scale quantum algorithms to handle real-world financial data. Alike any emerging technology, regulatory compliance must be adhered to, and ethical usage guard rails must be held on to while using quantum computing for portfolio optimization. Despite these challenges, the potential benefits of quantum portfolio optimization are significant.

Future Forward

Quantum portfolio optimization has the potential to revolutionize the finance industry by enabling investors to build more accurate and efficient portfolios. By using the above discussed quantum algorithms, investors could potentially optimize the portfolios in real-time, improve risk management and identify investment opportunities that were previously hidden or too complex to analyse using classical algorithms. However, there are several challenges that need to be addressed before quantum portfolio optimization becomes a reality. Some of them are the development of quantum hardware, specialised knowledge, expertise in both finance and quantum computing, regulatory and ethical considerations. Despite these challenges, many financial institutions and tech companies are investing heavily in quantum computing research and development. There have already been several successful demonstrations of quantum portfolio optimization using small-scale quantum computers. As quantum computing continues to develop, it is likely that more and more investors will turn to quantum algorithms to optimize their portfolios and maximize returns while minimizing risk. Also, Quantum Portfolio optimization will become an increasingly important tool for investment professionals and financial institutions.