# Quantum Portfolio Optimization with Investment Bands and Target Volatility

**Authors:** Samuel Palmer, Serkan Sahin, Rodrigo Hernandez, Samuel Mugel, Roman Orus  
**arXiv:** [2106.06735](https://arxiv.org/abs/2106.06735)  
**Date:** 2021-06-12  
**Summary page:** https://www.summarizepaper.com/en/paper/2106.06735v4/

## Key points

- The paper presents a novel approach to solving the portfolio optimization problem using quantum computing.
- The authors demonstrate how to incorporate real-life constraints into the optimization problem in a simple manner that makes it amenable to quantum optimization algorithms.
- Explaining how to obtain the best investment portfolio with a given target risk, which is crucial for producing portfolios with different risk profiles that financial institutions typically offer.
- Showing how to implement individual investment bands, which are minimum and maximum possible investments for each asset, essential for imposing diversification and avoiding corner solutions.
- The authors build the constrained cost function as a quadratic binary optimization (QUBO) problem, which is the natural input of quantum annealers.
- They validate their implementation by finding optimal portfolios using D-Wave Hybrid and its Advantage quantum processor on portfolios built with all assets from S&P100 and S&P500 under realistic market conditions.
- In combination with clustering algorithms, the methods presented in this paper would allow replicating more complex indexes' behavior such as Nasdaq Composite or others. This feature would be particularly useful for building and replicating Exchange Traded Funds (ETF).
- Overall, this paper presents an innovative approach to portfolio optimization using quantum computing that addresses practical challenges faced by financial institutions while demonstrating its feasibility under realistic market conditions.

## Summary

In their paper titled "Quantum Portfolio Optimization with Investment Bands and Target Volatility," Samuel Palmer, Serkan Sahin, Rodrigo Hernandez, Samuel Mugel, and Roman Orus present a novel approach to solving the portfolio optimization problem using quantum computing. The authors demonstrate how to incorporate complex real-life constraints into the optimization problem in a simple manner that makes it amenable to quantum optimization algorithms. The paper's main contributions are twofold: first, the authors explain how to obtain the best investment portfolio with a given target risk. This is crucial for producing portfolios with different risk profiles that financial institutions typically offer. Second, they show how to implement individual investment bands, which are minimum and maximum possible investments for each asset. This is essential for imposing diversification and avoiding corner solutions. The authors build the constrained cost function as a quadratic binary optimization (QUBO) problem, which is the natural input of quantum annealers. They validate their implementation by finding optimal portfolios using D-Wave Hybrid and its Advantage quantum processor on portfolios built with all assets from S&P100 and S&P500. The results demonstrate that practical daily constraints found in quantitative finance can be implemented easily in current NISQ quantum processors using real data under realistic market conditions. In combination with clustering algorithms, the methods presented in this paper would allow replicating more complex indexes' behavior such as Nasdaq Composite or others. This feature would be particularly useful for building and replicating Exchange Traded Funds (ETF). Overall, this paper presents an innovative approach to portfolio optimization using quantum computing that addresses practical challenges faced by financial institutions while demonstrating its feasibility under realistic market conditions.