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Quantum Hierarchical Risk Parity by Maxwell Rounds

At QuantCon NYC 2017, Maxwell Rounds presented the methodologies and results behind the algorithm that has been developed by 1QBit, named Quantum Hierarchical Risk Parity, or QHRP. This is an extension of the work done by QuantCon 2018 keynote speaker Dr. Marcos López de Prado on Hierarchical Risk Parity in his paper Building Diversified Portfolios that Outperform Out-of-Sample.

Quantum Hierarchical Risk Parity - A Quantum Inspired Approach to Portfolio Risk Minimization by Maxwell Rounds, Finance Specialist at 1QBit

QHRP tackles the problem of minimizing the risk of a portfolio of assets using a quantum-inspired approach. Although the ideas surrounding this go back to Markowitz’s mean-variance portfolio optimization of 1952’s Portfolio Selection, we have applied recent quantum-ready machine learning tools to the problem to demonstrate strong performance in terms of a variety of risk measures and lower susceptibility to inaccuracies in the input data. The quantum-ready approach to portfolio optimization is based on an optimization problem that can be solved using a quantum annealer. The algorithm utilizes a hierarchical clustering tree that is based on the covariance matrix of the asset returns. The results of real market data used to benchmark this approach against other common portfolio optimization methods will be shared in this presentation.

 Hierarchical Risk Parity

One of 1QBit’s advisors, Marcos Lopez de Prado, a renowned financial academic and keynote speaker at QuantCon 2017, developed an algorithm based on risk parity that he named hierarchical risk parity, or HRP, which utilizes the same basic idea as risk parity but does so by forming the portfolio across a hierarchical tree built from correlation data. This has the benefit of including some of the information in the correlations commonly used in portfolio construction, but in a manner that tends to reduce overfitting. Marcos’ results were exciting, and when he showed them to 1QBit, we took an interest in applying Ising-based formulations to this problem.


1QBit examined the method of hierarchy construction that Marcos used, a greedy heuristic known as agglomerative clustering. During a previous collaboration with NASA, 1QBit’s researchers learned of a NP-hard approach to clustering based on the max-cut algorithm, which we refer to as k-maxcut clustering. We implemented k-maxcut using the 1QBit SDK tools and used it to build a hierarchy tree in an approach known as divisive clustering. We suspected that we might be able to produce better results than Marcos with a more globally optimal procedure. We saw positive results.


Whereas Marcos saw a 10% improvement in measured risk out of sample in his trials versus a standard risk parity algorithm, we saw a 10% improvement on top of Marcos’ results using k-maxcut clustering. This resulted in a 20% total improvement, meaning that we were finding portfolios with 16% annualized standard deviation of returns, down from 20%, or 24% annualized standard deviation, down from 30%. These results vary somewhat based on the assets involved and the characteristics of their randomness, and as a result we have explored the specific circumstances in which QHRP is the most effective. We have released a white paper on the results discussing our findings.

QuantCon NYC 2018

QuantCon returns to NYC for the fourth consecutive year April 27th-28th. We have just announced that Dr. Marcos López de Prado, multi-billion dollar fund manager and author, and Dr. Lauren H. Cohen, L.E. Simmons Professor at Harvard Business School will be our keynotes. They will be presenting new talks you don't want to miss! Reserve your spot at


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