Market Graph Clustering via QUBO and Digital Annealing

We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimization modeling, to formulate the index-tracking problem as a binary quadratic K-medoid graph-clustering problem. Our initial results show we accurately replicate the returns of various market indices, using only a small subset of their constituent assets. Moreover, our binary quadratic formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the problem and obtain solutions faster than with traditional architectures and solvers.

我们提出了一种用于基数约束指数跟踪的新技术，这是金融行业中的一项常见任务。我们的方法基于市场图模型。我们将参考指数建模为市场图，并将指数跟踪问题表述为二次K - 中心点聚类问题。我们利用专门构建的硬件架构来规避该问题的NP - 难性质，并高效地求解我们的公式。本文的主要贡献是将文献中三个独立的领域——市场图模型、K - 中心点聚类和二次二进制优化建模——联系起来，将指数跟踪问题表述为二进制二次K - 中心点图聚类问题。我们的初步结果表明，我们仅使用其成分资产的一小部分就能够准确地复制各种市场指数的回报。此外，我们的二进制二次公式使我们能够利用近期的硬件进步来克服该问题的NP - 难性质，并且比使用传统架构和求解器更快地获得解决方案。