Abstract
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.
Highlights
We present a novel clustering-based formulation for cardinality-constrained indextracking, a common task in the financial industry
Our work is an empirical implementation of the K-medoid clustering technique expressed as a quadratic unconstrained binary optimization model (QUBO) and applied to market graphs, for the purpose of obtaining cardinality-contrained index-tracking portfolios
The main contribution in this paper consists of bridging these pieces of complementary but disjoint work, to formulate the index-tracking problem as a QUBO K-medoid clustering of a broader market graph problem
Summary
We present a novel clustering-based formulation for cardinality-constrained indextracking, a common task in the financial industry We apply it to data from eight different equity indices from the OR-Library open-source index-tracking data sets and obtain very promising results. Our work is an empirical implementation of the K-medoid clustering technique expressed as a quadratic unconstrained binary optimization model (QUBO) and applied to market graphs, for the purpose of obtaining cardinality-contrained index-tracking portfolios. Our QUBO formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the clustering problem Using these novel architectures we obtain better solutions within small fractions of the time required to solve equivalent problems formulated in traditional constrained form and solved on traditional hardware. We apply our technique to a set of equity indices
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