Index tracking and ETF construction are constrained optimization problems where fund managers need to replicate a benchmark index while restricting the number of assets held, managing transaction costs, and staying within allocation bounds. These cardinality constraints make the problem non-convex, placing it outside the reach of standard quadratic solvers. Ally Financial engaged Multiverse Computing and Protiviti to explore whether quantum methods could solve it at production scale.
The Challenge
Classical portfolio optimizers handle continuous, convex problems efficiently, but cardinality-constrained portfolios require discrete variable formulations that cause classical solvers to scale poorly as asset universes grow. Ally Financial needed a solution capable of constructing index-tracking portfolios across large asset universes while enforcing hard limits on the number of positions held. Standard commercial tools could not handle this combination of scale, cardinality constraints, and dynamic rebalancing with integrated transaction cost modeling across the NASDAQ-100 and S&P 500.