HIT: Solving Partial Index Tracking via Hierarchical Reinforcement Learning

Partial index tracking (PIT) is a popular passive investment strategy aiming at replicating the performance of a market index (e.g., S&P 500). Existing PIT methods typically treat it as a regression problem and divide it into two tasks: (i) asset selection (determining which assets to choose from the index constituents) and (ii) asset allocation (deciding how to allocate capital among the selected assets). However, these methods either optimize these two tasks jointly, which has been proven to be NP-hard and inefficient when tracking large-scale constituent indices (e.g., Russell 2000), or attempt an independent optimization, lacking a connection to ensure collaborative optimization. In this paper, we present a hierarchical model for partial index tracking (HIT), which formulates PIT as a hierarchical Markov decision process (MDP) and is optimized via hierarchical reinforcement learning (HRL). HIT consists of (1) a high-level policy learns to select assets from constituents to handle task (i) and (2) a low-level policy learns to allocate capital weights among the selected assets to handle task (ii). We further propose a novel cost-sensitive reward function that serves as a connection to collaboratively optimize the two policies, aiming to replicate the index closely while considering transaction cost. Compared with existing jointly optimized approaches, our model simplifies the problem by learning separate policies for the two tasks, and the reward function serves as a connection to ensure collaborative optimization between them, avoiding challenges faced by joint optimization methods in existing literature. Remarkable performance across 6 benchmarks, ranging from small to large-scale constituents demonstrate the superiority of HIT. Moreover, the experiments conducted on a real-world market dataset spanning over 10 years show its effectiveness and practicality.