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# Partial Index Tracking: A Meta-Learning Approach

*Proceedings of The 2nd Conference on Lifelong Learning Agents*, PMLR 232:415-436, 2023.

#### Abstract

Partial index tracking aims to cost effectively replicate the performance of a benchmark index by using a small number of assets. It is usually formulated as a regression problem, but solving it subject to real-world constraints is non-trivial. For example, the common $\ell_1$ regularised model for sparse regression (i.e., LASSO) is not compatible with those constraints. In this work, we meta-learn a sparse asset selection and weighting strategy that subsequently enables effective partial index tracking by quadratic programming. In particular, we adopt an element-wise $\ell_1$ norm for sparse regularisation, and meta-learn the weight for each $\ell_1$ term. Rather than meta-learning a fixed set of hyper-parameters, we meta-learn an inductive predictor for them based on market history, which allows generalisation over time, and even across markets. Experiments are conducted on four indices from different countries, and the empirical results demonstrate the superiority of our method over other baselines. The code is released at https://github.com/qmfin/MetaIndexTracker.