Large-Scale Asset Selection via Metric Dependence with Enriched High Frequency Information
Large-scale portfolio choice is highly sensitive to estimation error, making the preliminary asset selection essential in empirical implementation. Existing selection rules typically rely on scalar returns or low dimensional high frequency summaries, and thus discard intraday risk dynamics that may be relevant for risk adjusted allocation. We propose Metric Dependence Screening (MDS), an asset selection procedure that incorporates high frequency information as object valued data. Each asset day observation is represented as a point-curve object combining daily return with an intraday risk state curve, equipped with a weighted product metric that preserves both reward information and within day risk dynamics. MDS ranks assets by a Fr\'echet variation based dependence score, measuring how much a risk adjusted target explains the metric dispersion of the asset representations. This yields a simple two stage portfolio procedure: MDS first reduces the investable universe, and standard mean-variance or minimum variance allocation is then applied. We develop a target slicing estimator and establish concentration, sure selection, and rank consistency guarantees under $\alpha$-mixing time series dependence and ultrahigh dimensionality. Simulations show that MDS performs well across both Euclidean and non-Euclidean settings. Using high frequency data for $2938$ Chinese A-share stocks from July 2023 to December 2025, we demonstrate that MDS improves out of sample portfolio performance over return based and scalar dependence based benchmarks, highlighting the value of preserving intraday risk dynamics.