Quantitative trading and investment decision making are intricate financial tasks in the ever-increasing sixty trillion dollars global stock market. Despite advances in stock forecasting, a limitation of existing methods is that they treat stocks independent of each other, ignoring the valuable rich signals between related stocks’ movements. Motivated by financial literature that shows stock markets and inter-stock correlations show scale-free network characteristics, we leverage domain knowledge on the Web to model inter-stock relations as a graph in four major global stock markets and formulate stock selection as a scale-free graph-based learning to rank problem. To capture the scale-free spatial and temporal dependencies in stock prices, we propose ASTHGCN: Attentive Spatio-Temporal Hyperbolic Graph Convolution Network, the first neural hyperbolic model for stock selection. Our work’s key novelty is the proposal of modeling the complex, scale-free nature of inter-stock relations through temporal hyperbolic graph learning on Riemannian manifolds that can represent the spatial correlations between stocks more accurately. Through extensive experiments on long-term real-world data spanning over six years on four of the world’s biggest markets: NASDAQ, NYSE, TSE, and China exchanges, we show that ASTHGCN significantly outperforms state-of-the-art stock forecasting methods in terms of profitability by over 22%, and risk-adjusted Sharpe Ratio by over 27%. We analyze ASTHGCN’s components’ contributions through a series of exploratory and ablative experiments to demonstrate its practical applicability to real-world trading. Furthermore, we propose a novel hyperbolic architecture that can be applied across various spatiotemporal problems on the Web’s commonly occurring scale-free networks.