While antibodies provide significant protection from SARS-CoV-2 infection and disease sequelae, the specific attributes of the humoral response that contribute to immunity are incompletely defined. In this study, we employ machine learning to relate characteristics of the polyclonal antibody response raised by natural infection to diverse antibody effector functions and neutralization potency with the goal of generating both accurate predictions of each activity based on antibody response profiles as well as insights into antibody mechanisms of action. To this end, antibody-mediated phagocytosis, cytotoxicity, complement deposition, and neutralization were accurately predicted from biophysical antibody profiles in both discovery and validation cohorts. These predictive models identified SARS-CoV-2-specific IgM as a key predictor of neutralization activity whose mechanistic relevance was supported experimentally by depletion. Validated models of how different aspects of the humoral response relate to antiviral antibody activities suggest desirable attributes to recapitulate by vaccination or other antibody-based interventions.