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This article develops a probabilistic argument under the assumption that return data are generated by a multivariate L\u00e9vy process and shows that linear factor models are asymptotically adequate as the return frequency declines. Rate-of-convergence results are provided assuming finite or infinite second moments and the moment conditions that determine the convergence rate are analyzed. Separately, we consider the combination of cross-sectional and temporal aggregation, which concerns portfolio applications, and we find that the model error of the linear framework can be smaller for portfolios than individual stocks. 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