Bottom-up ERP Estimation by Deep Learning

Do stock-by-stock return forecasts from deep learning produce an exploitable aggregate equity risk premium (ERP) forecast? In the January 2025 revision of their paper entitled “The Aggregated Equity Risk Premium”, Vitor Azevedo, Christoph Riedersberger and Mihail Velikov predict ERP by first applying deep learning to predict returns for individual U.S. stocks and then aggregating these returns at the market level. The firm-level forecasts come from combined outputs of several neural networks of varying complexity applied to 290 firm-level characteristics, 14 U.S. economic variables and 49 industry classification indicators. They iterate these forecasts annually using an expanding training window and a rolling six-year validation window. For comparison, they consider some conventional ERP forecasting approaches. They quantify the economic value of aggregate ERP forecasts via a stock market timing strategy that each month allocates to stocks or U.S. Treasury bills with a 50% leverage limit and conservative 0.5% portfolio rebalancing frictions. Using the specified inputs during March 1957 through December 2021 (with out-of-sample testing commencing January 2000), they find that:

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