Machine Learning Predictions of Stock Returns and Volatilities

Are machine learning predictions for both stock returns and return volatilities attractively exploitable? In their March 2025 paper entitled “Deep Learning of Conditional Volatility and Negative Risk-Return Relation”, Qi Wu, Xing Yan and Wenxuan Ma apply non-linear deep learning models (neural networks of one to five layers) and likelihood estimation to forecast next-month stock returns and volatilities. They select model settings and hyperparameters based on established practices from the literature and common experience, without extensive searching. They apply the neural network models to 153 firm-specific variables for U.S. stocks annually during 1991 through 2020 using 11-year rolling windows (seven years of training, three years of validation and one year of testing) for a total of 20 years of out-of-sample testing. Specifically, they each month for each model variation:

• Double sort stocks first on next-month predicted volatility and then on next-month predicted return.
• Reform portfolios that are long (short) the tenth, or decile, of stocks with the best (worst) expected returns.

They also consider single-variable sorts for benchmarking. They focus on gross Sharpe ratio of resulting portfolios as the key performance statistic. Using monthly data as specified for a broad sample of U.S. stocks, excluding those priced under $1.00 or with market capitalizations below $5 million, during January 1991 through December 2020 (18,916 stocks, with some data grooming), they find that:

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