Enhancing stock ranking forecasting by modeling returns with heteroscedastic Gaussian Distribution

Accurately selecting stocks with the highest returns is crucial for profitable investing. However, predicting stock price movements is challenging due to the high degree of randomness caused by factors such as market opacity, unexpected events, erratic trades, etc. Previous research has primarily focused on extracting more information from inputs to map to the observed returns, such as modeling the complex relations of different stocks. However, they overlooked the uncertainty of returns caused by the randomness market. To mitigate it, we propose a novel analytical framework. The starting point is that the stock returns follow some distributions, so the observed returns are samples from them, and the variances are the source of randomness. After analysis, past studies were equivalent regarding the returns of different stocks at each time following homoscedastic Gaussian distributions, aiming to predict the mean of these distributions. We find that the hypothesis to be unreasonable and extend these distributions to the heteroscedastic case, presenting a revised model structure and learning objectives. The proposed method aims to simultaneously predict the mean and the standard deviation of distributions from inputs, and the model is trained based on the maximum likelihood principle. Experiment results on the stock members of the CSI 100, 300, and 500 Chinese market indexes show significant improvements compared with the previous methods. The annualized return of the Top 20 stock portfolios improved absolutely 2%, 20%, and 50%, proving the effectiveness of our framework. We discuss the roles of the obtained mean and standard deviation in pursuing more profits, and we extend our theory to a more general form through mathematical derivation.

Recommended citation: Yang J, Fang R, Zhang M, et al. Enhancing stock ranking forecasting by modeling returns with heteroscedastic Gaussian Distribution[J]. Physica A: Statistical Mechanics and its Applications, 2025, 664: 130442.
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