A Forest Full of Risk Forecasts for Managing Volatility

Abstract

We propose a novel approach to cross-sectional forecasting of stock return volatility, by utilizing a heterogeneous autoregressive (HAR) model with time-varying parameters in the form of a local linear forest. Unlike traditional random forests, which approximate volatility nonparametrically through local averaging, the foundation of our forest is composed of HAR panel models. These local models capture established linear relationships in realized variances, while the trees are utilized to model nonlinearities and interactions. This approach allows the model coefficients to be driven by both idiosyncratic stock information and changing market conditions. Our empirical analysis demonstrates our model’s superior risk forecasting performance across multiple forecast horizons and 186 S&P 500 constituents, resulting in significantly higher utility for volatility-managed investments. Furthermore, this superior performance of the HAR forest is observed uniformly across firm characteristics.

Keywords: Risk management, volatility forecasting, local linear forest, firm characteristics, pooled estimation

JEL Classification: C32, C53, C55, C58, G17