Models based on factors such as size, value, or momentum are ubiquitous in asset pricing. Therefore, portfolio allocation and risk management require estimates of the volatility of these factors. While realized volatility has become a standard tool for liquid individual assets, this measure is...

Researchers and practitioners employ a variety of time-series processes to forecast betas, using either short-memory models or implicitly imposing infinite memory. We find that both approaches are inadequate: beta factors show consistent long-memory properties. For the vast majority of stocks,...

We build an equilibrium model to explain why stock return predictability concentrates in bad times. The key feature is that investors use different forecasting models, and hence assess uncertainty differently. As economic conditions deteriorate, uncertainty rises and investors' opinions...

We derive a nonparametric test for constant (continuous) beta over a fixed interval of time. Continuous beta is defined as the ratio of the continuous covariation between an asset and observable risk factor (e.g., the market return) and the continuous variation of the latter. Our test is based...

This paper analyzes the implications of autoregressive betas in single factor models for the statistical properties of stock returns. It is demonstrated that this assumption alone is sufficient to account for the most important stylized facts of stock returns, namely conditional...

In this paper, we examine the Nigerian stock market sector returns and estimate the bull and bear betas using the Logistic Smooth Threshold Market (LSTM) model. The LSTM model specification follows from the linear Constant Risk Market (CRM) model. We estimate the LSTM model for the overall...

This paper applies machine learning algorithms to the modeling of realized betas for the purposes of forecasting stock systematic risk. Forecast horizons range from 1 week up to 1 month. The machine learning algorithms employed are ridge regression, decision tree learning, adaptive boosting,...

We propose a new approach to imposing economic constraints on forecasts of the equity premium. Economic constraints are used to modify the posterior distribution of the parameters of the predictive return regression in a way that better allows the model to learn from the data. We consider two...