Predicting the Equity Premium with a High-Threshold Risk Level and the Price of Risk 

Abstract

Over 1990 to 2023, we show that time-variation in the US equity premium is captured well by a parsimonious model with the CBOE’s implied-volatility index VIX and the sentiment index of Baker and Wurgler (2006).   The equity premium declines linearly with sentiment but increases nonlinearly with VIX, stepping up appreciably when VIX exceeds a threshold around its 80th to 85th percentile.   For 6-month and 12-month forecasting horizons, the predictive adjusted R-squared values are about 19% and 29%, respectively. Our predictive findings are robustly evident for 1-, 3-, 6-, and 12-month horizons, in subperiods, for in-sample and out-of-sample evaluations, and when adding control variables.    Our interpretation is that a high-VIX threshold identifies episodes of market stress that generally have both a sharply higher level of risk and an elevated price of risk. Sentiment complements VIX and seems particularly effective in identifying times with a low price of risk.

Keywords: nonlinear threshold risk-return relation, investor sentiment, stock market volatility

JEL Classification: G11, G12