Predicting the equity premium with a high-threshold risk level and the price of risk

Over 1990 to 2023, we show that time variation in the U.S. 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, Journal of Finance, 61, 1645–1680). 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- and 12-month forecasting horizons, the predictive adjusted R² 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.