The Multi-Horizon Dynamics of Risk and Returns

Abstract

I study the effects of changes in risk on asset prices across different time horizons (or time-scales) and provide a new insight into the dynamics of equity premia. I find that, contrary to the implication of standard models such as the Consumption-CAPM, risk premia are weakly related to consumption volatility at short horizons whereas long-run past volatility strongly determines the long-run dynamics of expected stock returns. More importantly I show that a model specified at a fixed time-scale may not necessarily lead to obtain a significant long-term risk-returns relation upon aggregation of the one-period dynamics of volatility and returns. I thus develop a consumption-based model that simultaneously characterizes both the short- and long-term behaviors of risk and returns and successfully replicates the pattern observed in the data. Whereas previous empirical literature has mainly focused on stock market volatility, when I estimate the model I am able to relate movements of equity premia at specific frequency intervals to sources of macroeconomic risk, as measured by conditional volatility of consumption. The empirical results emphasize the importance of simultaneously modeling consumption at multiple time-scales and point to changing consumption volatility as an important long-run priced factor.

Keywords: Risk-Return; Stock return predictability; Macroeconomic Uncertainty; Multi-scale time series models

JEL Classification: E32, E44, G11, G12