Equity Risk Premium and Time Horizon : What do the U.S. Secular Data Say ?

An ex-ante equity risk premium is the difference between the expected return of a risky asset at time t for a given future time horizon and an equivalent maturity risk-free interest rate. Using annual US secular data from 1871 to 2008, this study aims to model simultaneously the measures and the explanations of ex-ante equity risk premia for two polar horizons: the one period ahead horizon (i.e. the "short term" premium) and the infinite time horizon (i.e. the "long term" premium). Expectations being represented by traditional adaptive processes, large disparities in the dynamics of the two premia are evidenced. According to the conditional CAPM, each premium is at time t explained by the product of the price of risk by the expected variance of returns, these two magnitudes being horizon dependant. The expected variances depend on the past values of the centered squared returns (we found 5 and 8 years for the one year and the infinite horizon, respectively). For each horizon, the price of risk is determined by a spread of interest rates capturing economic factors of uncertainty and by an unobservable variable determined according to the kalman filter methodology (i.e. a state variable). The state variables are supposed to capture the influence of hidden variables and of non directly measurable psychological effects. The model gives a valuable representation of the "short term" and "long term" premia.