Equity Risk Premium and Time Horizon: what do the French secular data say ?

We consider a representative investor whose wealth is shared between a replica of the equity market portfolio and the riskless asset, and who maximizes the expected utility of their future wealth. For a given time-horizon, the solution of this program equalizes the required risk premium to the product of price of risk by the expected variance of stock returns. As a tentative to capture exogenous disturbing effects, the term spread of interest rates and US equity risk premia complement this relationship. Two traditional horizons are considered: the one-period-ahead horizon characterizing the ‘short-term’ investor and the infinite-time horizon characterizing the ‘long-term’ investor. For each horizon, expected returns are represented by mixing the three traditional adaptive, extrapolative and regressive process, expected variance is represented by a GARCH process, while the unobservable time-varying price of risk is estimated according to the Kalman filter methodology. Based on annual French data established by Le Bris and Hautcoeur (2010), large disparities in the dynamics of the short- and long term observed premia are evidenced from 1872 to 2018, while, due to risky arbitrage and transaction costs, the observed premia appeared to gradually converge towards their required values. Overall, although the French market had experienced very strong historical shocks, our model provides both measurements and explanations of French short- and long-term risk premia and so shed some additional light on the existence of a time-varying term structure of equity risk premia. Despite differences, results on the French market are rather in accordance with those by Prat (2013) based on US secular data.