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 their program equalizes the required risk premium to the product of price of risk by the expected variance of stock returns. As a tentative, 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. Expected returns are represented by mixing the three traditional adaptive, extrapolative and regressive process, expected variances are represented by GARCH process, while unobservable prices of risk are estimated according to the Kalman filter methodology. Based on annual French secular data elaborated 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. Due to risky arbitrage and transaction costs, the observed premia appeared to gradually converge towards their required values. Overall, our model simultaneously provides 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 some differences, these results are rather in accordance with those by Prat (2013) using secular US data