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It is well established in the literature the ex post risk premium is higher than the ex ante risk premium and can vary substantially, but little research has been conducted in modelling the dynamic process between the two. This paper contributes by providing a theoretical framework to model the long-term dynamic relationship between the two risk premia in the UK and US. Using an Ornstein-Uhlenbeck (OU) ex ante model, that dominates several competitive models, we reveal slow reversion toward a stable long term ex post mean of 4% in both the UK and US markets. Results extend prior research by using an extended data set (1923–2019), providing a more precise and flexible estimation model, confirming that inflation and interest rates provide additional explanatory power over the long term but significantly less so across several regime shocks, especially during high inflation and periods of negative risk premia. By highlighting potential mispricing through a flexible approach we provide financially useful information to investors and regulators, particularly when central banks are manipulating equity prices.

Long term equity risk premiums in the UK and US: A cautionary tale of weak mean reversion