Estimating the market risk premium for valuations: arithmetic or geometric mean or something in between?

It is well-known that using arithmetic averages of yearly return observations leads to downward biased discount rates estimations. Well-known corrections, however, lead to upward biased results under the presence of negative serial correlation. Using a simulation analysis, we first show that a specific variant of the Cooper estimator, labelled as C4 in this paper, leads to robust estimations even under the presence of both serial correlation and heteroscedasticity. We also show that among the simple estimators, i.e. the arithmetic (AM) or geometric mean (GM) or the mean of both (MoM), the first one tends to perform best unless there is a high degree of negative serial correlation. In that case using the so-called mean of means rule would be better. Secondly, using data from Jordà et al. (Q J Econ 134(3):1225–1298, 2019) we find negative serial correlation and heteroscedasticity in market risk premia to be a widely spread phenomenon. Finally, we use this data to derive presumably least biased market risk premia estimations based on the C4 estimator. For the majority of the countries we find that these estimations are somewhere between the arithmetic and geometric average. When comparing these simple estimators among each other based on the empirical data, we find the arithmetic mean and mean of means to perform almost equally well, while the geometric mean clearly underperforms. Moreover, we found some evidence that the MoM is slightly outperforming the AM under a local CAPM perspective, while the opposite tends to be true under a global CAPM perspective. This leads us the cautious conclusion that the mean of means rule used by practitioners has some empirical rationale when there is evidence for substantial negative serial correlation.