Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia

In considering a long-term investment in a common stock, an investor wants an estimate of the stock's long-run risk premia (and thus the long-run expected returns). Similarly, in evaluating a capital investment project, a firm seeks a reliable estimate of the required return on the proposed project. Given the empirical evidence of mean reversion in long-horizon common stock returns, we find that sample estimates based on the arithmetic or geometric averages of the past returns are biased.