Long-horizon asset and portfolio returns revisited: Evidence from US markets

This study revisits the widely used assumptions in long-term asset allocation: the normal distribution of long-horizon returns and the negligible impacts of estimation errors on the expected returns. This study uses the innovative simulation method of Fama and French (2018) for horizons of up to 30 years. The data in use are the U.S. value-weighted market returns of stocks, Treasury bonds, Treasury bills, commodities, and real estate investment trusts (REITs) for the 1970-2018 period. Distributions of continuously compounded returns from the 10-year horizon are normal across asset classes. Stock return distribution has the slowest rate of convergence to normality among groups of assets. Estimation errors of the expected monthly returns or annual returns are negligible relative to the standard deviation of the unexpected return. As the imprecisions persist over the investment horizons, the estimation errors of the monthly return have a strong effect on the variability of long-term asset returns. This study has significant implications for academics and investors based on the commonly accepted assumptions of long-term asset allocation.