Abstract
This study focuses on efficient asset allocations that properly include T-bills, T-bonds, and the S&P 500 stock index. It checks that their annual real rates of linear return are both normal and almost lognormal. It reexamines how efficient portfolios based on the rates of linear return may turn into efficient portfolios based on the rates of logarithmic return. It finds that each efficient asset allocation has the lowest possible standard deviation as well as the highest possible arithmetic and geometric means. It eventually reconsiders the relationship between the confidence interval of a geometric mean and an expected long-run capital accumulation. As a consequence, it bridges a gap in the scientific literature by enabling financial advisors to trade off the mean rate of return on a portfolio more rigorously against the value at risk.