This article considers the potential statistical problems resulting from the use of averaged rather than end-of-period data in financial research. Averaged data are widely employed throughout the literature without explicit recognition that the use of such data results in biased estimates of the...

We develop a simple measure of volatility based on extreme-day returns and apply it to market returns during 1885 - 2002. Because returns are not normally distributed, the extreme-day measure, which is distribution free, might provide a better measure of stock market risk than the traditional...

This article examines the changing nature of U.S. stock and bond risk from 1871 through 2000 and the implications for asset allocation. Using geometric means and standard deviations, we examine nominal and inflation-adjusted monthly returns over nonoverlapping 5-year periods, as well as annual...