Mean-reversion risk and the random walk hypothesis

The nature of risk and long-term returns is not fully understood. There is need for a measure of long-term risk at multiple horizons. Frequency domain digital signal processing, with an additive noise model, tests the random walk hypothesis for individual firm total and idiosyncratic risk at 2-month to 4-year periods. All firms have significant 12-month risk. Monthly effects influence small firms. Large firm total risk and mid-cap firm idiosyncratic risk are influenced by annual and 8-year mean reversions. Large firm idiosyncratic risk has 4-year mean-reversion risk. Results suggest that single-period risk is composed of multiple long-term calendar and non-calendar-length variances.