Mean‐reversion risk and the random walk hypothesis

Abstract

AbstractThe 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.