Random walks and the temporal dimension of risk

Abstract

The assumption that stock prices follow a random walk has critical implications for investors and firms. Among those implications is the fact that data frequencies and investment horizons are irrelevant (as defined below) when evaluating the risk of a security. However, if stock prices do not follow a random walk, ignoring either issue may lead investors to make misleading decisions. Using data from the first half of _the decade for thirteen European securities markets, I first argue that stock prices in these markets (not surprisingly) do not follow a random walk. Then, I show that investors that assume otherwise are bound to underestimate the total and systematic risk (and overestimate the compound and risk-adjusted returns) of European stocks. The underestimation of risk ranges between .53% and 2.94% a month, and averages 1.25% a month.