Risk and Volatility: A Differential View

Abstract

Investors and economists disagree on a proper definition of risk. To a value investor, risk is a permanent loss of capital; to a financial economist, risk is volatility. The author builds a formal model of risk, based on the value investor’s definition, and provides conditions for when it aligns with volatility. In general, the value notion of risk combines the first and second moments of the distribution of returns, which is why the two definitions can differ. The original definition of risk from economic theory is closer to the value definition of risk. Instead, the main problems arise from the empirical measure of risk, which leans on volatility because of ease of measurement.