Idiosyncratic volatility

Identifying stock returns' idiosyncratic volatility (IV) is essential for asset pricing, portfolio construction, and empirical studies. IV plays a central role in explaining the cross-section of returns, including "IV puzzle"and designing investment strategies. The existing literature defines IV as the difference between a stock's total return volatility and the portion explained by (linear beta) pricing models. We show that this conventional measure is fundamentally misspecified because in reality no traded asset has zero-variance returns. We identify the true IV measure and demonstrate that the ratio of the true to the literature's misspecified IV measure lies in the interval [0,1]. This implies measurement-error magnitudes ranging from zero to infinity, where zero misspecification occurs with probability zero. The mismeasurement is arbitrary - nonmonotonic and nonlinear in any stock or market parameter. These results suggest that, under the literature's definition of IV, no econometric method can correct for the misspecification. Empirical studies relying on this conventional IV measure are arbitrarily distorted.