Cross-Holdings: Estimation Issues, Biases, and Distortions

Cross-bolding occurs when listed corporations own securities issued by other corporations. We analyze the effect of cross-holdings on market capitalization and return measures as well as implications for econometric testing of asset pricing theories. We show that cross-holdings generally distort standard market return and risk measures. The magnitudes of such distortions are calculated for simulated economies by using a variety of cross-holding patterns. In addition, cross-holdings are shown to induce nonstationarity in the covariance matrix of security returns. We examine the effect of this nonstationarity for estimating efficient frontiers and factor structures. We also discuss the implications for risk-return estimates in equilibrium asset pricing models.