Cross-holdings: estimation issues, biases, and distortions

Cross-bolding occurs when listed corporations own securitiesissued by other corporations. We analyze the effect of cross-holdingson market capitalization and return measures as well as implicationsfor econometric testing of asset pricing theories. We show thatcross-holdings generally distort standard market return andrisk measures. The magnitudes of such distortions are calculatedfor simulated economies by using a variety of crossholding patterns.In addition, cross-holdings are shown to induce non-stationarityin the covariance matrix of security returns. We examine theeffect of this nonstationarity for estimating efficient frontiersand factor structures. We also discuss the implications forrisk-return estimates in equilibrium asset pricing models.