Transaction prices when insiders trade portfolios

Statistical properties of transaction prices are investigated in the context of a multi-asset extension of Kyle [1985]. Under the restriction that market makers cannot condition prices on volume in other markets, Kyle's model is shown to be consistent with well-documented lack of predictability of individual asset prices, positive autocorrelation of index returns, and low cross-sectional covariance. The covariance estimator of Cohen, e.a. [1983] provides the right estimates of the « true » covariance. However, Kyle's model cannot explain the asymmetry and rank deficiency of the matrix of first-order autocovariances. Asymmetry obtains when the insider limits his strategies to trading a set of pre-determined portfolios. If these portfolios are well-diversified, the matrix of first-order autocovariances is asymptotically rank-deficient. If the insider uses only one portfolio (as when « timing the market »), its asymptotic rank equals one, conform to the empirical results in Gibbons and Ferson [1985].