Cross-Asset Speculation in Stock Markets∗ - Econometrics at Illinois ...

the off-diagonal term in Γ = Γ ′ , γ ij , which is negative. Even though speculators trade directlyon their cross asset signals, they also subtract out the projections of these direct trades onto netorder flows, and with uncorrelated liquidity trade this latter effect dominates, leading to negativecross-correlations in net order flows.In contrast, with unobservable prices, speculator 1’s signal for asset 1 is correlated with speculator2’s signal for asset 2, and both trade with the same intensity on those signals. As a result, eventhough speculators only trade on direct signals, the cross-asset correlation in order flow is positive.Hence, with uncorrelated liquidity trade, observable and unobservable prices generate opposingpredictions—but they are the opposite of what a casual contemplation of direct cross-asset tradingintensities suggests. This result indicates that with observable prices, some correlation in liquiditytrade is needed to reconcile the positive cross-asset correlation in order flows found in the data.Numerical investigation reveals that with observable prices and modest correlation in liquiditytrade across assets (relative to the correlation in private signals), net order flows become positivelycorrelated across assets, but remain less correlated than liquidity trade. In contrast, withunobservable prices, net order flows are always more correlated than liquidity trade.C Factor StructureHasbrouck and Seppi (2001) apply a principal component decomposition of cross-asset order flowsand returns, and find that commonality in order flows explains roughly two-thirds of the commonalityin returns. We can apply the same decomposition in our model to cross-asset orderflows and price changes (our analogue of returns). This factor analysis reveals the dimensionsalong which our stylized model can reconcile the data. As important, the primitive parametersthat we generate—the correlation in information of speculators and the correlation in liquiditytrade—provide a theoretical underpinning for Hasbrouck and Seppi’s purely empirical findings.Hasbrouck and Seppi note that the principal common factors of cross-asset order flow andcross-asset returns are the eigenvectors of the covariance matrix of the relevant variable. Theeigenvectors are ordered by the magnitudes of the corresponding eigenvalues. Hasbrouck and Seppiinitially regress returns on the first principal component of order flow P X+u . This results in a setof residuals w t . They next calculate the principal components of those residuals, P w . Finally, they17