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

mation is highly correlated. Profits are far higher when one speculator has most of the information,than when information is evenly divided. In turn, comparing the Caballe and Krishnan setting withthe isolated markets benchmark surprisingly reveals that the observability of all prices by marketmakers only modestly reduces speculator profits when information is unevenly divided, but significantlysubstitutes for the observability of prices by speculators when information is evenly divided.Figure 2 shows how a speculator’s expected trading profit rises with his share of private information,ν. The figure reveals that the smaller is ν, the more a trader is hurt by the observability ofprices (the profit difference narrows with ν). This is because the smaller is ν, the less the speculatorcontributes to total order flow, and hence, the less he can back out from prices.[Figure 2 about here]Figure 3 shows how trading intensities vary with a speculator’s share of private information.The figure highlights that trading intensities are far higher if prices are observable. In part, thisreflects that when speculators see prices, they offset the impact of their trades on private signalsby subtracting their projections on net order flows via γ i . In addition, trading intensities with observableprices are higher due to the strategic “order-reduction” effect: speculators have incentivesto increase trading intensities to influence price, which causes other agents to scale down orders,thereby mitigating price impacts.The first panel of Figure 3 reveals that trade on direct information first rises rapidly with a speculator’sinformation share, before declining as ν is further increased. The second panel shows thatindirect trading intensities exhibit an entirely different pattern: when a speculator has little privateinformation, he uses his asset 1 signal to trade asset 2 extremely aggressively. In fact, when prices areobservable and ν = 0.1, speculator 1 uses his noisy signal e 1 1 of e2 2 to trade asset 2 more aggressively(b 2 1 = 1.56) than speculator 2 who sees e2 2 (b2 2= 1.15). This reflects that when ν is small, the expected(squared) size of speculator 1’s trade on indirect information, (b 2 1 )2 ν, is far less than (b 2 2 )2 (1−ν). As ν rises, indirect trading intensities fall sharply. Indeed, when prices are unobservable, thespeculator with more information trades against his asset 2 signal when trading asset 1 (see Corollary1): by doing so, the speculator gains more through the influence on the price of asset 2 thanhe loses through the (small) quadratic loss in market 1 due to his trade against his asset 2 signal.23