Multiple Insiders with Long Lived Flow of Private Information, and High Frequency Competition

Abstract

We analyze the imperfect competition among multiple informed traders in an economy with a risky asset whose liquidation value is private information and follows a mean-reverting process. The unique linear equilibrium has an analytic form and is explicitly analyzed. When there are more auctions per unit time of trading, informed traders reduce the size of their orders at the same rate as the reduction in liquidity trading. When time is continuous, neither informed trading nor liquidity trading dominates the trading volume. The competitive market maker concludes that not all orders are informed. Therefore, price sensitivity to trades is finite, and the rents from private information are strictly positive, in sharp contrast with the findings obtained by Holden and Subrahmanyam (1992). In addition, informed trades cannot collude in order to "smooth" their trades, as in the monopolist models by Kyle (1985) and Chau and Vayanos (2008). Thus, informed traders can add significantly to trading volume and price variance. Although informed trading can be very volatile, the risk associated with traders' profits can be arbitrarily small. We propose an alternative measure of strong-form efficiency based on the Euclidean distance between the equilibrium price and the true value of the asset. Price errors in our model can be arbitrarily small, but Euclidean distance over a finite time is always positive even when time is continuous. Under this alternative measure, different notions of market efficiency can be consistent. Our model provides a rationale for the competition among high frequency traders, and shows that batching orders less frequently does not necessarily improve market liquidity.