The Effect of Public Information and Competition on Trading Volume and Price Volatility

A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

“…See Section 4 for formal definitions and [8] for a detailed exposition. [9] presents many examples of elliptical distributions and provides references to applications in financial economics. 4 This assumption is made to ease comparison with the existing literature.…”

“…It is clear that this characterization fails without the independence assumption because it is known (cf. [9]) that the ellipticity of the joint distribution of (ũ,ṽ) is sufficient for the existence of linear equilibria for all N . In the following we thus investigate the question whether ellipticity of the distribution of (ũ,ṽ) is also necessary for (10).…”

“…Hence, assuming that F is not determined by its moments, there exists a distribution G over Euclidian distances from the origin such that G = G and G has the same moments as G. Define a distribution F by the elliptical distributions one would need to use implications of the equilibrium conditions that go beyond the rotation invariance of the moments, which appears difficult even under the assumption that all moments are finite. 9 It is clear, though, that Theorem 1 applies under any primitive assumption on the distribution function which, in conjunction with the equilibrium conditions, implies that the joint distribution of (ũ,ṽ) is determined by its moments. For instance, supposing that all moments are finite and that one of the marginal distributions is determined by its moments will do: 10 from Proposition 3 it then follows that both marginal distributions are determined by their moments which suffices to conclude that the joint distribution is determined by its moments [17].…”

“…1 We ask whether a similar characterization can be obtained without imposing the independence assumption. To motivate this question we observe, first, that Foster and Viswanathan [9] have shown that relaxing the independence assumption is essential in generating phenomena such as the dependence of price volatility and trading volume on the arrival of news in the context of a Kyle-type model. Second, while it may seem natural to assume that "pure" noise trading and asset payoff are independent, in the context of the Kyle-model noise trading should be interpreted as the aggregate market order of all traders whose strategic behavior is not explicitly taken into account.…”

“…From this perspective we see no compelling justification why noise trade and payoff must be independent. 2 Foster and Viswanathan [9] show that a linear equilibrium exists for any number of strategic traders if the joint distribution of the exogenous random variables is elliptical. 3 For the case in which asset payoff and noise trade are 1 [1] derive this result under an additional technical condition on the characteristic function of the random variables.…”