FIN 7446 lecture 19.pdfVIP

Lecture 19 Asset Pricing with Asymmetric Information Rational expectations are forecasts, which, while not necessarily correct, are the best that can be made using all available information. If expectations are rational, forecasting errors are random. Nash equilibrium (game theory) – A strategy profile s* is a Nash equilibrium if no player has incentive to deviate from their strategy given that other players do not deviate. * * * , ( , ) ( , ) i i i i i i i i V s s s s Vsπ π? ?≥ Kyle (1985) tells us how an informed trader will transact to maximize the value of private information. This tells us how information is incorporated into security prices through time given the strategic use of information by informed traders. Aggregate trade quantity (not the size of any individual trade) affects price behavior. The informed trader does not condition on uninformed trade quantity (u) or the equilibrium price, unlike most REE models. 0 0 ( ) ( ) 1 ( ) ( ) where = 2 u v y u x v v p P x u p x u σ σ σ λ λ σ = ? + = + + Caveats - P(x+u) can be negative if x+u is large and negative. - No ex ante price-volume relationship. Empirically, there is a strong link between absolute returns and trading volume. In this model, if ex ante, the uninformed volume doubled, the informed trader would always just double his order size, which doubles his profit. So the new ex ante price remains unchanged. 0 0 0 1 ( ) ( ) , doubles 2 = ( ) v u u u v P x u p v p u u P p u x σ σ σ σ σ λ ? ? + = + ? +? ? ? ? + + 1 λ is a measure of market depth. If λ is low, large volume changes the price by very little. To empirically estimate Kyle lambda, run the regression t [unexpected volume ] . t t p λ ε? = + Kyle lambda A. Penati - G. Pennacchi Notes on On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information by Sanford Grossman This model shows how the heterogeneous information of different investors can be reflec