Abstract
This paper describes equilibrium interactions between dynamic portfolio rebalancing given a private end-of-day trading target and dynamic trading on long-lived private information. Order-splitting for portfolio rebalancing injects multifaceted dynamics in the market. These include autocorrelated order flow, sunshine trading, endogenous learning, and short-term speculation. The model has testable implications for intraday patterns in volume, liquidity, price volatility, order-flow autocorrelation, differences between informed-investor and rebalancer trading strategies, and for how these patterns comove with trading-target volatility and other market conditions.
Highlights
Price discovery and liquidity in financial markets arise from the interactions of different investors with different information and trading motives using a variety of order execution strategies.[2]
An important insight from Akerlof (1970), Grossman and Stiglitz (1980), Kyle (1985), and Glosten and Milgrom (1985) is that trading noise plays a critical role in markets subject to adverse selection when some investors trade on superior private information
The presence of the rebalancer introduces several new features: i) the aggregate order flow is autocorrelated, ii) expected trading volume for the insider and rebalancer is U -shaped over time, and iii) the price impact of the order flow is S-shaped with initial price impacts above those in Kyle and later price impacts below Kyle’s
Summary
We characterize sufficient conditions for existence of a linear Bayesian Nash equilibrium of the form in (1.5) through (1.8). Satisfy the pricing coefficient relations (1.25)-(1.28), the variances and covariance recursions (1.29)-(1.31), the rebalancer’s target constraint (1.13), the value function coefficient recursions (B.1)-(B.3) and (B.4)-(B.9), the second-order-conditions (1.39) and (1.49) as well as the equilibrium conditions (1.40) and (1.50), a linear Bayesian Nash equilibrium exists of the form given in (1.5)-(1.8). The new feature in our model, compared to Foster and Viswanathan (1996) and Kyle (1985), is the presence of the qn process in the equilibrium price dynamics (1.7) This produces new stylized features including autocorrelation of the equilibrium aggregate order flow: E[yn|σ(y1, ..., yn−1)] = E[∆θnI + ∆θnR + ∆wn|σ(y1, ..., yn−1)] = αnR qn−1 + E[βnI (v − pn−1) + βnR(a − θnR−1)|σ(y1, ..., yn−1)] = (αnR + βnR) qn−1,. The last equality follows, in part, from the earlier observation that, in equilibrium, qn−1 is the conditional expectation of a − θnR−1 given the prior trading history
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