We analyze competition among informed traders in the continuous‐time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.

We propose and estimate a model of endogenous informed trading that is a hybrid of the PIN and Kyle models. When an informed trader trades optimally, both returns and order flows are needed to identify information asymmetry parameters. Empirical relationships between parameter estimates and price impacts and between parameter estimates and stochastic volatility are consistent with theory. We illustrate how the estimates can be used to detect information events in the time series and to characterize the information content of prices in the cross-section. We also compare the estimates to those from other models on various criteria. Received April 5, 2017; editorial decision September 21, 2017 by Editor Itay Goldstein.

Recent work uses option prices to derive lower bounds for the risk premia of the market portfolio and individual stocks. We test the bounds conditionally. We cannot reject that they are valid, but we do reject that they are tight. Using the market bounds as forecasts appears unreasonable in many cases due to their high slackness. Adding past mean slackness is a potential improvement but is hampered by the brevity of the available data series. The correlation of the stock bounds with subsequent returns stems primarily from the time series rather than the cross section.

Mutual funds seek alpha, but coskewness is also an important performance attribute. Coskewness of fund returns is associated with market timing, liquidity management, and derivative use. Measures of active management associated with positive alphas are also associated with undesirable coskewness. When controlling for other characteristics, coskewness is positively associated with activity measures related to market timing and negatively associated with activity measures related to stock picking. In the cross-section of funds, the latter effect dominates, so funds generate undesirable coskewness in the pursuit of alpha. Money flows to funds with desirable coskewness. Received October 25, 2016; editorial decision January 29, 2018 by Editor Stijn Van Nieuwerburgh.

Portfolio turnpike theorems show that if preferences at large wealth levels are similar to power utility, then the investment strategy converges to the power utility strategy as the horizon increases. We state and prove two simple and general portfolio turnpike theorems. Unlike existing literature, our main result does not assume independence of returns and depends only on discounting of future cash flows. We also provide a critique of portfolio turnpike results, based on the observations that (1) the time required for convergence is often too large to be relevant, and (2) there is no convergence for consumption withdrawal problems. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.