[We analyze event abnormal returns when returns predict events. In fixed samples, we show that the expected abnormal return is negative and becomes more negative as the holding period increases. Asymptotically, abnormal returns converge to zero provided that the process of the number of events is stationary. Nonstationarity in the process of the number of events is needed to generate a large negative bias. We present theory and simulations for the specific case of a lognormal model to characterize the magnitude of the small-sample bias. We illustrate the theory by analyzing long-term returns after initial public offerings (IPOs) and seasoned equity offerings (SEOs).]

Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, the authors derive explicit formulas for various European lookback options and provide some results about their American counterparts.

[In a one-period model of market making with many exogenously informed traders, we first show that the variance of prices and expected trading volume depend on the public information released at the start of trading. This is accomplished by representing beliefs with elliptically contoured distributions, for which the form of optimal decision rules does not depend on the specific distribution used. Second, if the model is altered so that the decision to become informed is made endogenous, then the decision rules of the market-maker and informed traders depend on the public information. Third, in a multiperiod model with many informed traders and long-lived private information, recursion formulas similar to those of Kyle (1985) hold for all elliptically contoured distributions, trading volume is autocorrelated, and, unless per period liquidity trading is bounded away from zero as new trading periods are added, informed traders' profits vanish.]

[In an adverse selection model of a securities market with one informed trader and several liquidity traders, we study the implications of the assumption that the informed trader has more information on Monday than on other days. We examine the interday variations in volume, variance, and adverse selection costs, and find that on Monday the trading costs and the variance of price changes are highest, and the volume is lower than on Tuesday. These effects are stronger for firms with better public reporting and for firms with more discretionary liquidity trading.]

The authors argue that arbitrage pricing theories (APT) imply the existence of a low-dimensional nonnegative nonlinear pricing kernel. In contrast to standard constructs of the APT, they do not assume a linear factor structure on the payoffs. This allows the authors to price both primitive and derivative securities. Seminonparametric techniques are used to estimate the pricing kernel and test the theory. Empirical results using size-based portfolio returns and yields on bonds reject the nested capital asset pricing model and linear APT and support the nonlinear APT. Diagnostics show that the nonlinear model is more capable of explaining variations in small firm returns.

[In dealership markets disclosure of size and price details of public trades is typically incomplete. We examine whether full and prompt disclosure of public-trade details improves the welfare of a risk-averse investor. We analyze a model of dealership market where a market maker first executes a public trade and then offsets her position by trading with other market makers. We distinguish between quantity risk and price revision risk. We show that if the market maker learns some information about the motive behind public trade, neither regime is unambiguously welfare superior. This is because greater transparency improves quantity risk sharing but worsens price revision risk sharing.]

The authors analyze a multiperiod model of trading with differentially informed traders, liquidity traders, and a marketmaker. Each informed trader's initial information is a noisy estimate of the long-term value of the asset and the different signals received by informed traders can have a variety of correlation structures. With this setup, informed traders not only compete with each other for trading profits, they also learn about other traders' signals from the observed order flow. The authors' work suggests that the initial correlation among the informed traders' signals has a significant effect on the informed traders' profits and the informativeness of prices.

Patterns in stock market trading volume, trading costs, and return volatility are examined using New York Stock Excha nge data from 1988. Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half-hour of the day. This eviden ce is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatilit y are high. Interday test results show that, for actively traded firms , trading volume is low and adverse selection costs are high on Monday , which is consistent with the predictions of the Foster and Viswanath an (1990) model.

F. Douglas Foster, S. Viswanathan, Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models, The Journal of Finance, Vol. 48, No. 1 (Mar., 1993), pp. 187-211

We analyze event abnormal returns when returns predict events. In fixed samples, we show that the expected abnormal return is negative and becomes more negative as the holding period increases. Asymptotically, abnormal returns converge to zero provided that the process of the number of events is stationary. Nonstationarity in the process of the number of events is needed to generate a large negative bias. We present theory and simulations for the specific case of a lognormal model to characterize the magnitude of the small-sample bias. We illustrate the theory by analyzing long-term returns after initial public offerings (IPOs) and seasoned equity offerings (SEOs). The Author 2008. Published by Oxford University Press on behalf of the Society for Financial Studies. All rights reserved. For permissions, please e-mail: [email protected]., Oxford University Press.