Statistical model selection criteria provide an informed choice of the model with best external (i.e., out-of-sample) validity. Therefore they guard against overfitting (“data snooping”). We implement several model selection criteria in order to verify recent evidence of predictability in excess stock returns and to determine which variables are valuable predictors. We confirm the presence of in-sample predictability in an international stock market dataset, but discover that even the best prediction models have no out-of-sample forecasting power. The failure to detect out-of-sample predictability is not due to lack of power.

An asymmetric information model of the bid–ask spread is developed for a foreign exchange market subject to occasional government interventions. Traditional tests of the unbiasedness of the forward rate as a predictor of the future spot rate are shown to be inconsistent when the rates are measured as the average of their respective bid and ask quotes. Larger bid–ask spreads on Fridays are documented. Reliable evidence of asymmetric bid–ask spreads for all days of the week, albeit more pronounced on Fridays, are presented. The null hypothesis that the forward rate is an unbiased predictor of the future spot rate continues to be rejected. The regression slope coefficients increase toward unity, however, indicating a less variable risk premium.

As a centralized, computerized, limit order market, the Paris Bourse is particularly appropriate for studying the interaction between the order book and order flow. Descriptive methods capture the richness of the data and distinctive aspects of the market structure. Order flow is concentrated near the quote, while the depth of the book is somewhat larger at nearby valuations. We analyze the supply and demand of liquidity. For example, thin books elicit orders and thick books result in trades. To gain price and time priority, investors quickly place orders within the quotes when the depth at the quotes or the spread is large. Consistent with information effects, downward (upward) shifts in both bid and ask quotes occur after large sales (purchases).

There appear to be no anomalies in the aftermarket of a sample of 4,848 U.S. IPOs over the period 1975 to 1995, except issues offered below $6. Risk is priced in the aftermarket in accordance with Rubin-stein's asset-pricing model. Unlike under the efficient markets hypothesis (EMH), however, market priors about the probability of future default are not unbiased at the IPO date. Still, subsequent learning is rational: the market uses Bayes' law with a correct-likelihood function (of news given the eventual fate of an issue). That is, the hypothesis of an efficiently learning market (ELM) cannot be rejected. We produce direct evidence in support of these statements, based on a new class of tests. We also provide indirect evidence, by documenting a gradual convergence of IPO prices towards EMH as issues mature.