Weekly and intradaily patterns in common stock prices are examined using transaction data. For large firms, negative Monday close-to-close returns accrue between the Friday close and the Monday open; for smaller firms they accrue primarily during the Monday trading day. For all firms, significant weekday differences in intraday returns accrue during the first 45 minutes after the market opens. On Monday mornings, prices drop, while on the other weekday mornings, they rise. Otherwise the pattern of intraday returns is similar on all weekdays. Most notable is an increase in prices on the last trade of the day.

Stock price discreteness adds noise to price series. The noise increases return variances and adds negative serial correlation to return series. Standard variance and serial covariance estimators therefore overestimate the variance and serial covariance of the underlying stock values. Discreteness-induced variance and serial covariance depend on underlying volatility and on the size of the bid/ask spread. Simple formulas for approximating the effects of discreteness on variance and serial correlation are derived and presented. The approximations, which are accurate in daily data, can be used to adjust the standard variance and serial covariance estimators.

A large mean price change is observed on the last daily NYSE transaction. This suggests that closing prices may not consistently represent stock values. Transaction prices are studied to further characterize the day-end price rise and to determine whether it is due to any limited subsample of stocks or dates. The results indicate that the phenomenon is pervasive over most firms and days. Some evidence suggests that it is caused by a change in the frequency of ask prices at day-end.

This paper presents new tests of the mixture of distributions hypothesis. Previous tests examined security prices and volume measured only at daily intervals. Here, differential implications of the hypothesis for transaction data are derived and tested. The new predictions emanate from the assumption that prices and volume evolve at uniform rates in transaction time. The results support this assumption and the mixture of distributions hypothesis in general. In addition, the tests suggest that the daily transaction-count may be a useful instrumental variable for estimating unobserved realizations of stochastic price variances.

New cross-sectional tests of the Mixture of Distributions Hypothesis are presented. The tests assume that the distribution of the mixing variable (often interpreted as the daily rate of flow of information) is not identical for all securities. Cross-security differences in the mixing distribution cause cross-security differences in the joint distribution of returns and volume. The Hypothesis provides predictions about how these differences appear in the joint distribution. The predictions are confirmed in tests based on cross-security correlations among summary statistics that characterize shape and covariational attributes of the joint distribution of returns and volume. The results are consistent with the Mixture of Distributions Hypothesis.

Stock prices cluster on round fractions. Clustering increases with price level and volatility, and decreases with capitalization and transaction frequency. Clustering is pervasive. Price clustering will occur if traders use discrete price sets to simplify their negotiations. Exchange regulations require that most stocks be traded on eighths. Clustering on larger fractions will occur if traders choose to use discrete price sets based on quarters, halves, or whole numbers. An econometric model of clustering is derived and estimated. Projections from the results suggest that traders would frequently use odd sixteenths when trading low-price stocks, if exchange regulations permitted trading on sixteenths. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

[Stock prices cluster on round fractions. Clustering increases with price level and volatility, and decreases with capitalization and transaction frequency. Clustering is pervasive. Price clustering will occur if traders use discrete price sets to simplify their negotiations. Exchange regulations require that most stocks be traded on eighths. Clustering on larger fractions will occur if traders choose to use discrete price sets based on quarters, halves, or whole numbers. An econometric model of clustering is derived and estimated. Projections from the results suggest that traders would frequently use odd sixteenths when trading low-price stocks, if exchange regulations permitted trading on sixteenths.]

Exchange minimum price variation regulations create discrete bid-ask spreads. If the minimum quotable spread exceeds the spread that otherwise would be quoted, spreads will be wide and the number of shares offered at the bid and ask may be large. A cross-sectional discrete spread model is estimated by using intraday stock quotation spread frequencies. The results are used to project $1/16 spread usage frequencies given a $1/16 tick. Projected changes in quotation sizes and in trade volumes are obtained from regression models. For stocks priced under $10, the models predict spreads would decrease 38 percent, quotation sizes would decrease 16 percent, and daily volume would increase 34 percent. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

[Exchange minimum price variation regulations create discrete bid-ask spreads. If the minimum quotable spread exceeds the spread that otherwise would be quoted, spreads will be wide and the number of shares offered at the bid and ask may be large. A cross-sectional discrete spread model is estimated by using intraday stock quotation spread frequencies. The results are used to project 1/16 spread usage frequencies given a 1/16 tick. Projected changes in quotation sizes and in trade volumes are obtained from regression models. For stocks priced under $10, the models predict spreads would decrease 38 percent, quotation sizes would decrease 16 percent, and daily volume would increase 34 percent.]

ABSTRACT Exact small sample population moments of the standard serial covariance and variance estimators are derived under the assumptions of the Roll bid/ask spread model. Noise explains why serial covariance estimates are often positive in annual samples of daily and weekly returns. Small sample estimator bias partially explains why weekly estimates are more negative than daily estimates. Noise causes the Roll spread estimator to be severely biased by Jensen's inequality. The French‐Roll adjusted variance estimator is unbiased but noisy. Empirical tests confirm the major implications.