We examine the implications of portfolio theory for the cross-sectional behavior of equity trading volume. Two-fund separation theorems suggest a natural definition for trading activity: share turnover. If two-fund separation holds, share turnover must be identical for all securities. If (K + 1)-fund separation holds, we show that turnover satisfies an approximately linear K-factor structure. These implications are examined empirically using individual weekly turnover data for NYSE and AMEX securities from 1962 to 1996. We find strong evidence against two-fund separation, and a principal-components decomposition suggests that turnover is well approximated by a two-factor linear model.

"We examine the implications of portfolio theory for the cross-sectional behavior of equity trading volume. Two-fund separation theorems suggest a natural definition for trading activity: share turnover...We find strong evidence against two-fund separation, and a principal-components decomposition suggests that turnover is well approximated by a two-factor linear model" -- Abstract.

Continuous-time stochastic processes are approximations to physically realizable phenomena. We quantify one aspect of the approximation errors by characterizing the asymptotic distribution of the replication errors that arise from delta-hedging derivative securities in discrete time, and introducing the notion of temporal granularity which measures the extent to which discrete-time implementations of continuous-time models can track the payoff of a derivative security. We show that granularity is a particular function of a derivative contract's terms and the parameters of the underlying stochastic process. Explicit expressions for the granularity of geometric Brownian motion and an Ornstein–Uhlenbeck process for call and put options are derived, and we perform Monte Carlo simulations to illustrate the empirical properties of granularity.

Technical analysis, also known as “charting,” has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis—the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and automatic approach to technical pattern recognition using nonparametric kernel regression, and we apply this method to a large number of U.S. stocks from 1962 to 1996 to evaluate the effectiveness of technical analysis. By comparing the unconditional empirical distribution of daily stock returns to the conditional distribution—conditioned on specific technical indicators such as head‐and‐shoulders or double bottoms—we find that over the 31‐year sample period, several technical indicators do provide incremental information and may have some practical value.