Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory2000
We examine the implications of portfolio theory for the cross-sectional behavior of equity trading volume. We begin by showing that a two-fund separation theorem suggests a natural definition for trading volume: share turnover. If two-fund separation holds, share turnover must be identical for all securities. If (K+1)-fund separation holds, we show that share turnover satisfies and approximate linear K-factor structure, These implications are empirically tested using weekly turnover data for NYSE and AMEX securities from 1962 to 1996. We find strong evidence against two-fund separation and an eigenvalue decomposition suggests that volume is driven by a two-factor linear model.
For instructions on how to create your own MiniCRSP database, please see Trading Volume and the MiniCRSP Database: An Introduction and User’s Guide.
When Is Time Continuous?2000
In this paper we study the tracking error resulting from the discrete-time application of continuous-time delta-hedging procedures for European options. We characterize the asymptotic distribution of the tracking error as the number of discrete time periods increases, and its joint distribution with other assets. We introduce the notion of temporal granularity of the continuous-time stochastic model that enables us to characterize the degree to which discrete-time approximations of continuous time models track the payoff of the option. We derive closed form expressions for the granularity for a put and call option on a stock that follows a geometric Brownian motion and a mean-reverting process. These expressions offer insight into the tracking error involved in applying continuous-time delta-hedging in discrete time. We also introduce alternative measures of the tracking error and analyze their properties.
A Non-Random Walk Down Wall Street1999
For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future.
Optimal Control of Execution Costs1998
We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block S of shares to be executed within a fixed finite number of periods T, and given a price-impact function that yields the execution price of an individual trade as a function of the shares traded and market conditions, we obtain the optimal sequence of trades as a function of market conditions—closed-form expressions in some cases—that minimizes the expected cost of executing S within T periods. Our analysis is extended to the portfolio case in which price impact across stocks can have an important effect on the total cost of trading a portfolio.
Nonparametric Estimation of State-Price Densities Implicit In Financial Asset Prices1998
Implicit in the prices of traded financial assets are Arrow-Debreu state prices or, in the continuous-state case, the state-price density [SPD]. We construct an estimator for the SPD implicit in option prices and derive an asymptotic sampling theory for this estimator to gauge its accuracy. The SPD estimator provides an arbitrage-free method of pricing new, more complex, or less liquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility "smiles" for option prices. We perform Monte Carlo simulation experiments to show that the SPD estimator can be successfully extracted from option prices and we present an empirical application using S&P 500 index options.
The Econometrics of Financial Markets1997
The past twenty years have seen an extraordinary growth in the use of quantitative methods in financial markets. Finance professionals now routinely use sophisticated statistical techniques in portfolio management, proprietary trading, risk management, financial consulting, and securities regulation. This graduate-level textbook is intended for PhD students, advanced MBA students, and industry professionals interested in the econometrics of financial modeling. The book covers the entire spectrum of empirical finance, including: the predictability of asset returns, tests of the Random Walk Hypothesis, the microstructure of securities markets, event analysis, the Capital Asset Pricing Model and the Arbitrage Pricing Theory, the term structure of interest rates, dynamic models of economic equilibrium, and nonlinear financial models such as ARCH, neural networks, statistical fractals, and chaos theory.
Market Efficiency: Stock Market Behaviour In Theory and Practice, Volumes I & II1997
The efficient markets hypothesis is one of the most controversial and hotly contested ideas in all the social sciences. It is disarmingly simply to state, has far-reaching consequences for academic pursuits and business practice, and yet is surprisingly resilient to empirical proof or refutation. Even after three decades of research and literally thousands of journal articles, economists have not yet reached a consensus about whether markets - particularly financial markets - are efficient or not.
Maximizing Predictability in the Stock and Bond Markets1997
We construct portfolios of stocks and of bonds that are maximally predictable with respect to a set of ex ante observable economic variables, and show that these levels of predictability are statistically significant, even after controlling for data-snooping biases. We disaggregate the sources for predictability by using several asset groups—sector portfolios, market-capitalization portfolios, and stock/bond/utility portfolios—and find that the sources of maximal predictability shift considerably across asset classes and sectors as the return-horizon changes. Using three out-of-sample measures of predictability—forecast errors, Merton's market-timing measure, and the profitability of asset allocation strategies based on maximizing predictability—we show that the predictability of the maximally predictable portfolio is genuine and economically significant.
The Industrial Organization and Regulation of the Securities Industry1996
The regulation of financial markets has for years been the domain of lawyers, legislators, and lobbyists. In this unique volume, experts in industrial organization, finance, and law, as well as members of regulatory agencies and the securities industry, examine the securities industry from an economic viewpoint.
Ten original essays address topics including electronic trading and the "virtual"stock exchange; trading costs and liquidity on the London and Tokyo Stock Exchanges and in the German and Japanese government bond markets; international coordination among regulatory agencies; and the impact of changing margin requirements on stock prices, volatility, and liquidity.
This clear presentation of groundbreaking research will appeal to economists, lawyers, and legislators who seek a refreshingly new perspective on policy issues in the securities industry.
Implementing Option Pricing Models When Asset Returns Are Predictable1995
The predictability of an asset's returns will affect option prices on that asset, even though predictability is typically induced by the drift which does not enter the option pricing formula. For discretely-sampled data, predictability is linked to the parameters that do enter the option pricing formula. We construct an adjustment for predictability to the Black-Scholes formula and show that this adjustment can be important even for small levels of predictability, especially for longer-maturity options. We propose several continuous-time linear diffusion processes that can capture broader forms of predictability, and provide numerical examples that illustrate their importance for pricing options.
A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks1994
We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a six-month training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For purposes of comparison, we perform similar simulation experiments for four other methods of estimation: OLS, kernel regression, projection pursuit, and multilayer perceptron networks. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1992.
The non-trading or non-synchronous effect arises when time series, usually financial asset prices, are taken to be recorded at time intervals of one length when in fact they are recorded at time intervals of another, possibly irregular, lengths. For example, the daily prices of securities quoted in the financial press are usually "closing" prices, prices at which the last transaction in each of those securities occurred on the previous business day. these closing prices generally do not occur at the same time each day, but by calling them "daily" prices, we have implicitly and incorrectly assumes that they are equally spaces at 24-hour intervals. Such an assumption can generate spurious predictability in price changes and returns even if true price changes or returns are statistically independent. The non-trading effect induces potentially serious biases in the moments and co-moments of asset returns such as their means, variances, covariances, and autocorrelation and cross-autocorrelation coefficients.
Empirical Issues in the Pricing of Options and Other Derivative Securities1992
The pricing of options, certificates, and other derivatives or assets—financial assets whose payments depend on the prices of other assets—is one of the great successes of modern financial economics. Although the pricing of derivatives is computationally intensive, there is little done in terms of the traditional empirical analysis since by the very nature of the determination of prices and arbitrage there is no error term to minimize. There are, however, many issues of statistical inference that affect the pricing of options and other derivatives. This paper analyzes two of the most common issues neglected in the literature: reduced form empirical instruments for the determination of prices and how to use Monte Carlo simulations to calculate option prices depend on a path.
An Ordered Probit Analysis of Transaction Stock Prices1992
We estimate the conditional distribution of trade-to-trade price changes using ordered probit, a statistical model for discrete random variables. This approach recognizes that transaction price changes occur in discrete increments, typically eighths of a dollar, and occur at irregularly-spaced time intervals. Unlike existing models of discrete transaction prices, ordered probit can quantify the effects of other economic variables like volume, past price changes, and the time between trades on price changes. Using 1988 transactions data for over 100 randomly chosen U.S. stocks, we estimate the ordered probit model via maximum likelihood and use the parameter estimates to measure several transaction-related quantities, such as the price impact of the trades of a given size, the tendency towards price reversals from one transaction to the next, and the empirical significance of price discreteness.
Long-Term Memory in Stock Market Prices1991
A test for long-run memory that is robust to short-range dependence is developed. It is an extension of the "range over standard deviation" or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory. This test is applied to daily and monthly stock returns indexed over several time periods and, contrary to previous findings, there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-range dependence is taken into account. Illustrative Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns.