A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks
with James Hutchinson and Tomaso Poggio, Journal of Finance 49 (1994), 851-889.
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.
An Ordered Probit Analysis of Transaction Stock Prices
with Craig MacKinlay and Jerry Hausman, Journal of Financial Economics 31 (1992), 319–379.
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 Prices
Econometrica 59 (1991), 1279–1313.
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.
Data Snooping Biases in Tests of Financial Asset Pricing Models
with Craig MacKinlay, Review of Financial Studies 3 (1990), 431–468.
Tests of financial asset pricing models may yield misleading inferences when properties of the data are used to construct the test statistics. In particular, such tests are often based on returns to portfolios of common stock, where portfolios are constructed by sorting some empirically motivated characteristic of the securities such as market value of equity. Analytical calculations, Monte Carlo simulations, and two empirical examples show the effects of this type of data snooping can be substantial.
Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation
with Harry Mamaysky and Jiang Wang, Journal of Finance 55 (2000), 1705–1765.
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 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.
Finance: A Selective Survey
Journal of the American Statistical Association 95 (2000), 629-635.
Ever since the publication in 1565 of Girolamo Cardano's treatise on gambling, Liber de Ludo Aleae (The Book of Games of Chance), statistics and financial markets have become inextricably linked. Over the past few decades many of these links have become part of the canon of modern finance, and it is now impossible to fully appreciate the workings of financial markets without them. This selective survey covers three of the most important ideas of finance—efficient markets, the random walk hypothesis, and derivative pricing models—that illustrate the enormous research opportunities that lie at the intersection of finance and statistics.
When Is Time Continuous?
with Dimitris Bertsimas and Leonid Kogan, Journal of Financial Economics 55 (2000), 173–204.
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.
Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory
with Jiang Wang, Review of Financial Studies 13 (2000), 257–300.
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.
Optimal Control of Execution Costs for Portfolios
with Dimitris Bertsimas and Paul Hummel, Computing in Science & Engineering 1 (2000), 40–53.
The dramatic growth in institutionally managed assets, coupled with the advent of internet trading and electronic brokerage for retail investors, has led to a surge in the size and volume of trading. At the same time, competition in the asset management industry has increased to the point where fractions of a percent in performance can separate the top funds from those in the next tier. In this environment, portfolio managers have begun to explore active management of trading costs as a means of boosting returns. Controlling execution cost can be viewed as a stochastic dynamic optimization problem because trading takes time, stock prices exhibit random fluctuations, and execution prices depend on trade size, order flow, and market conditions. In this paper, we apply stochastic dynamic programming to derive trading strategies that minimize the expected cost of executing a portfolio of securities over a fixed period of time, i.e., we derive the optimal sequence of trades as a function of prices, quantitites, and other market conditions. To illustrate the practical relevance of our methods, we apply them to a hypothetical portfolio of 25 stocks by estimating their price-impact functions using historical trade data from 1996 and deriving the optimal execution strategies. We also perform several Monte Carlo simulation experiments to compare the performance of the optimal strategy to several alternatives.
An Econometric Model of Serial Correlation and Illiquidity in Hedge-Fund Returns
with Mila Getmansky and Igor Makarov, Journal of Financial Economics 74 (2004), 529–609.
The returns to hedge funds and other alternative investments are often highly serially correlated in sharp contrast to the returns of more traditional investment vehicles such as long-only equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure, i.e., investments in securities that are not actively traded and for which market prices are not always readily available. For portfolios of illiquid securities, reported returns will tend to be smoother than true economic returns, which will understate volatility and increase risk-adjusted performance measures such as the Sharpe ratio. We propose an econometric model of illiquidity exposure and develop estimators for the smoothing profile as well as a smoothing-adjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedge-fund style categories and may be a useful proxy for quantifying illiquidity exposure.