Risk Management for Hedge Funds: Introduction and Overview2001
Although risk management has been a well-plowed field in financial modeling for over two decades, traditional risk management tools such as mean-variance analysis, beta, and Value-at-Risk do not capture many of the risk exposures of hedge-fund investments. In this article, I review several aspects of risk management that are unique to hedge funds - survivorship bias, dynamic risk analytics, liquidity, and nonlinearities - and provide examples that illustrate their potential importance to hedge-fund managers and investors. I propose a research agenda for developing a new set of risk analytics specifically designed for hedge-fund investments, with the ultimate goal of creating risk transparency while, at the same time, protecting the proprietary nature of hedge-fund investment strategies.
Artificial intelligence has transformed financial technology in many ways and in this review article, three of the most promising applications are discussed: neural networks, data mining, and pattern recognition. Just as indexes are meant to facilitate the summary and extraction of information in an efficient manner, sophisticated automated algorithms can now perform similar functions but at higher and more powerful levels. In some cases, artificial intelligence can save us from natural stupidity.
Agent-Based Models of Financial Markets: A Comparison with Experimental Markets2001
We construct a computer simulation of a repeated double-auction market, designed to match those in experimental-market settings with human subjects, to model complex interactions among artificially-intelligent traders endowed with varying degrees of learning capabilities. In the course of six different experimental designs, we investigate a number of features of our agent-based model: the price efficiency of the market, the speed at which prices converge to the rational expectations equilibrium price, the dynamics of the distribution of wealth among the different types of AI-agents, trading volume, bid/ask spreads, and other aspects of market dynamics. We are able to replicate several findings of human-based experimental markets, however, we also find intriguing differences between agent-based and human-based experiments.
The Sources and Nature of Long-Term Dependence in the Business Cycle2001
This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, and focuses on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-term dependence, a consequence of aggregation in the presence of real business cycles. We derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data, and discuss how fiscal policy may alter their stochastic behavior. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test is robust to short-term dependence, and is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle.
Asset Allocation and Derivatives2001
The fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets suggests the possibility of constructing buy-and-hold portfolios of options that mimic certain dynamic investment policies, e.g., asset-allocation rules. We explore this possibility by solving the following problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon which will come closest to the optimal dynamic investment policy. We solve this problem for several combinations of preferences, return dynamics, and optimality criteria, and show that under certain conditions, a portfolio consisting of just a few options is an excellent substitute for considerably more complex dynamic investment policies.
Hedging Derivative Securities and Incomplete Markets: An Epsilon-Arbitrage Approach2001
Given a European derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based, we solve the dynamic replication problem: find a self-financing dynamic portfolio strategy—involving only the underlying securities—that most closely approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a mean-squared-error loss function under Markov state-dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or "epsilon" of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. To investigate the practical significance of these epsilon-arbitrage strategies, we consider several numerical examples including path-dependent options and options on assets with stochastic volatility and jumps.
Computational Challenges in Portfolio Management2001
The financial industry is one of the fastest-growing areas of scientific computing. Two decades ago, terms such as financial engineering, computational finance, and financial mathematics did not exist in common usage. Today, these areas are distinct and enormously popular academic disciplines with their own journals, conferences, and professional societies. One explanation for this area’s remarkable growth and the impressive array of mathematicians, computer scientists, physicists, and economists that are drawn to it is the formidable intellectual challenges intrinsic to financial markets. Many of the most basic problems in financial analysis are unsolved and surprisingly resilient to the onslaught of researchers from diverse disciplines. In this article, we hope to give a sense of these challenges by describing a relatively simple problem that all investors face when managing a portfolio of financial securities over time. Such a problem becomes more complex once real-world considerations factor into its formulation. We present the basic dynamic portfolio optimization problem and then consider three aspects of it: taxes, investor preferences, and portfolio constraints. These three issues are by no means exhaustive—they merely illustrate examples of the kinds of challenges financial engineers face today. Examples of other computational issues in portfolio optimization appear elsewhere.
Nonparametric Risk Management and Implied Risk Aversion2000
Typical value-at-risk (VAR) calculations involve the probabilities of extreme dollar losses, based on the statistical distributions of market prices. Such quantities do not account for the fact that the same dollar loss can have two very different economic valuations, depending on business conditions. We propose a nonparametric VAR measure that incorporates economic valuation according to the state-price density associated with the underlying price processes. The state-price density yields VAR values that are adjusted for risk aversion, time preferences, and other variations in economic valuation. In the context of a representative agent equilibrium model, we construct an estimator of the risk-aversion coefficient that is implied by the joint observations on option prices and underlying asset value.
Optimal Control of Execution Costs for Portfolios2000
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.
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.