Sergio M. Focardi

Trends in quantitative equity management: survey results

In the second half of the 1990s, there was so much skepticism about quantitative fund management that Leinweber (1999), a pioneer in applying advanced techniques borrowed from the world of physics to fund management, wrote an article entitled: ‘Is quantitative investment dead?’ In the article, Leinweber defended quantitative fund management and maintained that in an era of ever faster computers and ever larger databases, quantitative investment was here to stay. The skepticism towards quantitative fund management, provoked by the failure of some high-profile quantitative funds, was related to the fact that investment professionals felt that capturing market inefficiencies could best be done by exercising human judgement. Despite mainstream academic opinion that held that markets are efficient and unpredictable, the asset managers’ job is to capture market inefficiencies for their clients. At the academic level, the notion of efficient markets has been progressively relaxed. Empirical evidence led to the acceptance of the notion that financial markets are somewhat predictable and that systematic market inefficiencies can be detected (see Granger (1992) for a review of various models that accept departures from efficiency). Using the variance ratio test, Lo and MacKinlay (1988) disproved the random walk hypothesis. Additional insights on return predictability were provided by Jegadeesh and Titman (1993), who established the existence of momentum phenomena. Since then, a growing number of studies have accumulated evidence that there are market anomalies that can be systematically exploited to earn excess profits after considering risk and transaction costs (see Pesaran (2005) for a modern presentation of the status of market efficiency). Lo (2004) proposed replacing the Efficient Market Hypothesis with the Adaptive Market Hypothesis as market inefficiencies appear as the market adapts to changes in a competitive environment. *Corresponding author. Email: frank.fabozzi@yale.edu

Index-Exciting CAViaR: A New Empirical Time-Varying Risk Model

Instead of assuming the distribution of return series, Engle and Manganelli (2004) propose a new Value-at-Risk (VaR) modeling approach, Conditional Autoregressive Value-at-Risk (CAViaR), to directly compute the quantile of an individual assets returns which performs better in many cases than those that invert a return distribution. In this paper we explore more flexible CAViaR models that allow VaR prediction to depend upon a richer information set involving returns on an index. Specifically, we formulate a time-varying CAViaR model whose parameters vary according to the evolution of the index. The empirical evidence reported in this paper suggests that our time-varying CAViaR models can do a better job for VaR prediction when there are spillover effects from one market or market segment to other markets or market segments.

Can We Predict Stock Market Crashes

In this article, the authors suggest how to think about a new framework for the analysis of financial bubbles and a possible vector of variables able to signal when an economy enters a state of disequilibrium. The working hypothesis is that market crashes are preceded by a bubble. The authors define a bubble as an anomalous increase in asset prices with respect to the economy. An exponentially growing spread between asset prices and the economy is therefore an indicator of the probability that a bubble is in the making. However, as the authors point out, this indicator alone is not sufficient as anomalous price growth can be generated by different macroeconomic scenarios. The authors discuss different macroscenarios that can lead to bubbles and the related indicators.

What’s Wrong with Today’s Economics? The CurrentCrisis Calls for an Approach to Economics Rooted Moreon Data Than on Rationality

Focardi and Fabozzi argue that current mainstream economics is not a science in the sense of the physical sciences, and they draw some conclusions from the point of view of asset management. Their key point is that economics as embodied in the general equilibrium theories describes an idealized rational economic world as opposed to one based on empirical data. Although this argument has already been made, it has been virtually ignored by economists. The current crisis, however, requires an economic understanding anchored on a solid empirical basis. The authors review a number of facts, including the following: 1) market efficiency is a quantitative concept, with efficiency defined in terms of the magnitude of realistic profit opportunities; 2) the dynamic vector-like nature of inflation challenges current theories about inflation and the generation of money, making growth path-dependent; 3) economic conservation laws are key to understanding growth; and 4) a market economy cannot support an unbounded level of wealth and income inequality because they become a destabilizing factor. The overall lesson for asset management is that economics matters and that the culture of pure speculation would be replaced profitably for society as a whole with a true culture of investment.

Economics: An Empirical Science Capable of Forecasting Economic Events?

In the aftermath of the 2007–2009 financial crisis, mainstream economics was criticized for having failed to either forecast or help prevent the market crash, which resulted in large losses for investors, although markets were back to pre-crisis levels by the end of the first quarter of 2013. Some have suggested that the crash itself was the result of bad or poorly applied theory. What parts of the theory are bad? What parts were poorly applied? What parts are truly relevant to investment management? Is there better science in the making? The authors of this article address these questions.

Is economics an empirical science? If not, can it become one?

Today’s mainstream economics, embodied in Dynamic Stochastic General Equilibrium (DSGE) models, cannot be considered an empirical science in the modern sense of the term: it is not based on empirical data, is not descriptive of the real-world economy, and has little forecasting power. In this paper, I begin with a review of the weaknesses of neoclassical economic theory and argue for a truly scientific theory based on data, the sine qua non of bringing economics into the realm of an empirical science. But I suggest that, before embarking on this endeavor, we first need to analyze the epistemological problems of economics to understand what research questions we can reasonably ask our theory to address.. I then discuss new approaches which hold the promise of bringing economics closer to being an empirical science. Among the approaches discussed are the study of economies as complex systems, econometrics and econophysics, artificial economics made up of multiple interacting agents as well as attempts being made inside present main stream theory to more closely align the theory with the real world

Issues in Applying Financial Econometrics to Factor-Based Modeling in Investment Management

In this article, the authors provide a nontechnical discussion of a number of practical and theoretical issues associated with implementing factor models used to explain or forecast equity returns. The first issue is determining the number of factors (i.e., the number of variables needed to explain or forecast returns). In finite markets such as stock markets, the problem of determining the true number of factors cannot be solved theoretically. Instead, asset managers must be content with approximations using model selection criteria. The authors then discuss the questions of overfitting and dimensionality reduction—both of which can lead to poor out-of-sample performance of investment or trading strategies. Overfitting entails using a model that is too complex for the data available to the modeler; thus, the resulting model fits noise. Dimensionality reduction solves the problem of dimensionality by using approximate models of reduced dimensionality that can be estimated with small samples. An important instance of applying dimensionality reduction techniques is using factor GARCH models to forecast covariance matrices. Finally, the authors discuss problems associated with backtesting. In trying to choose the best-performing model or strategy, a modeler may be tempted to run multiple backtests, thereby creating the risk of using out-of-sample backtesting as a form of in-sample testing. In turn, this leads to overfitting.

Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management

The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.

Fractional Partial Differential Equation and Option Pricing

There are different approaches for studying the behavior of a stochastic process. A stochastic process can be studied as a stochastic differential equation, a partial integro-differential equation, and a fractional partial differential equation. The efficiency of these different approaches depends on the dynamics of the asset price process and the numerical approach for solving them.

Fractional calculus and fractional processes: an overview

In this monograph we discuss how fractional calculus and fractional processes are used in financial modeling, finance theory, and economics. We begin by giving an overview of fractional calculus and fractional processes, responding upfront to two important questions: 1. What is the fractional paradigm for both calculus and stochastic processes?