Models do not have much to do with the financial crisis - an interview with Sergio Focardi

In this month's interview, we speak to Sergio Focardi, Professor of Finance at EDHEC Business School, about the role of mathematical models in the financial crisis, his new book on investment management entitled "Quantitative Equity Investing: Techniques and Strategies," and his current research work.

Sergio Focardi

**In the press, the financial crisis of 2008-2009 has often been attributed to the use of defective mathematical models. Do you agree with this view?**

**Sergio Focardi:** No, I do not think the crisis can be blamed on mathematical models. The crisis has deep financial and economic roots that do not have anything to do with mathematical models. Simply put, before the crisis there was tremendous asset inflation for a number of reasons, including the level of leverage present in the market. At a certain point the situation had become unsustainable. There were also fundamental economic problems, that are far from being resolved. Models do not have much to do with this.

I co-authored with Frank Fabozzi a chapter in the book "Insights into the Global Financial Crisis," edited by Laurence Siegel and Rodney Sullivan for CFA Institute. In our chapter we argue that models have little to do with the crisis. Actually, models are indeed able to describe financial markets in an approximate manner. However, we have to understand that financial markets are human artifacts designed to be unpredictable in order to leave opportunities. We cannot blame models if we design systems where we do not even collect data. For example, prior to the crisis the global amount of leverage was not known.

Financial systems could be designed to be more or less predictable. A fundamental point in making systems predictable is collecting data. In the aftermath of this crisis a number of proposals have been made to collect data on the structure of connections. This would be a major step forward in itself.

Whether we will go towards a system that is more or less predictable is in itself a question that we do not know how to answer. It has something to do with the theory of complex systems. In general we are able to analyse complex systems but we do not know how complexity itself is generated.

**You have co-authored a new book on investment management entitled "Quantitative Equity Investing: Techniques and Strategies." Could you say something about the ideas behind this book?**

**Sergio Focardi:** This new book is part of an editorial project that has been driven by Frank Fabozzi. Frank is an exceptional teacher who has played a major role in educating many generations of students at Master and PhD levels in the US. I have co-authored many books with Frank and others. The key idea is to offer students and practitioners an updated treatment of financial modelling which is both rigorous and accessible. We make use of many illustrations and real life examples.

This most recent book is primarily devoted to equity modelling and econometric subjects. Econometrics is a field in rapid evolution. The state of the art of the asset management profession requires familiarity with concepts such as cointegration, ARCH behavior, fat tailed distributions, regime shifting, Bayesian techniques, and copula functions in addition to classic subjects such as regression analysis. In this book we made an effort to illustrate these concepts.

We also touch on questions of model design and the many pitfalls. With examples from other scientific fields we illustrate the key difference between the analytical and the constructive, engineering approach. Our science, including economics, is primarily analytical while engineering is a much less formalised discipline. We illustrate with many examples and we draw a number of useful lessons for the model builder.

**Could you tell us a little about your current research projects?**

**Sergio Focardi:** Presently I am working on two lines of research. The first is the representation of stock prices with factor models. Classic factor models represent returns as regressions on a small number of factors. This approach is appealing for many reasons, in particular because regressions of returns which are stationary variables over factors which are also stationary variables are always meaningful.

I follow a different approach, constructing factor models of prices. As prices are integrated variables and factors are also integrated variables, factor models of prices make sense only if there are long-run relationships between prices and factors, that is, if prices are cointegrated. My research hinges on proving empirically that price factors do exist and can be determined with a generalisation of principal component analysis.

In my view, this approach has many advantages over the classic approach based on returns, because prices carry more information than returns. In fact, prices are the history of returns. Modelling prices we can capture phenomena such as mean reversion which are more difficult to represent in a framework based only on returns.

My second line of research is based on modelling trends and trend reversals, where trends have to be thought of as trends relative to some central market behaviour. This work is a generalisation of the previous work insofar as it allows long-run relationships to be represented in terms of reversals of trends.

There are two challenges associated with this research. The first is the theoretical challenge of representing local trends using regime switching models with transition matrices with variable probability.

The second challenges is to define large enough samples without introducing severe biases. In fact, a significant fraction of empirical price processes exist only for relatively short periods of time as firms begin and/or cease to exist, split, merge and are subject to other corporate actions. If we only consider stock prices that exist for very long periods of time we introduce significant biases. Overcoming this problem is a serious theoretical and practical challenge.

**About Sergio Focardi**

Sergio Focardi is Professor of Finance at EDHEC Business School. He was previously a partner at the Intertek Group, a firm specialised in research, training and consulting in quantitative portfolio management and mathematical
finance. Prior to founding the Intertek Group in 1993, he was the Managing Director of the Italian subsidiary of Control Data Corporation. His research interests include the econometrics of large equity portfolios and the modelling
of interactions between multiple heterogeneous agents. He has developed proprietary models for equity management. His work on quantitative equity management, trading, investment management, portfolio optimisation, credit
risk contagion, and financial econometrics has appeared in leading academic and practitioner journals. He is a member of the editorial board of the *Journal of Portfolio Management*. Professor Focardi has authored and co-authored award-winning books on financial modelling and investment
management and CFA Institute monographs on equity management and quantitative finance.