Agenda

Presented by Northfield President Dan diBartolomeo. 

Many users of optimization tools add quadratic penalties to tailor portfolio attributes that are not directly related to return and risk (a target income yield, an ESG score). Many people think of such penalties as “soft constraints” that are less costly to pure return and risk objectives than a hard constraint.

In this presentation we will illustrate how the numerical properties of quadratic penalties are often misunderstood leading to economically counterproductive uses. It will be shown that adding one or more quadratic penalties to the optimization is mathematically equivalent to adding an extra orthogonal risk factor to the risk model. The “scale” of the penalty magnitude is equivalent to the variance of factor returns within a factor model. The use of such penalties is effectively broadening the definition of risk from the definition in Markowitz and Levy (1979) to the more arbitrary concern of “the risk of not having a portfolio that looks like I want it to look.” It can also be shown that quadratic penalties are closely related to the concept of Lagrangian multipliers in convex optimizations. Such multipliers describe the sensitivity of the optimization objective to relaxation of a hard constraint. It is easily understood one way to enforce a constraint is to target a “goal” value between minimum and maximum of the hard constraint and then vary the scale of the quadratic penalty until the constraint is satisfied. While the definition of quadratic penalties on portfolio attributes can be flexible, the numeric magnitudes associated with penalties must be bounded by economic rationality.

Our last topics will be the use of asymmetric quadratic penalties, and the parallels between quadratic penalties and non-parametric methods of portfolio construction methods such as the Analytic Hierarchy Process.

About Dan diBartolomeo

Dan diBartolomeo is President and founder of Northfield Information Services, Inc. He is also a former Visiting Professor at the CARISMA Research Center of Brunel University in London and serves on the Board of Directors of the Chicago Quantitative Alliance and the advisory board of the International Association for Quantitative Finance. He is a regional director of the Professional Risk Managers International Association, (PRMIA), and the Quantitative Work Alliance for Applied Finance, Education and Wisdom (QWAFAFEW). He is past president and director of the Boston Economic Club.

Dan has been admitted as an expert witness in US federal courtsand state courts for litigation matters regarding investment managementpractices and derivatives.

In 2010, Dan received an award from Institutional Investor magazine as one of the forty most influential executives in financial technology in connection with his analytical work that helped uncover the Madoff investment fraud.

Dan is a director of the American Computer Foundation, and formerly served on the industry liaison committee of the Department of Statistics and Actuarial Sciences at New Jersey Institute of Technology. He continues his more than twenty years of service as a judge in the Moskowitz Prize competition, given by the University of California at Berkeley for excellence in academic research on socially responsible investing.

Dan has a long list of publications including books, book chapters and research papers in professional journals such as Financial Analyst Journal, Quantitative Finance and Journal of Investing. In 2017, he was named co-editor of the Journal of Asset Management.