Santa Fe Institute

Regularized Portfolio Optimization


April 22, 2011
12:15 PM
Collins Conference Room

Susanne Still (Department of Information and Computer Science, University of Hawaii)

Abstract.  One of the textbook investment strategies, known as portfolio optimization, displays an inherent instability to estimation error when applied to large portfolios, such as those of banks or insurance companies. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk.

I will talk about a novel approach to the portfolio selection problem. From the point of view of statistical learning theory (or machine learning), the occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. I will discuss how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint, however, dictates a modification resulting in a slightly different algorithm. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach I provide here allows for the simultaneous treatment of optimization and diversification in one
framework which enables the investor to trade-off between the two, depending on the size of the available data set. I will discuss how one can characterize the typical behavior, in the limit of large portfolio sizes, and show how regularization removes the instability. The necessity to regularize the portfolio selection problem, besides being a statistical consideration, can also be derived from the following reasoning: If an investor considers the cash flow that could be generated by liquidating a portfolio, and if the investor takes into account that the liquidation of large positions will have an impact on the market, then the need to regularize portfolio optimization emerges naturally from considering the feedback on prices.

This is joint work with F. Caccioli (SFI), M. Marsili (ICTP), and I.
Kondor (IAS Budapest).

Papers — available at:

S.Still and I. Kondor. "Regularizing Portfolio Optimization."  New Journal of Physics 12 (2010): 075034 (15pp). Special Issue on Statistical Physics Modeling in Economics and Finance.

F. Caccioli, S. Still, M. Marsili, and I. Kondor. "Optimal Liquidation Strategies Regularize Portfolio Selection." To be published in The European Journal of Finance. Special issue on "New Facets of Economic Complexity in Modern Financial Markets."

Purpose: Research Collaboration

SFI Host: Fabio Caccioli

More Info

  • * SFI community lectures are free, open, & accessible to the public.
  • * Seminars & colloquia are geared for scientists but free & open to the interested public.
  • * All other SFI events are by invitation only.
  • * Note: We are unable to accommodate members of the public for SFI's limited lunch service; you're welcome to bring your own.

Events News

Working group: What T cells have in common with ants July 29, 2015 -

A working group at SFI this week aims to further the linkages between experiment and theory in immune cell motility, or movement.

SFI’s Krakauer, McCarthy’s new work to be featured in August 5 art event July 24, 2015 -

A singular conversation between artist James Drake and incoming SFI President David Krakauer will unfold August 5 in Santa Fe, in conjunction with the first public reading from SFI Trustee ...

SFI to co-host Systems Analysis 2015 conference July 9, 2015 -

In November SFI will co-host the 2015 Systems Analysis conference in Austria.

A Mayan, a Roman, and a New Yorker walk into a bar… June 12, 2015 -

A diverse collection of social and natural scientists, archeologists, and historians are at SFI to share data and techniques for quantitatively comparing ancient and pre-modern cities.

Audio: Why goals, objectives, and metrics inhibit innovation June 11, 2015 -

In podcast interview on the Santa Fe Radio Café, SFI Sabbatical Visitor Ken Stanley discusses the role of serendipity in making great discoveries and the dangers of constraint by objective.

More News