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: http://www2.hawaii.edu/~sstill/pubs.html
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."