Regularizing Portfolio Optimization

TL;DR

This paper introduces a regularization approach to portfolio optimization using support vector regression concepts, aiming to improve stability and diversification in large portfolios affected by estimation errors.

Contribution

It links regularized portfolio optimization with support vector regression and proposes a method that balances optimization and diversification based on data size.

Findings

Regularization improves portfolio stability.

Support vector regression framework applied to risk measures.

Diversification acts as a regularizer for portfolio stability.

Abstract

The optimization of large portfolios displays an inherent instability to estimation error. 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. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. 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 we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set.