Regularizing Portfolio Optimization

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

Exposure-Based Cash-Flow-At-Risk for Value-Creating Risk Management Under Macroeconomic Uncertainty

A strategically minded CFO will realize that strategic corporate risk management is about finding the right balance between risk prevention and proactive value generation. Efficient risk and performance management requires adequate assessment of risk and risk exposures on the one hand and performance on the other. Properly designed, a risk measure should provide information on to what extend the firm's performance is at risk, what is causing that risk, the relative importance of non-value-adding and value-adding risk, and the possibilities to use risk management to reduce total risk. In this chapter, we present an approach exposure-based cash-flow-at-risk to calculating a firm's downside risk conditional on the firm's exposure to non-value-adding macroeconomic and market risk and to analyzing corporate performance adjusted for the impact of non-value-adding risk