Robust methods to deal with model risk in financial portfolio decisions

Over the past years, the realized losses of many investment portfolios turned out to be much higher than predicted by portfolio risk models. The estimation problem is especially acute for the assessment of dependence among assets, which is however crucially needed to measure the gains of portfolio diversification. The first challenge that we tackle is the curse of dimensionality in estimating dependence across a large set of financial assets. We propose a data reduction technique that summarizes the information that is inherent in the N assets into a much smaller number of K statistical factors. Unlike principal component analysis, our approach selects factors using the higher order comoments that matter for the estimation of extreme risks. The use of data reduction methods comes at the price of potential specification error. This leads to a trade-off in estimation. Should we use the unbiased estimator that suffers from the curse of dimensionality, or the data reduction method that is potentially biased? We develop an outlier-robust solution to the trade-off. Irrespective of the chosen methodology, it remains that the model may miss some features of the data. Our third contribution will be to improve the measurement of the portfolio risk measure sensitivity to the issue of model risk and include it into the portfolio optimization framework. We will evaluate the practical relevance of each of the contributions in simulation studies and real-life financial portfolios.