A Generalized Description Length Approach for Sparse and Robust Index Tracking

We develop a new minimum description length criterion for index tracking, which deals with two main issues affecting portfolio weights: estimation errors and model misspecification. The criterion minimizes the uncertainty related to data distribution and model parameters by means of a generalized q-entropy measure, and performs model selection and estimation in a single step, by assuming a prior distribution on portfolio weights. The new approach results in sparse and robust portfolios in presence of outliers and high correlation, by penalizing observations and parameters that highly diverge from the assumed data model and prior distribution. The Monte Carlo simulations and the empirical study on financial data confirm the properties and the advantages of the proposed approach compared to state-of-art methods.