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

Tracking hedge funds returns using sparse clones

Whetherhedgefundreturnscouldbeattributedtosystematicriskexposuresrather than managerial skills is an interesting debate among academics and practitioners. Academic literature suggests that hedge fund performance is mostly determined by alternative betas, which justifies the construction of investable hedge fund clones or replicators. Practitioners often claim that management skills are instrumental for successful performance. In this paper, we study the risk exposure of different hedge fund indices to a set of liquid asset class factors by means of style analysis. We extend the classical style analysis framework by including a penalty that allows to retain only relevant factors, dealing effectively with collinearity, and to capture the out-of-sample properties of hedge fund indices by closely mimicking their returns. In particular, we introduce a Log-penalty and discuss its statistical properties, showing then that Log-clones are able to closely track the returns of hedge fund indices with a smaller number of factors and lower turnover than the clones built from state-of-art methods