Smooth monotone covariance for elliptical distributions and applications in finance

Xiaoping Zhou, Dmitry Malioutov, Frank J. Fabozzi, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Sample covariance is known to be a poor estimate when the data are scarce compared with the dimension. To reduce the estimation error, various structures are usually imposed on the covariance such as low-rank plus diagonal (factor models), banded models and sparse inverse covariances. We investigate a different non-parametric regularization method which assumes that the covariance is monotone and smooth. We study the smooth monotone covariance by analysing its performance in reducing various statistical distances and improving optimal portfolio selection. We also extend its use in non-Gaussian cases by incorporating various robust covariance estimates for elliptical distributions. Finally, we provide two empirical examples using Eurodollar futures and corporate bonds where the smooth monotone covariance improves the out-of-sample covariance prediction and portfolio optimization.

Original languageEnglish
Pages (from-to)1555-1571
Number of pages17
JournalQuantitative Finance
Issue number9
StatePublished - 2014


  • Elliptical distributions
  • Regularization
  • Smooth monotone covariance


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