Robust estimation of covariance and its application to portfolio optimization

Lijuan Huo, Tae Hwan Kim, Yunmi Kim

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Outliers can have a considerable influence on the conventional measure of covariance, which may lead to a misleading understanding of the comovement between two variables. Both an analytical derivation and Monte Carlo simulations show that the conventional measure of covariance can be heavily influenced in the presence of outliers. This paper proposes an intuitively appealing and easily computable robust measure of covariance based on the median and compares it with some existing robust covariance estimators in the statistics literature. It is demonstrated by simulations that all of the robust measures are fairly stable and insensitive to outliers. We apply robust covariance measures to construct two well-known portfolios, the minimum-variance portfolio and the optimal risky portfolio. The results of an out-of-sample experiment indicate that a potentially large investment gain can be realized using robust measures in place of the conventional measure.

Original languageEnglish
Pages (from-to)121-134
Number of pages14
JournalFinance Research Letters
Issue number3
StatePublished - Sep 2012


  • Covariance
  • Median
  • Robust estimation


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