Statistical Risk Models

The Journal of Investment Strategies 6(2) (2017) 1-40

44 Pages Posted: 15 Feb 2016 Last revised: 12 Mar 2017

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology

Date Written: February 14, 2016


We give complete algorithms and source code for constructing statistical risk models, including methods for fixing the number of risk factors. One such method is based on eRank (effective rank) and yields results similar to (and further validates) the method set forth in an earlier paper by one of us. We also give a complete algorithm and source code for computing eigenvectors and eigenvalues of a sample covariance matrix which requires i) no costly iterations and ii) the number of operations linear in the number of returns. The presentation is intended to be pedagogical and oriented toward practical applications.

Keywords: statistical risk models, multi-factor risk model, risk factors, optimization, regression, specific risk, factor risk, mean-reversion, covariance matrix, correlation matrix, factor loadings, dollar neutrality, style factors, industry factors, principal components, shrinkage

JEL Classification: G00

Suggested Citation

Kakushadze, Zura and Yu, Willie, Statistical Risk Models (February 14, 2016). The Journal of Investment Strategies 6(2) (2017) 1-40, Available at SSRN: or

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

680 E Main St #543
Stamford, CT 06901
United States
6462210440 (Phone)
6467923264 (Fax)


Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology ( email )

8 College Road
Singapore, 169857

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