Russian-Doll Risk Models

Journal of Asset Management 16(3) (2015) 170-185

25 Pages Posted: 15 Dec 2014 Last revised: 30 Jul 2015

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Date Written: March 15, 2015


We give a simple explicit algorithm for building multi-factor risk models. It dramatically reduces the number of or altogether eliminates the risk factors for which the factor covariance matrix needs to be computed. This is achieved via a nested "Russian-doll" embedding: the factor covariance matrix itself is modeled via a factor model, whose factor covariance matrix in turn is modeled via a factor model, and so on. We discuss in detail how to implement this algorithm in the case of (binary) industry classification based risk factors (e.g., "sector -> industry -> sub-industry"), and also in the presence of (non-binary) style factors. Our algorithm is particularly useful when long historical lookbacks are unavailable or undesirable, e.g., in short-horizon quant trading.

Keywords: 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

JEL Classification: G00

Suggested Citation

Kakushadze, Zura, Russian-Doll Risk Models (March 15, 2015). Journal of Asset Management 16(3) (2015) 170-185, 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

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