Russian-Doll Risk Models
Journal of Asset Management 16(3) (2015) 170-185
25 Pages Posted: 15 Dec 2014 Last revised: 30 Jul 2015
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: Suggested Citation