Russian-Doll Risk Models

TL;DR

This paper introduces a nested 'Russian-doll' algorithm for constructing multi-factor risk models that simplifies computations by hierarchically modeling factor covariance matrices, especially useful in short-horizon trading.

Contribution

The paper presents a novel explicit algorithm for building multi-factor risk models using nested factor modeling to reduce the need for extensive covariance matrix computations.

Findings

Reduces the number of risk factors requiring covariance matrix estimation.

Applicable to both industry classification and style factors.

Effective for short-horizon quant trading with limited historical data.

Abstract

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.