Russian-doll risk models

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 (FCM) needs to be computed. This is achieved via a nested ‘Russian-doll’ embedding: the FCM itself is modeled via a factor model, whose FCM 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 (for example, ‘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, for example, in short-horizon quant trading.

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