Notes on the convergence of the estimated risk factor matrix in linear regression models

Julien Riposo () and E G Klepfish
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Julien Riposo: Quant Aspects
E G Klepfish: Quant Aspects

Journal of Asset Management, 2023, vol. 24, issue 2, No 2, 97-107

Abstract: Abstract A two-step iterative estimation of a risk model, alternating between a cross-sectional and time-series regression, aims to achieve an in-sample consistent representation of risk factors, such that the security exposure matrix input of the cross-sectional step is equal to the output exposure matrix estimated in the subsequent time-series step. The sequence of estimated exposure matrices is proven to converge to a fixed point. The condition for a fixed point is identified and proven necessary and sufficient. The presented mathematical proof of viability of the two-step iterative estimation is complementary to earlier research in this area.

Date: 2023
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DOI: 10.1057/s41260-022-00285-x

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