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

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  • Julien Riposo

    (Quant Aspects)

  • E G Klepfish

    (Quant Aspects)

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.

Suggested Citation

  • Julien Riposo & E G Klepfish, 2023. "Notes on the convergence of the estimated risk factor matrix in linear regression models," Journal of Asset Management, Palgrave Macmillan, vol. 24(2), pages 97-107, March.
    • Handle: RePEc:pal:assmgt:v:24:y:2023:i:2:d:10.1057_s41260-022-00285-x
    DOI: 10.1057/s41260-022-00285-x
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