Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315459 
Authors: 
Year of Publication: 
2024
Citation: 
[Journal:] Mathematics and Financial Economics [ISSN:] 1862-9660 [Volume:] 18 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 151-170
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
Within the one-factor capital asset pricing model (CAPM), the minimum-variance portfolio (MVP) is known to have long positions in those assets of the underlying investment universe whose betas are less than a well-defined long-short threshold beta. We study the structure of MVPs in more general multi-factor asset pricing models and clarify the low-beta puzzle for multi-factor models: For multi-factor models we derive a similar criterion in terms of the betas with explicit closed-form formulas. But the structural relationship is now more involved and the long-short threshold turns out to be asset-specific. The results rely on recursive inverse-free formulas for the precision matrix, which hold for multi-factor models and allow quick computation of that inverse matrix without the need to invert matrices going beyond diagonal ones. We illustrate our findings by analyzing S &P 500 asset returns. Our empirical results of the S &P 500 constituents between 2019 and 2022 confirm the theoretical findings and shows that the minimum variance portfolio is long in low-beta assets when applying estimates of the established asset-specific thresholds.
Subjects: 
Asset pricing models
Factor models
Minimum-variance portfolio
PCA
Portfolio optimization
Long-short strategies
JEL: 
G11
G12
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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