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Are minimum variance portfolios in multi-factor models long in low-beta assets?

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  • Ansgar Steland

    (RWTH Aachen University)

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.

Suggested Citation

  • Ansgar Steland, 2024. "Are minimum variance portfolios in multi-factor models long in low-beta assets?," Mathematics and Financial Economics, Springer, volume 18, number 6, September.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:1:d:10.1007_s11579-024-00366-y
    DOI: 10.1007/s11579-024-00366-y
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    References listed on IDEAS

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    7. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    8. Joshua Traut, 2023. "What we know about the low-risk anomaly: a literature review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(3), pages 297-324, September.
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    More about this item

    Keywords

    Asset pricing models; Factor models; Minimum-variance portfolio; PCA; Portfolio optimization; Long-short strategies;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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