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Location-scale portfolio selection with factor-recentered skew normal asset returns

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  • Gan, Quan

Abstract

This paper analyzes the single period portfolio selection problem on the location-scale return family. The skew normal distribution, after recentering and reparameterization, is shown to be in this family. The recentered and reparameterized distribution, called factor-recentered skew normal, can be expressed as a skew factor model which is characterized by a location parameter and two scale parameters. Risk preference on scale parameter is non-monotonic and risk averse investors prefer larger (smaller) scale when the scale is negative (positive). The three-parameter efficient set is a part of conical surface bounded by two lines. Positive-skewness portfolios and negative-skewness portfolios do not coexist in the efficient set. Numerical cases under constant absolute risk aversion are analyzed with its closed-form certainty equivalent. An asset pricing formula which nests the CAPM is obtained.

Suggested Citation

  • Gan, Quan, 2014. "Location-scale portfolio selection with factor-recentered skew normal asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 176-187.
    • Handle: RePEc:eee:dyncon:v:48:y:2014:i:c:p:176-187
    DOI: 10.1016/j.jedc.2014.09.002
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    Cited by:

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    2. Zhen, Fang & Chen, Jingnan, 2022. "A closed-form mean–variance–skewness portfolio strategy," Finance Research Letters, Elsevier, vol. 47(PB).

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    More about this item

    Keywords

    Portfolio selection; Skew normal; Certainty equivalent; Non-monotonicity; Factor model;
    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
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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