Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation

Mencía, Javier Juste; Sentana, Enrique

doi:10.2139/ssrn.1092010

Cited by 26 publications

(38 citation statements)

References 49 publications

(17 reference statements)

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“…Mencía and Sentana (2009) consider the mean-variance-skewness portfolio selection with a location-scale mixture distribution of normals. The mixture distribution is flexible and its first three moments are fully characterized by three parameters.…”

Section: Simaan's Framework Vs Other Higher Moments Portfolio Selectmentioning

confidence: 99%

“…The mixture distribution is flexible and its first three moments are fully characterized by three parameters. Mencía and Sentana (2009) show that the mean-variance-skewness frontier is spanned by three funds in the "mean-variance-skewness" space. Although their work has similarity to Simaan (1993).…”

Section: Simaan's Framework Vs Other Higher Moments Portfolio Selectmentioning

confidence: 99%

“…The mean-variance efficient frontier is spanned by two funds and the two-fund separation simplifies the calculation of efficient portfolios. The portfolio selection with higher moments however have several frameworks (Simaan 1993, Athayde & Flôres 2004, Briec et al 2007, Mencía & Sentana 2009, and Low et al 2012. Although each of these frameworks has its own merits, the lack of a unified framework is certainly a drawback.…”

Section: Introductionmentioning

confidence: 99%

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Performance of Equity REITs: Does a Skew Factor Matter?

Gan¹,

Tsolacos²,

Güloğlu³

2013

Proceedings of the 20th Annual European Real Estate Society Conference - Vienna, Austria

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This paper examines the portfolio selection problem with skew normal asset returns. By exploring an alternative parameterization of Azzalini & Dalla Valle (1996)'s multivariate skew normal distribution I show that the multivariate skew normal distribution is a special case of Simaan (1993)'s three-parameter model. All Simaan (1993)'s results are applicable to the skew normal asset returns. The three-parameter efficient frontier is spanned by three funds which include two funds from the mean-variance portfolio selection. Combining the skew normal asset returns with the CARA utility, I obtain the closed-form certainty equivalent and skewness premium. I show that the skewness premium is positive (negative) when asset returns have negative (positive) skewness. The magnitude of the skewness premium is increasing in market risk aversion. I use the skew normal certainty equivalent to evaluate the economic value of incorporating higher moments in portfolio selection. I find that when investors face broad investment opportunities, the economic value of considering higher moments is negligible under realistic margin requirements.(JEL. G11, G12, D81)

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Section: Simaan's Framework Vs Other Higher Moments Portfolio Selectmentioning

confidence: 99%

Section: Simaan's Framework Vs Other Higher Moments Portfolio Selectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Performance of Equity REITs: Does a Skew Factor Matter?

Gan¹,

Tsolacos²,

Güloğlu³

2013

Proceedings of the 20th Annual European Real Estate Society Conference - Vienna, Austria

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“…A number of papers are devoted to questions like, e.g., how an optimal portfolio can be constructed, monitored, and/or estimated by using historical data (see, e.g., Alexander and Baptista (2004) , Golosnoy and Schmid (2007), Bodnar (2009)), what is the influence of parameter uncertainty on the portfolio performance (cf., Okhrin and Schmid (2006) , Bodnar and Schmid (2008)), how do the asset returns influence the portfolio choice (see, e.g., Jondeau and Rockinger (2006), Mencía and Sentana (2009), Adcock (2009), Harvey et al (2010), Amenguala and Sentana (2010)), how is it possible to estimate the characteristics of the distribution of the asset returns (see, e.g., Jorion (1986), Wang (2005), Frahm and Memmel (2010)), how can the structure of optimal portfolio be statistically justified (Gibbons et al (1989), Britten-Jones (1999), Bodnar and Schmid (2009)). …”

Section: Introductionmentioning

confidence: 99%

A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function

2015

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In the present paper, we derive a closed-form solution of the multiperiod portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices.If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.

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“…There have been some other attempts to model portfolio selection taking into account third (see Mencíya and Sentana (2009)) and third/fourth moments (see Jondeau and Rockinger (2006) and Martellini and Ziemann (2010)). The main problem with these models is that they generally use weekly or monthly returns to estimate the parameters.…”

Section: Introduction and Literaturementioning

confidence: 99%

Realised higher moments: theory and practice

Buckle

Chen

Williams

2014

The European Journal of Finance

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper examines incorporation of higher moments in portfolio selection problems utilizing high frequency data. Our approach combines innovations from the realized volatility literature with a portfolio selection methodology utilising higher moments. We provide an empirical study of the measurement of higher moments from tick by tick data and implement the model for a selection of stocks from the DOW 30 over the time period 2005 to 2011. We demonstrate a novel estimator for moments and co moments in the presence of microstructure noise.

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Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation

Cited by 26 publications

References 49 publications

Performance of Equity REITs: Does a Skew Factor Matter?

Performance of Equity REITs: Does a Skew Factor Matter?

A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function

Realised higher moments: theory and practice

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