Linearity properties of a three-moments portfolio model

Pressacco, Flavio; Stucchi, Patrizia

doi:10.1007/s102030070004

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…Therefore, coherently with the classic arbitrage pricing theory the mean returns can be approximated by the linear pricing relation 0 where δ j for j=1,...,k, are the risk premiums relative to the different factors. In particular, when we consider a three-fund separation model which depend on the first three moments, we obtain the so called Security Market Plane (SMP) (see, among others,Ingersoll (1987),Pressacco and Stucchi (2000), and Adcock et al (2005)). However, the approaches (6),(7), and (8) generalize the previous fund separation approach.…”

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confidence: 99%

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The Proper Use of Risk Measures in Portfolio Theory

Ortobelli

Rachev

Stoyanov

et al. 2005

Int. J. Theor. Appl. Finan.

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This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor's portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety-risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.

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confidence: 99%

“…See, among others, Horvarth and Scott (1980),Gamba and Rossi (1998), andPressacco and Stucchi (2000).…”

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confidence: 99%

The Proper Use of Risk Measures in Portfolio Theory

Ortobelli

Rachev

Stoyanov

et al. 2005

Int. J. Theor. Appl. Finan.

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“…However, there are other asymmetric distributions that satisfy this property. Specifically, Simaan (1993) shows that if one adds an independent scalar asymmetric variable times a vector to an elliptical random vector, then (5) holds with s 2t = 0 (see also Gamba and Rossi, 1998;Pressacco and Stucchi, 2000). In addition, it is possible to show that (5) would also hold with s 1t + 3s 2t s 3t = 0 for a multivariate Hermite expansion in which asymmetry is a common feature (see Mencía and Sentana, 2009, for a formal definition of this density).…”

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confidence: 98%

Multivariate location–scale mixtures of normals and mean–variance–skewness portfolio allocation

Mencía

Sentana

2009

Journal of Econometrics

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a b s t r a c tWe show that the distribution of any portfolio whose components jointly follow a location-scale mixture of normals can be characterised solely by its mean, variance and skewness. Under this distributional assumption, we derive the mean-variance-skewness frontier in closed form, and show that it can be spanned by three funds. For practical purposes, we derive a standardised distribution, provide analytical expressions for the log-likelihood score and explain how to evaluate the information matrix. Finally, we present an empirical application in which we obtain the mean-variance-skewness frontier generated by the ten Datastream US sectoral indices, and conduct spanning tests.

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