Optimal portfolio positioning within generalized Johnson distributions

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite ge...

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Bibliographic Details
Published in:Quantitative finance Vol. 17; no. 7; pp. 1037 - 1055
Main Authors: Naguez, N., Prigent, J. L.
Format: Journal Article
Language:English
Published: Routledge 03-07-2017
Taylor & Francis (Routledge)
Subjects:
Hedge funds
Humanities and Social Sciences
Johnson distributions
Mathematics
Optimal portfolio positioning
Quantitative Finance
Statistics
Structured asset management
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Summary:Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279-300], Leland [J. Finance, 1980, 35, 581-594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9-37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2016.1253859