Abstract
Portfolios are selected in non-Gaussian contexts to maximize a Cherny and Madan index of acceptability. Analytical gradients are developed for the purpose of optimizing portfolio searches on the unit sphere. It is shown that though an acceptability index is not a preference ordering, many utilities will concur with acceptability maximization. A stylized economy illustrates the advantages from the perspective of acceptability of nonlinear securities and options. In sample results for the year 2008 indicate that maximizing the acceptability index can lead to portfolios that second order stochastically dominate their Gaussian counterparts. Backtests over the period 1997 to 2008 reflect gains to maximizing acceptability over holding a maximal Sharpe ratio portfolio.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)
Agarwal, V., Naik, N.: Risk and portfolio decisions involving hedge funds. Rev. Financ. Stud. 17, 63–98 (2004)
Bernardo, A., Ledoit, O.: Gain, loss, and asset pricing. J. Polit. Econ. 108, 144–172 (2000)
Biglova, A., Ortobelli, S., Rachev, S., Stoyanov, S.: Different approaches to risk estimation in portfolio theory. J. Portf. Manag. 31, 103–112 (2004)
Carr, P., Geman, H., Madan, D.: Pricing and hedging in incomplete markets. J. Financ. Econ. 62, 131–167 (2001)
Cherny, A.: Weighted VAR and its properties. Finance Stoch. 10, 367–393 (2006)
Cherny, A., Madan, D.B.: New measures for performance evaluation. Rev. Financ. Stud. 22, 2571–2606 (2009)
Eberlein, E., Madan, D.B.: Hedge fund performance: sources and measures. Int. J. Theor. Appl. Finance 12, 267–282 (2009)
Eberlein, E., Madan, D.B.: On correlating Lévy processes. J. Risk 13, 1 (2010)
Goetzmann, W., Ingersoll, J., Spiegel, M., Welch, I.: Sharpening Sharpe ratios. NBER Working Paper 9116, Cambridge (2002)
Khanna, A., Madan, D.V.: Non-Gaussian models of dependence in returns. SSRN 1540875 (2010)
Jin, H., Zhou, X.Y.: Behavioral portfolio selection in continuous time. Math. Finance 18, 385–426 (2008)
Malevergne, Y., Sornette, D.: High-order moments and cumulants of multivariate Weibull asset return distributions: analytical theory and empirical tests: II. Finance Lett. 3, 54–63 (2005)
Acknowledgements
Dilip Madan acknowledges support from the Humboldt foundation as a Research Award Winner.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Eberlein, E., Madan, D.B. (2014). Maximally Acceptable Portfolios. In: Kabanov, Y., Rutkowski, M., Zariphopoulou, T. (eds) Inspired by Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02069-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-02069-3_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02068-6
Online ISBN: 978-3-319-02069-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)