A THEORETICAL MODEL FOR PORTFOLIO OPTIMIZATION DURING CRISIS

Authors

  • Colin Cheong Kiat Gan School of Business and Management, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132, Indonesia
  • Sudarso Kaderi Wiryono School of Business and Management, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132, Indonesia
  • Deddy Priatmodjo Koesrindartoto School of Business and Management, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132, Indonesia
  • Budhi Arta Surya School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand

DOI:

https://doi.org/10.11113/jt.v78.9006

Keywords:

Generalized hyperbolic distribution, portfolio optimization

Abstract

The premise of this paper is providing a theoretical model for a novel way to portfolio optimization using generalized hyperbolic distribution during crisis with risk measures, expected shortfall and standard deviation. Getting good expected returns from investing in portfolio assets like stocks, bonds and currencies during crisis period chosen is harder where the risks cannot be diverted because of disruptive financial jolts i.e. sudden and unprecedented events like subprime mortgage crises in 2008. Multivariate generalized hyperbolic distribution on joint distribution of risk factors from stocks, bonds and currencies is used because it can simplify the risk factors calculation by allowing them to be linearized. The results show the premise is true. The contributions are discovering both the appropriate probability distribution and risk measure will determine whether the portfolio is optimal or not. The practical application will be taking care of the risk to take care of the profit.

References

Knowles, J. K. and Sternberg, E. 1975. On The Ellipticity of The Equations of Nonlinear Elastostatics for a Specialmaterial. J. Elasticity. 5: 341-361.

Knowles, J. K. and Sternberg, E. 1977. On The Failure of Ellipticity of The Equations for Finite Elastostatic Plane Strain. Arch. Ration. Mech. Anal. 63: 321-336.

Rosakis, P. 1990. Ellipticity and Deformations with Discontinuous Deformation Gradients in Finite Elastostatics. Arch. Ration. Mech. Anal. 109: 1-37.

Wang, Y. and Aron, M. 1996. A Reformulation of The Strong Ellipticity Conditions for Unconstrained Hyperelasticmedia. J. Elasticity. 44: 89-96.

Dahl, D., Leinass, J. M. Myrheim, J. and Ovrum, E. 2007. A Tensor Product Matrix Approximation Problem in Quantum Physics. Linear Algebra Appl. 420: 711-725.

Einstein, A., Podolsky, B. and Rosen, N. 1935. Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Phys. Rev. 47: 777-780.

Chang, K., Qi, L. and Zhou, G. 2010. Singular Values of a Real Rectangular Tensor. Journal of Mathematical Analysis and Applications. 370: 284-294.

Wood, R. J. and O'Neill, M. J. 2007. Finding The Spectral Radius of A Large Sparse Non-Negative Matrix. ANZIAM J. 48: C330-C345.

Wood, R. J. and O'Neill, M. J. 2007. An Always Convergent Method for Finding The Spectral Radius of An Irreducible Non-Negative Matrix. ANZIAM J. 45: C474-C485.

Ng, M., Qi, L. and Zhou, G. 2009. Finding The Largest Eigenvalue of A Nonnegative Tensor. SIAM J. Matrix Anal. Appl. 31: 1090-1099.

Zhou, G., Caccetta, L. and Qi, L. 2013. Convergence of An Algorithm for The Largest Singular Value of A Nonnegative Rectangular Tensor. Linear Algebra and its Applications. 438: 959-968.

Jordehi, A. R. 2015. Enhanced Leader PSO (ELPSO): A New PSO Variant for Solving Global Optimisation Problems. Applied Soft Computing. 26: 401-417.

Jordehi, A. R., Jasni, J., Wahab, N. A., Kadir M. Z., and Javadi, M. S. 2015. Enhanced leader PSO (ELPSO): A New Algorithm for Allocating Distributed TCSC’s in Power Systems. International Journal of Electrical Power & Energy Systems. 64: 771-784.

Jordehi, A. R. 2015. Brainstorm Optimisation Algorithm (BSOA): An efficient Algorithm for Finding Optimal Location and Setting of FACTS Devices in Electric Power Systems. International Journal of Electrical Power & Energy Systems. 69: 48-57.

Jordehi, A. R. 2014. A Chaotic-Based Big Bang-Big Crunch Algorithm for Solving Global Optimisation Problems. Neural Computing and Applications. 25: 1329-1335.

Jordehi, A. R. 2015. Chaotic Bat Swarm Optimisation (CBSO). Applied Soft Computing. 26: 523-530.

Varga, R. 1965. Matrix Iterative Analysis. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. Englewood Cliffs.

Minc, H. 1988. Nonnegative Matrices. New York: John Wiley and Sons.

Golub, G. H. and Loan, C. F. V. 1996. Matrix Computations. Baltimore: Johns Hopkins University Press.

Horn, R. A. and Johnson, C. R. 1985. Matrix Analysis. Cambridge University Press.

Friedland, S., Gaubert, S. and Han, L. 2011. Perron-Frobenius Theorem for Nonnegative Multilinear forms and Extensions. Linear Algebra Appl. 438: 738-749.

Zhou, G., Qi, L., and Wu, S. 2013. Efficient Algorithms for Computing The Largest Eigenvalue of A Nonnegative Tensor. Front. Math. China. 8: 155-168.

Zhang, L. 2013. Linear Convergence of An Algorithm for Largest Singular Value of A Nonnegative Rectangular Tensor. Front. Math. China, 8: 141-153.

Ibrahim, N. F. 2014. An Algorithm for The Largest Eigenvalue of Nonhomogeneous Nonnegative polynomials. Numerical Algebra, Control and Optimization. 4: 75-91.

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Published

2016-06-13

Issue

Vol. 78 No. 6-5: Sciences and Mathematics Part II

Section

Science and Engineering

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Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.

How to Cite

A THEORETICAL MODEL FOR PORTFOLIO OPTIMIZATION DURING CRISIS. (2016). Jurnal Teknologi, 78(6-5). https://doi.org/10.11113/jt.v78.9006