Abstract
This article proposes a simulation-based approach to find the optimal values of discretionary parameters in portfolio optimization problems. An algorithm is developed for finding jointly optimal values of required expected returns and of diversification restrictions.
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Notes
For a low-dimensional problem, such as in the example of Sect. 4, a fixed grid over the space of discretionary parameters can be used instead. For a multidimensional problem the use of Monte Carlo methods is likely to be preferable in order to deal with the curse of dimensionality.
It is more appropriate to think of these three assets not as individual companies, but as diversified asset classes, such as U.S. equity and Emerging markets equity. Broad Exchange Traded Funds could proxy these asset classes. Within the context of our preceding theoretical discussion, these returns can be thought of as sector-specific Internal Rates of Returns computed from the Net Present Value calculations, discussed in problem (1)–(4).
In the context of our theoretical formulation, the diversification restrictions are represented by the parameters Ak in the inequalities 3.
References
1st Global. 2017. The efficient diversification of multi asset-class portfolios: A user’s guide to strategic asset allocation. http://www.legacywealthmt.com/legacywealthmt.com/userfiles/modules/file_upload_library_3/6/efficientdiversification.pdf. Accessed 30 Aug 2019.
Dontchev, A.L. 1983. Perturbations, approximations and sensitivity analysis of optimal control systems. Berlin: Springer.
Markowitz, H.M. 1952. Portfolio selection. Journal of Finance 7: 7–91.
Nikolouzou, E.G., P.D. Sampatakos, and I.S. Venieris. 2001. Evaluation of an algorithm for dynamic resource distribution in a differentiated services network. In Proceedings of the IEEE international conference on networking, Colmar, France.
Pervozvanskyi, A.A. 1979. Optimization of system with weak coupling. Systems Science 2: 23–32.
Sharpe, W.F. 1963. A simplified model for portfolio analysis. Management Science 9: 277–293.
Shukaev, D.N., and E.R. Kim. 2010. Extension method in location problem with discrete objects. In Proceedings of the 21st IASTED international conference “modelling and simulation (MS 2010), 270–274. Banff.
Shukayev, D.N. 2004. Computer simulation. Almaty: KazNTU.
Shukayev, D.N., V.Z. Abdullina, N.O. Yergaliyeva, and ZhB Lamasheva. 2014. Modeling the processes of distribution of resource flows. Proceedings of the Romanian Academy, Series A 15(1): 85–94.
Shukayev, D.N., E.R. Kim, A.D. Shukayev, and N.O. Yergaliyeva. 2016a. Formation of an investment portfolio with “perturbation” parameters. Fundamental Research 1(10): 228–233.
Shukayev, D.N., N.O. Yergaliyeva, and ZhB Lamasheva. 2016b. Simulation analysis of resource allocation problems with time varying parameters. Proceedings of the Romanian Academy, Series A 17(1): 76–83.
Tikhonov, A.N., and V.Y. Arsenin. 1996. Methods for solving ill-posed problems. Science, Moscow.
Weikard, H.-P., and D. Seyhan. 2009. Distribution of phosphorus resources between rich and poor countries: The effect of recycling. Ecological Economics 68(8): 1749–1755.
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Bimurat, Z., Abdibekov, D.U., Shukayev, D.N. et al. Sensitivity of optimal portfolio problems to time-varying parameters: simulation analysis. J Asset Manag 20, 395–402 (2019). https://doi.org/10.1057/s41260-019-00132-6
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DOI: https://doi.org/10.1057/s41260-019-00132-6