Large-scale portfolio investments (Beyond the Markowitz portfolio theory)

10.04.2018 - 12.04.2018 | Warsaw


 Aims and Scope

 The event is meant to bring together a group of researchers actively working in the area of portfolio investments. The overall goal is to achieve a synergy from diverse  specific expertise represented by the participants to produce methodologies with a potential to go beyond the classic Harry Markowitz, a Nobel prize laureate in 1970, portfolio theory, both in the theoretical and computational aspects.

 It is expected that the specific topics listed below (the list is not exclusive) will be framed within large-scale portfolio investments context.






Specific topics

Understanding and capturing market behavior

 Methodological issues of market behavior and its modelling are still under investigation (see e.g. Prekopa, Lee 2018). Risk, the inherent factor of investing, still needs to  be researched and new measures possessing plausible computational characteristics allowing to be accommodated in large-scale computing, are to be proposed.

Accounting for multiple perspectives of portfolio investments

Taking into account the complex nature of the portfolio investments, it is not surprising that over the last sixty–five years there were numerous attempts to extend the generic bi–criteria mean–variance model to three or more criteria. The recent papers by Kolm et al. (2014) and Qi et al (2015) bring detailed surveys on those attempts. Various authors have proposed adding criteria pertaining to dividends, skewness (of return distributions), tracking error, transaction costs, liquidity, social responsibility, the amount invested in R&D, growth–in sales, and sustainability. Especially social responsible investment have recently attracted much interest (Qi et al. 2015 lists seven papers concerned with social responsible portfolio investment published since 2012).

Methodologies enabling to navigate over the set of efficient (in the sense of Pareto) portfolios, capable to deal with large-scale problems still need to be enhanced.

Dynamic portfolio investments

Whereas static portfolio investments (and related portfolio optimization) is a necessary first step, the true nature of investments is that they are, almost as a rule, multi-period, thus dynamic. Despite intensive researches in that topic in the past (e.g. Samuelson 1969), this is still a vivid area, constantly bringing new results. There are various approaches to the dynamic theory of risk and portfolio optimization under risk. One example of such papers is Pitera, Stettner 2016.

Solvability of large-scale problems of portfolio investments by modern methods technologies

To keep the extended models solvable by analytical methods (like that one by Merton 1972), all the additional criteria listed above have been formulated as linear. Beyond that, any departure from the original mean–variance Markowitz model makes it unsolvable by analytical approaches. Moreover, exact optimization methods do not provide effective algorithms for solving mean–variance model extensions for the problem sizes (the number of assets to select from) dictated by practical needs. On the other hand, heuristic optimization methods, like evolutionary optimization, usually cope well with nonlinearities and find approximate solutions quickly but have no proofs of correctness and, thus, are theoretically unsupported. Methods providing accuracy measures for heuristic optimization methods (e.g. along lines proposed in Kaliszewski, Miroforidis 2017) have to be developed. Likewise, hybrid techniques, combining the strength of exact and heuristic methods, await elaboration.

Kaliszewski I., Miroforidis J., 2017. On Upper Approximations of Pareto Fronts, 2017, arXiv: 2056634 .

Kolm P.N.; Tütüncü, R., Fabozzi, F.J., 2014. 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research , 234, 356 – 371.

Prékopa A., Lee J., 2018. Risk tomography. European Journal of Operational Research, 265, 149–168.

Qi Y., Steuer R.E., Wimmer M., 2015. An Analytical Derivation of the Efficient Surface in Portfolio Selection with Three Criteria. Annals of Operations Research, 1 – 17.

Samuelson P.A., (1969), Lifetime Portfolio Selection By Dynamic Stochastic Programming. The Review of Economics and Statistics, 51, 3, 239-246.

Pitera, M., Stettner L., (2016), Long run risk sensitive portfolio with general factors, Math. Meth. Oper. Res. 83, 265-293.


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