Construction of stable financial investment portfolios using generalised structured weighted average operators

Financing: Narodowe Centrum Nauki under the Opus programme.

The project was carried out Zespół Optymalizacji i Wspomagania Decyzji IAiIS, Politechnika Warszawska.

The amount of the grant awarded: PLN 442 949.
The basis for the construction of the financial investment portfolio is to determine the shares of individual assets. This is an optimisation problem typically formalised by means of the Markowitz model, where one of the criteria is the expected value of a random variable describing future profits from the portfolio, and the other is a measure of its dispersion reflecting the degree of risk associated with the investment. The assumptions of the Markowitz model should guarantee the generation of portfolios that are stable over time, i.e. those characterised by no fluctuations in the shares of investment instruments and by risk and average rate of return corresponding to those determined on the basis of historical data. In practice, there is no clear information about the distribution of rates of return and the assumptions of the Markowitz model are not met. The aim of the project was to develop and study a new approach to the construction of financial investment portfolios ensuring stability of their composition for the assumed set of financial assets. The developed method is based on the concept of the worst case distribution of rates of return of financial assets, which used in the Markowitz model allows to obtain results not worse than in the sample in the sense of considered quality indicators.

Attempts to achieve stability of portfolios were made independently in two research areas relating to different stages of the portfolio construction process. With regard to the data generation and estimation phase, work was carried out on the development and use of appropriate statistical and econometric methods. With regard to the proper portfolio construction phase, we developed new models and methods of decision support under risk conditions, aimed at resistance to ambiguous distributions. The project concerned new approaches in both areas. The research should significantly strengthen the theoretical basis and quality of portfolio analysis results, in particular through the interpenetration of statistical and econometric methods in the process of data generation and estimation with operational research and decision support methods in risk conditions for optimizing the portfolio structure.