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Fundamental Portfolio Construction Based on Semi-Variance

100%

Rutkowska-Ziarko A.

nr 2

151-162

In models for creating a fundamental portfolio, based on the classical Markowitz model, the variance is usually used as a risk measure. However, equal treatment of negative and positive deviations from the expected rate of return is a slight shortcoming of variance as the risk measure. Markowitz defined semi-variance to measure the negative deviations only. However, finding the fundamental portfolio with minimum semi-variance is not possible with the existing methods.The aim of the article is to propose and verify a method which allows to find a fundamental portfolio with the minimum semi-variance. A synthetic indicator is constructed for each company, describing its economic and financial situation. The method of constructing fundamental portfolios using semi-variance as the risk measure is presented. The differences between the semi-variance fundamental portfolios and variance fundamental portfolios are analysed on example of companies listed on the Warsaw Stock Exchange.

A condition for asset redundancy in the mean-variance model of portfolio investment

88%

Juszczuk P. , Kaliszewski I. , Miroforidis J. , Podkopaev D.

tom Vol. 49, No. 2

179--191

The mean-variance approach to portfolio investment exploits the fact that the diversification of investments by combination of different assets in one portfolio allows for reducing the financial risks significantly. The mean-variance model is formulated as a bi-objective optimization problem with linear (expected return) and quadratic (variance) objective functions. Given a set of available assets, the investor searches for a portfolio yielding the most preferred combination of these objectives. Naturally, the search is limited to the set of non-dominated combinations, referred to as the Pareto front. Due to the globalization of financial markets, investors nowadays have access to large numbers of assets. We examine the possibility of reducing the problem size by identifying those assets, whose removal does not affect the resulting Pareto front, thereby not deteriorating the quality of the solution from the investor’s perspective. We found a sufficient condition for asset redundancy, which can be verified before solving the problem. This condition is based on the possibility of reallocating the share of one asset in a portfolio to another asset without deteriorating the objective function values. We also proposed a parametric relaxation of this condition, making it possible to removemore assets for a price of a negligible deterioration of the Pareto front. Computational experiments conducted on five real-world problems have demonstrated that the problem size can be reduced significantly using the proposed approach.

Can we invest on the basis of equity risk premia and risk factors from multi-factor models ?

75%

Pawel S. , Robert Ś. , Mateusz W.

nr 3

78-98

We examine two investment algorithms built on the weekly data of world equity indices for emerging and developed countries in the period 2000-2015. We create seven risk factors using additional data about market capitalization, book value, country GDP and betas of equity indices. The first strategy utilizes the theoretical value of equity risk premium from the seven-factor Markov-switching model with exogenous variables. We compare theoretical with the realized equity risk premium for a given index to undertake the buy/sell decisions. The second algorithm works only on eight risk factors and applies them as input variables to Markowitz models with alternative optimization criteria. Finally we note that the impact of risk factors on the final results of investment strategy is much more important than the selection of a particular econometric model in order to correctly evaluate the equity risk premium.

Random approximations in multiobjective programming - with an application to portfolio optimization with shortfall constraints

51%

Vogel S.

tom Vol. 28, no 4

703-724

Decision makers often heave to deal with a programming problem vhere some of the quantities are unknown. They will usually estimate these quantities and solve the problem as it then appears - the "approximate problem". Thus, there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. The paper summarizes such results for multiobjective programming problems. The results ase illustrated by means of the Markowitz model of portfolio optimization. In order to show how probabilistic constraints may be dealt with using this framework, a shortfall constraint is taken into account.