Fuzziness and Funds Allocation in Portfolio Optimization

Each individual investor is different, with different financial goals, different levels of risk tolerance and different personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It's really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook - essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about two-dozen questions that each has to be answered with values from 1 to 5. The questions range from personal background (age, marital state, number of children, job type, education type, etc.) to what the customer expects from an investment (capital protection, tax shelter, liquid assets, etc.). A fuzzy logic system has been designed for the evaluation of the answers to the above questions. We have investigated the notion of fuzziness with respect to funds allocation.Comment: 21 page

How to Handle Uncertainty

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Transfer Entropy Approach for Portfolio Optimization: An Empirical Approach for CESEE Markets

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Distribution-based entropy weighting clustering of skewed and heavy tailed time series

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties, such as heavy tails and skewness. Thanks to its flexibility, the skewed exponential power distribution (also called skewed generalized error distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is shown by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.Peer ReviewedPostprint (published version

Geneettinen Algoritmi Optimaalisten Investointistrategioiden Määrittämiseen

Investors including banks, insurance companies and private investors are in a constant need for new investment strategies and portfolio selection methods. In this work we study the developed models, forecasting methods and portfolio management approaches. The information is used to create a decision-making system, or investment strategy, to form stock investment portfolios. The decision-making system is optimized using a genetic algorithm to find profitable low risk investment strategies. The constructed system is tested by simulating its performance with a large set of real stock market and economic data. The tests reveal that the constructed system requires a large sample of stock market and economic data before it finds well performing investment strategies. The parameters of the decision-making system converge surprisingly fast and the available computing capacity turned out to be sufficient even when a large amount of data is used in the system calibration. The model seems to find logics that govern stock market behavior. With a sufficient large amount of data for the calibration, the decision-making model finds strategies that work with regard to profit and portfolio diversification. The recommended strategies worked also outside the sample data that was used for system parameter identification (calibration). This work was done at Unisolver Ltd.Investoijat kuten pankit, vakuutusyhtiöt ja yksityissijoittajat tarvitsevat jatkuvasti uusia investointistrategioita portfolioiden määrittämiseen. Tässä työssä tutkitaan aiemmin kehitettyjä sijoitusmalleja, ennustemenetelmiä ja sijoitussalkun hallinnassa yleisesti käytettyjä lähestymistapoja. Löydettyä tietoa hyödyntäen kehitetään uusi päätöksentekomenetelmä (investointistrategia), jolla määritetään sijoitussalkun sisältö kunakin ajanhetkenä. Päätöksentekomalli optimoidaan geneettisellä algoritmilla. Tavoitteena on löytää tuottavia ja pienen riskin investointistrategioita. Kehitetyn mallin toimintaa simuloidaan suurella määrällä todellista pörssi- ja talousaineistoa. Testausvaihe osoittaakin, että päätöksentekomallin optimoinnissa tarvitaan suuri testiaineisto toimivien strategioiden löytämiseksi. Rakennetun mallin parametrit konvergoivat optimointivaiheessa nopeasti. Käytettävissä oleva laskentateho osoittautui riittäväksi niissäkin tilanteissa, joissa toisten menetelmien laskenta laajan aineiston takia hidastuu. Malli vaikuttaa löytävän logiikkaa, joka ymmärtää pörssikurssien käyttäytymistä. Riittävän suurella testiaineistolla malli löytää strategioita, joilla saavutetaan hyvä tuotto ja pieni riski. Strategiat toimivat myös mallin kalibroinnissa käytetyn aineiston ulkopuolella, tuottaen hyviä sijoitussalkkuja. Työ tehtiin Unisolver Oy:ssä

Multi-objective possibilistic model for portfolio selection with transaction cost

AbstractIn this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples

Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails

A methodology for the selection of new technologies in the aviation industry

The purpose of this report is to present a technology selection methodology to quantify both tangible and intangible benefits of certain technology alternatives within a fuzzy environment. Specifically, it describes an application of the theory of fuzzy sets to hierarchical structural analysis and economic evaluations for utilisation in the industry. The report proposes a complete methodology to accurately select new technologies. A computer based prototype model has been developed to handle the more complex fuzzy calculations. Decision-makers are only required to express their opinions on comparative importance of various factors in linguistic terms rather than exact numerical values. These linguistic variable scales, such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’, are then converted into fuzzy numbers, since it becomes more meaningful to quantify a subjective measurement into a range rather than in an exact value. By aggregating the hierarchy, the preferential weight of each alternative technology is found, which is called fuzzy appropriate index. The fuzzy appropriate indices of different technologies are then ranked and preferential ranking orders of technologies are found. From the economic evaluation perspective, a fuzzy cash flow analysis is employed. This deals quantitatively with imprecision or uncertainties, as the cash flows are modelled as triangular fuzzy numbers which represent ‘the most likely possible value’, ‘the most pessimistic value’ and ‘the most optimistic value’. By using this methodology, the ambiguities involved in the assessment data can be effectively represented and processed to assure a more convincing and effective decision- making process when selecting new technologies in which to invest. The prototype model was validated with a case study within the aviation industry that ensured it was properly configured to meet the

A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market

[EN] This paper extends the stochastic mean-semivariance model to a fuzzy multiobjective model, where apart from return and risk, also liquidity is considered to measure the performance of a portfolio. Uncertainty of future return and liquidity of each asset are modeled using L-R type fuzzy numbers that belong to the power reference function family. The decision process of this novel approach takes into account not only the multidimensional nature of the portfolio selection problem but also realistic constraints by investors. Particularly, it optimizes the expected return, the semivariance and the expected liquidity of a given portfolio, considering cardinality constraint and upper and lower bound constraints. The constrained portfolio optimization problem resulting is solved using the algorithm NSGA-II. As a novelty, in order to select the optimal portfolio, this study defines the credibilistic Sortino ratio as the ratio between the credibilistic risk premium and the credibilistic semivariance. An empirical study is included to show the effectiveness and efficiency of the model in practical applications using a data set of assets from the Latin American Integrated Market.García García, F.; Gonzalez-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J. (2020). A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market. Enterpreneurship and Sustainability Issues. 8(2):1027-1046. https://doi.org/10.9770/jesi.2020.8.2(62)S102710468