Black-Litterman model with intuitionistic fuzzy posterior return

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On the side, intensive discussion shows that the experts' views are under knightian uncertainty. For this reason, we propose such variant of the Black - Litterman model in which the experts' views are described as intuitionistic fuzzy number. The existence of posterior return is proved for this case.We show that then posterior return is an intuitionistic fuzzy probabilistic set.Comment: SSRN Electronic Journal 201

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

Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

FUZZY LOGIC AND COMPROMISE PROGRAMMING IN PORTFOLIO MANAGEMENT

The objective of this paper is to develop a portfolio optimization technique that is simple enough for an individual with little knowledge of economic theory to systematically determine his own optimized portfolio. A compromise programming approach and a fuzzy logic approach are developed as alternatives to the traditional EV model.Agricultural Finance,

Asset Allocation with Aversion to Parameter Uncertainty: A Minimax Regression Approach

This paper takes a minimax regression approach to incorporate aversion to parameter uncertainty into the mean-variance model. The uncertainty-averse minimax mean-variance portfolio is obtained by minimizing with respect to the unknown weights the upper bound of the usual quadratic risk function over a fuzzy ellipsoidal set. Beyond the existing approaches, our methodology offers three main advantages: first, the resulting optimal portfolio can be interpreted as a Bayesian mean-variance portfolio with the least favorable prior density, and this result allows for a comprehensive comparison with traditional uncertainty-neutral Bayesian mean-variance portfolios. Second, the minimax mean-variance portfolio has a shrinkage expression, but its performance does not necessarily lie within those of the two reference portfolios. Third, we provide closed form expressions for the standard errors of the minimax mean-variance portfolio weights and statistical significance of the optimal portfolio weights can be easily conducted. Empirical applications show that incorporating aversion to parameter uncertainty leads to more stable optimal portfolios that outperform traditional uncertainty-neutral Bayesian mean-variance portfolios.Asset allocation, estimation error, aversion to uncertainty, min-imax regression, Bayesian mean-variance portfolios, least favorable prior

A fuzzy decision‐making approach for portfolio management with direct real estate investment

This study incorporated expert knowledge into the classical quadratic programming approach, i.e., Modern Portfolio Theory (MPT), through fuzzy set theory; in obtaining portfolio return optimization involving direct real estate investment. Two fuzzy mathematical programming models were uniquely specified and estimated in this study, namely, Zimmer‐mann's (2001) fuzzy tactical asset allocation (FTAA) flexible programming model and Ramik and Rimanek's (1985) FTAA robust programming model. These approaches try to overcome the drawbacks of traditional asset allocation models by including expert adjustment in the presence of imprecise information. The findings suggest that the fuzzy tactical asset allocation (FTAA Flexible Model), with the inclusion of expert judgments which contain information usually not found in historical data, is able to produce a portfolio just as efficient as traditional asset allocation models while minimizing the potential issues due to imprecision and vagueness of information. Meanwhile, the FTAA Robust Model proffers a more evenly‐distributed, yet with higher risks and lower returns, portfolio. Aside from the lack of emphasis on portfolio risks minimization, one reason attributed to such anomaly is the low level of returns of high‐risk stocks that are not selected by MPT and FTAA Flexible Models. It results in a unique situation where portfolio diversification does not necessarily guarantee an efficient investment decision. Santruka Šis tyrimas itraukia ekspertines žinias i klasikine kvadratinio programavimo metodika, pavyzdžiui, moderniaja portfelio valdymo teorija, per neapibrežtuju aibiu teorija, siekiant optimizuoti portfelio graža, apimant tiesiogines nekilnojamojo turto investicijas. Šiame tyrime išsamiai aprašomi ir ivertinami du neapibrežtojo matematinio programavimo modeliai. Tai Zimmermann (2001) neapibrežtasis aktyvu paskirstymo lankstusis programavimo modelis ir Ramik bei Rimanek (1985) neapibrežtasis aktyvu paskirstymo robustinis programavimo modelis. Juos taikant bandoma pašalinti tradiciniu aktyvu paskirstymo metodu trūkumus itraukiant ekspertu siūlomus pakeitimus nesant tikslios informacijos. Nustatyta, kad neapibrežtasis aktyvu paskirstymas (neapibrežtasis aktyvu paskirstymo lankstusis programavimo modelis) kartu su ekspertu vertinimais, paprastai apimančiais informacija, kurios negalima rasti tarp istoriniu duomenu, leidžia sudaryti toki pati efektyvu portfeli, kaip ir tradiciniai aktyvu paskirstymo modeliai, tačiau minimizuojant potencialius nesutarimus, kuriu atsiranda del netikslios ir neapibrežtos informacijos. Neapibrežtasis aktyvu paskirstymo robustinis programavimo modelis siūlo tolygiau paskirstyta, tačiau rizikingesni ir ne toki pelninga portfeli. Be portfelio rizikos minimizavimo trūkumo, dar viena priežastis, priskiriama prie šios anomalijos, yra maža dideles rizikos akciju graža, kuri nera pasirenkama moderniojoje portfelio valdymo teorijoje ir neapibrežtuju aktyvu paskirstymo lanksčiuosiuose programavimo modeliuose. Kaip rezultatas gaunama unikali situacija, kai portfelio diversifikavimas nebūtinai garantuoja efektyvu investavimo sprendima. First Publish Online: 18 Oct 201

Portfolio optimization using a hybrid of fuzzy ANP, VIKOR and TOPSIS

One of the primary questions in asset management is to find good combinations of different assets and this has been an interesting area of research for over half a century. The proposed model of this paper uses decision makers' feedbacks based on multiple criteria decision making technique to find an appropriate portfolio. We first select some important financial criteria and then using decision makers' opinions and by implementation of some fuzzy network analysis we find appropriate weights of the asset. The proposed model uses two multiple criteria techniques namely TOPSIS and VIKOR and the model is examined for some real-world data from Tehran Stock Exchange. The results of the implementation of the proposed model have been examined against Markowitz traditional model. The preliminary results indicate that the proposed model of this paper performs reasonably well compared with alternative method