A FUZZY DECISION‐MAKING APPROACH FOR PORTFOLIO MANAGEMENT WITH DIRECT REAL ESTATE INVESTMENT
Authors: Hui Eddie Chi Man , Lau Otto Muk Fai , Lo Kak Keung 
Published: June 2009

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.