Three fuzzy goal programming models for index portfolios

• Published in: The Journal of the Operational Research Society Vol. 65; no. 8; pp. 1155 - 1169
• Main Authors: Wu, Liang-chuan, Tsai, I-chan
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.08.2014; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Benchmarks; Business and Management; Costs; ETF; Exchange traded funds; Financial portfolios; fuzzy goal programming; Fuzzy sets; General Paper; General Papers; Genetic algorithms; Goal programming; Heuristic; index fund; Index funds; Integer programming; Investments; Investors; Management; Mathematical programming; Membership functions; Mutual funds; Operations research; Operations Research/Decision Theory; Optimization; Portfolio management; Programming models; Securities markets; Set theory; Stock exchanges; Stock market indices; Studies; tracking error; Volatility; fuzzy goal programming; tracking error; index fund; ETF
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2013.47

Studies show that most actively managed mutual funds struggle to beat the market, driving an increase in the popularity of index investing. Index investing instruments, including index funds and Exchange-traded Funds, aim to track market performance. This study pursues both tracking error minimization and excess return maximization, two conflicting objectives, to construct an index portfolio. In the real-world financial environment, the desires and expectations of decision makers are generally imprecise. This study applies fuzzy theory to deal with imprecise objectives. This study represents minimizing tracking error and maximizing excess return as 'fuzzy goals' to improve traditional goal programming, which is suitable for handling multiple conflicting objectives, but subject to establishing crisp goals. Three fuzzy goal programming (FGP) models that track indexes are compared and discussed, and the results show that through certain membership functions and tracking models, an index tracking portfolio with a tracking error lower than the 0050 index fund, and a similar excess return to 0050 index fund can be constructed using additive type FGP. max-min type FGP underperforms the additive type FGP in index fund construction.