Credit unions are operated as member-owned, tax-exempt, not-for-profit financial cooperatives and are democratically governed by a volunteer member elected board of directors (Walker and Chandler, 1976 and 1977). Credit unions consistently offer higher interest rates on deposits than commercial banks, charge lower interest rates on loans, and have lower fees on transactions due to lower operational expenses and tax exemptions.
Customer service at credit unions is personal, friendly and usually highly ranked by credit union members. Under provisions of the credit union Act of 1934, U.S. credit unions are chartered by their respective states or by the federal government. The investment decisions of these institutions are also very challenging because of several conflicting objectives including maximization of returns, minimization of risk, and allocation of funds to different types of loan programs (products).
The product offerings are selective as their main resources are the savings collected from the members. However, their financial risks, specifically credit and liquidity risks are similar to commercial banks but are somewhat different because of the size, geographic concentration, liquidity needs and extension of credit only to their members.
Geographic concentration limits the need for evaluation of relative financial strengths and ability to assess and adequately monitor the risks of the investments. A small size credit union may manage the risks by investing all of its surplus funds in a corporate credit union instead of investing in securities. However, with the growth of credit union’s size, the risk-reward opportunities and credit evaluations needs (including continuous monitoring and measuring acceptable level of risks), against available reserves depending on economic conditions, also change.
Credit union management often uses a laddered portfolio as a tool for managing liquidity needs and exposure to interest rate risk. In this approach, investment maturities are laddered to provide necessary cash flow to meet the ongoing liquidity needs and to some extent minimizing exposure to interest rate risk. However, this approach can not be successful in a volatile economic environment. The current dynamics of the domestic and global economic environment is drawing academicians’ attention as well as corporate professionals to identify why their credit and forecasting models failed to warn of and predict the current domestic and global financial situation. The recent financial crisis has also affected adversely the local credit unions. Local credit unions borrow money from corporate credit unions for their funding needs, but now have run into liquidity problems and are unable to borrow to meet their needs due to the recent financial crisis.
Credit unions that have more exposure to real estate loans are facing more liquidity problems because of high delinquencies and foreclosures of these loans. Although credit policy guidelines for loan approvals are strict and sub-prime lending or non-traditional mortgage lending is not one of the main reasons for liquidity issues for most of the credit unions, yet they are also facing similar challenges for their survival as are other commercial banks. Credit unions that have followed strict rules and have not been involved in non-prime lending, their portfolios have not been directly affected by the inability of mortgagees to pay their mortgages nor do they have a portfolio riddled with non-performing mortgage loans. However, their members may have a sub-prime loan from another lender, or may have been laid off due to economic conditions, which are impacting their ability to make payments of credit loans including credit cards and auto loans. The subprime or non-prime mortgage crisis, rising unemployment rates, and increased consumer debt have made the economy a top concern for everybody in the United States. Although big financial institutions develop their own risk management systems, credit unions, due to their limited resources, rely only on third party risk management systems.
Risk management systems available for credit unions are very generic and include a wide range of features related to risk analysis including borrower risk analysis, financial risk analysis, deficiency tracking and credit tracking. These systems have adequate features to analyze and integrate the data and information from various sources and help in investment decision-making process. However, analysts deal with large amount of data, complex policy guidelines, and several other historical factors that need to be considered for making future investment decisions. They are required to weigh all the data and information and make the recommendation that puts the credit union in the best spot- balancing the upside opportunity with minimum possible risk.
To accomplish this task, analysts need flexible professional tools and techniques for construction of efficient portfolio from available loan products given the economic environment. The basic portfolio model was developed in 1952 by Harry Markowitz, who not only emphasized the importance of diversification to reduce the total risk of a portfolio but also demonstrated how to construct an effective diversified portfolio. Since then, several studies have explored applications of Markowitz theory using linear and goal programming (GP) modeling approaches for constructing efficient portfolios and provide optimal solutions for investment decisions.
A comprehensive review of the literature reveals that Lee and Lerro (1973) developed a GP model for mutual fund portfolio selection and Kumar et al. (1978) developed a conceptual GP model for portfolio selection of dual-purpose funds. Lee and Chesser (1980) in their model demonstrated how the linear beta coefficient could be incorporated into GP models for investment decisions. Levary and Avery (1984) incorporated the investor’s priorities in their GP model for selecting optimal portfolio and compared the results with a linear programming (LP) model. Schniederjans et al. (1992) constructed a GP model for investment planning purposes. Sharma et al. (1995) presented GP models for investors or financial planners by incorporating beta coefficients and other important parameters. Pendaraki et al. (2004) developed a GP model and demonstrated its applicability via a sample of Greek mutual funds.
Most of these studies have identified the system development needs of commercial banks. There are a few studies which have focused on credit unions. Walker and Chandler (1977 & 1978) used GP models for allocation of credit unions’ net revenues and net monetary benefits to its members. Kusy and Ziemba (1986) also developed an application using stochastic LP model for the Vancouver City Savings credit union’s portfolio. The optimal solutions provided by these models, based on targeted goals and constraints, reveal that the goals assigned to the lower priority levels are usually redundant. Real world problems involve estimation of desired target levels which cannot be precisely defined because a condition with a strictly binding condition has no practical value. Therefore, assigning imprecise target levels to some or all objectives rather than fixed targets is more reasonable and is possible in modeling using Fuzzy Goal Programming technique.
Fuzzy Goal Programming (FGP) approach facilitates the concept of “fuzzy goals” that are more practical in defining constraints with imprecise targets and flexible technological coefficients and are also called fuzzy criteria (Bellman and Zadeh, 1970). The application of fuzzy set theory for real world problems was first advocated by Zadeh (1965). Later on, Tanaka et al. (1974) and Zimmermann (1978) applied the concept of fuzzy mathematical programming in their research. Several other researchers including Narasimhan (1980 & 1981), Hannan (1981 & 1982), and Ignizio (1982) have enhanced their models and have demonstrated applications of FGP modeling technique. Researchers are enhancing capabilities of quantitative models using FGP technique (Rubin and Narasimhan, 1984; Tiwari et al., 1986 & 1987; Chen, 1994). However, in initial studies, researchers simply transformed multi-objective decision making problems into equivalent LP problems by using max-min operators.
Chen and Tsai (2001) developed an application using preemptive priorities in FGP in an additive model to maximize the achievement degrees of all fuzzy goals. Kim et al. (2002) developed an application of FGP for the optimal planning of an unbalanced development policy for developing countries. The FGP model developed by Parra et al. (2001) for investment portfolio selection included investor’s preferences and aspiration levels for profitability, risk and liquidity. Bilbao-Terol et al. (2006) applied fuzzy compromise programming for developing portfolio selection model. These studies focused more on for-profit financial institutions with less attention to not-for-profit financial institutions such as credit unions.
This study presents FGP models for credit unions’ portfolio management problems. FGP applications can provide better solutions in creating efficient portfolios as compared to LP and GP models. We propose simple and weighted additive FGP models for creating and rebalancing efficient portfolios for credit union portfolio management considering multiple and conflicting fuzzy objectives. Section two presents the mathematical models for the problem, the algorithm, solution procedure and flowchart of the solution procedure. Section three demonstrates applications of both models. Section four analyzes and presents the results of both models. Finally, Section five concludes the findings and contributions of the research.
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