Criteria Determining Optimal Portfolio Selection : A Case Study

The paper examines the evaluation of the significance of the criteria that influence two groups of investors, who reside in different areas of Greece, in selecting their investments: (a) Investors from a metropolitan city (Athens) and (b) investors from regional Greece (Peloponnese). The study is grounded in the current and potential criteria and sub-criteria influencing investors in selecting financial investment products. The methodology applied in order to satisfy the research aims is the Analytic Hierarchy Process (AHP). The quantitative research analysis is based on a sample of data collected via a questionnaire answered by a sample of key experts: Specifically, bank executives specialized in financial investment products. The general conclusions stemming from the comparative study are: Metropolitan city Investors (MIs) are more experienced, more dispassionate, more patient and conservative than the Regional Investors. Furthermore, the MIs are more tolerant, provident and informed. The Regional Investors (RIs) can be perceived as more enthusiastic and interested in taking risks than the MIs, but they also appear to feel less secure when it comes to investing. Future research should address larger number of participants from other metropolitan cities and regions and, eventually, from other countries.

INTRODUCTION
Modern portfolio theory concerns the construction of an investment portfolio. In other words, it refers to the combination of financial products invested and possessed by an investor. Consequently, the portfolio comprises an aggregate of different investments in titles (shares, bonds, mutual funds) and in cash possessed by an individual or a legal entity. The combination of different investments may level out positive and negative returns with the result of reduced unsystematic investment risk. According to this concept, for optimal portfolio selection, the combination of financial products that would incorporate high-expected output and safety, based on the available liquidity of the investor, is anticipated. The following categories of titles that express pecuniary value are included in the financial investments (Rachmawati et al., 2014): • Shares • Certificates of deposits • Bonds • Bank deposits • Promissory notes • New issues of shares • Call/Put options

Elements Contributing to a Successful Portfolio
Modern portfolio theory originated in the study of Markowitz (1952), who recognized that by combining assets that are not perfectly correlated, an investor could reduce his or her investment risk without reducing expected returns. It is theoretically possible to derive a portfolio of risky assets that returns the smallest amount of risk for a given return (Haugen, 2001;Strong, 1993).

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Diversification plays a very important role in modern portfolio theory. Because a portfolio is a collection of securities, the selection decision is equivalent to selecting an optimal portfolio from a set of possible portfolios.
Apart from the expected appreciation of individual investments, the success of a portfolio is determined by the investment risk that it encompasses. The risks of an investment can be separated into two general categories: The systematic investment risk and unsystematic investment risk (CI, 2011). The nature of these two risks is absolutely different. Systematic investment risk is associated with the market (purchasing power risk, interest rate risk, liquidity risk). The management of systematic risk is exceptionally difficult. It cannot be forecasted, because it results from the macroeconomic environment (legislative changes with impact in the investments, potential martial clash).
On the contrary, unsystematic investment risk is unique to an individual asset (business risk, financial risk, other risks related to investment in a particular asset).
The unsystematic investment risk can be forecasted and eliminated with the process of risk differentiation, in which different forms of investments with different risk are selected in a portfolio. Some important categories of investment risks are presented below (Cooper and Edjett, 2001): • The business risk concerns all business actions, in which, investments in shares and bonds are included • The market risk arises from the changes of the prices of certain products either at the national or international level • The credit risk or default risk is reported in all investments that are realized with transactions that include payments in the future and result from the probability of breach of some future payment that will influence negatively the cash inflows • The liquidity risk arises from investments that are difficult or impossible to liquidate and in consequence, they can cause lack of cash flow and lead to breach of other agreements of payment • The interest-rate risk refers to the rise of interest rates that make the investments appear less attractive, since the investors can acquire high return from savings • The financial risk lies in the investments that include foreign capital and arises from the disability of future obligations settlement • The inflation risk or purchasing-power risk can affect all the investments but especially those of constant income, such as banking deposits or government bonds • The exchange-rate risk concerns investments realized in foreign currencies that include the exchange risk, since they can lose part of their value from variation in the exchange parity • The political risk or country risk refers to the effect of investments on an economy from sudden changes in the current legal framework that has impact on the market • The systemic risk derives from the collapse of the entire economic system and, even if it is a rare occurrence, can involve devastating consequences to the investments

Strategies of Configuration and Management of Portfolios
The choice of individual investments that will form an investment portfolio is a complicated process determined by the following factors: • The conditions that prevail in the market • The personal expectations of the investor (Agwuegbo et al., 2010) • The type of stocks that are traded in the market (see also : Chen, 2005) Based on the aforementioned parameters, two strategies exist that determine the configuration of the portfolio: The active and the passive strategies (Burton, 2003).
The choices are usually made according to the characteristics of the investor.
Included in these are the expected return, the time of return, the risk taken by the investor, the profession, the income, the possession of financial assets.
The question is "to what degree do these factors influence the investor when selecting savings-based investments in a portfolio?" This study aims to answer the above question. For the completion of this research, the Analytic Hierarchy Process (AHP) method was applied.

MATERIALS AND METHODS
The aim of this study is to present the results of an empirical research to (a) identify the criteria determining the financial products comprising the investment portfolios of private investors in Greece and (b) conclude on the hierarchy that each of these criteria has.The methodology that was used is illustrated in Fig. 1. More precisely, the first Step was to identify the key parameters that affect the factors that influence the decisions of potential investors concerning the structure of their portfolio and particularly the key parameters that affect their private savings investment. Literature on this specific area is rather scant. Therefore, a brainstorming session was performed, in order to map the total number of factors that could influence this kind of decision.
The next step of the research was the development of a questionnaire based on the findings of the previous Step. The structure of the questionnaire comprises 34 pairwise comparisons on a 9-point Likert type scale. The final stage was the data elaboration and the calculation of the importance of each factor by using the Analytic Hierarchy Process (AHP) (Diakomihalis and Stefanidaki, 2012).
The Analytic Hierarchy Process (AHP) uses hierarchical decision models that have a mathematical basis. AHP is a multi-criteria method developed by Saaty (1977;1980b;1999) for decision making and priorities ranking. This method combines subjective and objective estimations or perceptions in an integrated framework, which is based on scale ratios from pair comparisons (Saaty, 1980a). The judgments from the pair comparisons are made by experts or decision makers and in combination with the use of the AHP algorithm produce the final outcome. The criteria with which the comparisons are made and the final hierarchy deriving from them, are not necessarily determined. It is possible and acceptable to be based on non-measurable factors such as experience and subjective judgment. After the completion of the process, the most important factors have the highest gravity coefficients (Saaty, 1999;. AHP method has the ability to structure complex, multi-person, multi-attribute and multi-period problem hierarchically. AHP method is useful in solving problems connected with choose of the best solution, especially when the choice of certain solution is based on subjective preferences of examined group (Parlinska and Petrovska, 2011). Pairwise comparisons of the element (usually, alternatives and attributes) can be established using a scale indicating the strength with which one element dominates another with respect to a higher-level element. This scaling process can then be translated into priority weights-scores (Yusuff et al., 2001).

Identification of Critical Decision Factors and Questionnaire Development
The first Step includes the identification of factors that influence the decisions of potential investors concerning the structure of their portfolio and particularly the key parameters that affect their private savings investment. Given the limited research in this area brainstorming was firstly used to identify the broad area of factors that may play an important role in the decision for an investment portfolio. This process was performed with major stakeholders of the Greek investment experts (bank investment consultants) who were asked to confirm or to eliminate the factors which consider as relevant or irrelevant to private savings investment, from a number of listed items. Following discussion with local banking executives the list of the key factors was narrowed to a set of 4 major criteria categories each of which can be further broke down into sub-criteria.
These categories are the following: • Characteristics of potential investors: Includes all the characteristics of the potential investor such as gender, age, education, marital status and familiarity with technology • Financial situation of potential investors: Refers to the profession or occupation of the investor, his or her possession of assets and annual income and lastly the forecast for future personal or family income Science Publications

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The type of investor: Includes his or her investment experience, the time of holding the investment, the psychological reaction in times of negative fluctuations and his or her tolerance of losses during a recession period.
The type of investment: Refers to the purpose of the investment, the level of return fluctuation, the risk the investor is willing to take and the time of return.
The hierarchic structure of the levels of criteria as well as the number of criteria on each level, are quite significant in the implementation of AHP. For this reason, the structure of the present research is relatively simple, with data present of two levels (the 'criteria' and the 'sub-criteria'). The groups of criteria selected with the sub-criteria of each group of criteria are presented below per couple in the form of the final questionnaire.
A questionnaire consisting of a total number of 34 questions (comparisons per couples) was developed. The questionnaire simply asks for a pairwise comparison of the 'sub-criteria' for the 4 major criteria categories which is the major input of the AHP analysis.
It should be mentioned that the structure of the questionnaire was such that, the respondents were asked to compare each sub-criterion included in the Criterion, with the remaining sub-criteria of the Criterion. Therefore there is no comparison of all the sub-criteria separately with the remaining belonging to other criteria. This was done for purposes of abridging the number of the questions. Despite all these, with the Expert Choice™ software that was used, the gravity coefficients were calculated without the aid of such a comparison.

Field Research and Data Analysis
The questionnaire was addressed to bank executives with major job duty the provision of investment consulting. The sample consisted of 52 questionnaires from the following bank branches situated in the metropolitan Athens area: National Bank, Agricultural Bank, Eurobank, Alpha Bank, Emporiki Bank, Piraeus Bank and Probank. Another 60 questionnaires were completed by bank executives from the same bank branches located within the greater Peloponnese region with the addition of the Bank of Peloponnese. The study is conducted the first two months of 2013.
As discussed above, the answers to the questionnaire were the used in the AHP method to analyze the data and determine the rank of each alternative criterion on a numerical scale. AHP aims to identify the experts' opinions by using questionnaires in which the criteria and sub-criteria of each criterion are prioritized in couples.
These can determine the impact of the criteria influencing the selection of investment products in a portfolio.

RESULTS
This section presents the results derived by using the Expert Choice™ software. The degree of participation of each criterion and sub-criterion, which depicts its gravity for the achievement of the objective, reveals the existing differences and ranks the decision factors. Figure 2 and 3 present the Local (L) and Global (G) priorities based on our goal. Global priorities (G) are obtained for nodes by applying each node's Local priority (L) and its parent's Global priority (G). The global priorities for each alternative are then summed to yield overall or synthesized priorities. The preferred alternative is the one with the highest priority.
The ranking of factors and their significance presented in Table 1 is also illustrated in Fig. 4. As described, "financial situation of potential investors" is the major drive for portfolio investment. Based on the results of the data analysis, "financial situation of potential investors," is indeed a very important factor, ranked as the top criterion for both the Metropolitan city Investor (MI) and for the Regional Investor (RI).
In summation, the criteria, "financial situation of potential investors," "the type of investor," "the type of investment," "characteristics of potential investors," receive the same ranking, from both the MI and the RI, with some difference in their significance ( Table 2). Regarding the differences in significance among the criteria, the results (gravities) from the AHP analysis of the research with the questionnaires clearly demonstrates the greatest significance for the factor concerning the "financial situation of potential investors," with 0.453 of the RI over the significance of 0.378 for the MI. Contrary to that, all the rest of the criteria including "the type of investor," and "the type of investment," depict the greatest significance for the MI compared to that of the RI, 0.253 to 0.219 and 0.231 to 0.195, respectively (illustrated in Fig. 4). The significance of the "characteristics of potential investors," is relatively the same, 0.139 for the MI compared to 0.134 for the RI.
The synthesis with respect to our goal for both the MI and the RI was also calculated by the Expert Choice™ software and is shown in Fig. 5. Note that synthesis is the process of weighting and combining priorities throughout the model to yield the final result after judgments have been made.

Fig. 4. Criteria differences between investors from Athens and from Peloponnese
The significance differences of the sub-criteria between the MI and the RI are illustrated in Fig. 5. For comparison purposes, we selected all the subcriteria to present the difference in significance between MI and RI.
The significance differences of the sub-criteria between the MI and the RI are illustrated in Fig. 5. For comparison purposes, we selected all the sub-criteria to present the difference in significance between MI and RI.
According to significance comparison ( Table 2 and Fig. 5), the highest difference is located in the "possession of assets," which is almost double (109%) the significance for RI compared to MI. Such difference is expected due to the ranking difference of the specific sub-criterion, which is 1st for RI and 5th for MI (-0.086).
The second highest difference occurred in the "risk level" sub-criteria, by 82% higher significance for MI compared to RI. The difference is justified by the ranking gap of the sub-criterion, which is 3rd for MI and 10th for RI (+0.042).
The third highest difference occurred in the "tolerance of losses during 1 year of recession period," by 50% higher significance for MI compared to RI (+0.027). The decline of the difference is justified by the ranking mitigation of the sub-criterion, which is 4th for MI and 7th for RI. The following highest difference concerns the "length of time holding investment," with 65% higher significance for RI to MI. The ranking difference is quite high, placing 5th for RI and 12th for MI (-0.024).
The fifth highest difference concerns the "investment experience," with 36% higher significance for MI to RI. The ranking difference is only two positions, 6th for MI and 8th for RI (+0.019).

DISCUSSION
This study dealt with the complex issue of portfolio investment and, specifically, the factors that determine the selection of financial investment products. An investment portfolio synthesis is characterized by high complexity. According to the literature, the success of a Science Publications AJEBA portfolio is determined by the expected return and the investment risk, while the suitable combination of different investment products decreases the unsystematic risk. The decisions involved in conducting an investment portfolio synthesis are affected by a number of different factors and determined by those factors and how they relate to the specific investor. The geographic origin or the residence of the investor is decisive in investment choices. Therefore, this work tries to identify and rank the key decision parameters for investors residing in a metropolitan city versus investors residing in a region or province.
To this end, the methodology presented in section 3 was applied. At the beginning, a set of key factors was identified based on the literature review and discussions with experts ( (Diakomihalis and Stefanidaki, 2012). Based on that, a questionnaire was developed and addressed to two sample groups, one from the metropolitan city of Athens and another from regional Greece, specifically the Peloponnese.
The responses were analyzed with specialized software using the Analytic Hierarchy Process (AHP) to determine the key decision factors regarding an optimal portfolio investment. The AHP method, which is analyzed in section 2, is the most widely used Multi-Criteria Decision-Making Method (MCDM).
Regarding the criteria, the analysis revealed that the factor of "financial situation of potential investors" is the top drive for portfolio investment for both Metropolitan City Investors and Regional Investors, but quite more significantly for Regional Investors. In addition, the three other criteria are relatively significant in the same order among Metropolitan City Investors and Regional Investors. "Type of investor" and "type of investment" are somewhat more significant for MI, while "characteristics of potential investors" is of equal significance for both groups.

CONCLUSION
From the above it might be concluded that the fact that Regional Investors more significantly evaluate the criterion of "financial situation of potential investors," is a sign of feeling less secure than the investors from the Metropolitan City. The minor significance of the criteria "type of investor" and "type of investment" by the Metropolitan City Investors compared to the Regional Investors indicates that MI are more familiar and experienced with evaluating issues concerning their private savings investments.
A clear difference between the two groups of investors concerns the sub-criteria. The highest difference, for the RI, concerns the sub-criterion "possession of assets," confirms the lower level of security of the RI. The next most significant differences, for the MI, "risk level" and "tolerance of losses during one year of recession period," could be attributed to the more demographically widespread professionalism of the investors of MI compared to the RI. The fourth highest difference, for the RI, concerning the sub-criterion "length of time holding investment," supports lower level of professionalism that influenced their approach to their investment choices compared to the MI. The subcriterion "investment experience" is evaluated more significantly for the MI.
The sub-criteria with less notable difference in significance between Metropolitan City investors and regional investors are the last five in significance for both groups: "Gender," "education," "marital status," "aim of investment," and "age." General conclusions stemming from the comparative study of these two groups of investors and based on the judgments of banking executives specializing in investment consulting, are the following concept correlations characterizing each group of investors compared to the other.
The Metropolitan City Investors seem to be more experienced, more dispassionate, more patient and conservative than the Regional Investors. Furthermore, the MIs are more tolerant, provident and informed. The Regional Investors can be perceived as more enthusiastic and interested in taking risks than the MIs. However, they also appear to feel less secure when it comes to investing.
The research aimed to identify and evaluate the factors that influence the decisions of portfolio investors and to contribute to the knowledge of the field.
In this context, we make distinct comparisons among the decision criteria of investors from the metropolitan city and from a more rural region respectively. Even if this research had not been conducted before, we believe that the results cannot be generalized due to the small number of participants. Another limitation of the study is that the Metropolitan City Investors sample was selected only from Athens and the Regional Investors sample was selected only from the Peloponnese.
Future research should address these limitations and include investors from other metropolitan cities (e.g., Thessaloniki), other regions of Greece (e.g., Ionian, Aegean, Thrace, Macedonia,) and, eventually, from other countries.


DFAHP MULTICRITERIA RISK ASSESSMENT MODEL FOR REDEVELOPING DERELICT PUBLIC BUILDINGS

Reusing abandoned public buildings is a positive strategy in sustainable urban development. An appropriate assessment method is needed to reduce the risks of redeveloping derelict public properties. The Delphi method is an optimal group decision-making technique; whereas the analytical hierarchy process (AHP) method is useful for solving multicriteria decision-making problems. In addition, fuzzy logic manages artificial uncertainty and ambiguity, where an explicit number or ratio can express the level of preference. This study uses the Delphi method, fuzzy logic, and AHP (DFAHP) as a risk assessment model to redevelop derelict public buildings. The DFAHP provides an objective reference for investment decisions and is beneficial in reducing the risk of the public sector investing in the reuse of abandoned public buildings, in aiding in reuse cases that revitalize urban economic development, and in appreciating the value of sustainable city development.

INTRODUCTION
Sustainable development is one goal of many redevelopment projects intending to improve older urban spaces (Dale and Newman, 2009). Redeveloping derelict public buildings in urban areas has been a crucial focus of such development. In general, derelict public buildings are either obsolete or unusable and severely affect the appearance of cities. Building demolition projects must consider the economy, culture, alternative usage, urban development, and environmental influences, such as the treatment and management of building pollution (Begum et al., 2009), environmental pollution and damage (Cheng et al., 2006;Moodley et al., 2008), and resource use and pollution control (Briassoulis, 2001). According to Ding (2008), construction may cause environmental problems ranging from excessive consumption of global resources, both in terms of construction and building operations, to the pollution of the surrounding environment. From an environmental perspective, demolishing such buildings is not the best option. Rossi (2003) claimed that reconfiguring existing buildings for entirely new functions and benefits has many positive outcomes.
Among 309 townships in Taiwan, approximately 230 new construction sites may be derelict public buildings. Of these, 119 new construction sites are closed and unused, with 28 failed development projects. Consequently, 147 new construction sites qualify as derelict public buildings. The total construction cost is approximately NTD 47.4 billion (Yao, 2010). According to Taipei County's Government Ethics Monthly issued in May 2006, reasons for the disuse of public buildings include failure to pre-assess the use rate, inadequate planning and design, lack of funds for follow-up execution or repair, remote location of facilities, and failure to meet public needs (Taipei County Government, 2006). These buildings waste public resources; they also cause environmental pollution and seriously compromise security. When professional decision-making groups consistently repeat similar mistakes, the construction industry develops a poor ethical reputation in the public eye. It is also generally accepted that the construction industry leads to immoral behavior in society, by engaging in fraud and bribery (Moodley et al., 2008). Before approving public building projects, professional governmental departments, politicians, engineers, and scholars from professional fields must review them. Theoretically, the number of derelict public buildings should be minimal.
Such a serious circumstance demonstrates the lack of an effective risk assessment model during decision-making processes (Hsueh et al., 2007) and indicates substantial professional and ethical defects during the overall review process. When people further obtain ethics-related knowledge, they uphold an ethical attitude (Hungerford and Volk, 1989) and are thus willing to exhibit positive ethical behavior (Glazer and Glazer, 1989). As long as professionals strongly believe in and insist on professional values and emphasize the importance of expertise during implementation, people with more knowledge or who exhibit an aggressive attitude are responsible for their behavior (Hines et al., 1987).
Planning and assessing the development of derelict public buildings is difficult because renewal analysis of such buildings is a complex process (Antucheviciene and Zavadskas, 2008). Pre-assessing risk is highly critical; moreover, risk analysis and management should permeate the entire spectrum of project activities (Jaafari, 2001). Varying concerns among people of different positions cause problems in reuse selection. Solving such problems necessitates an effective knowledge communication tool that enables decision-makers to understand more clearly the complex relationships of the relevant attributes in reuse selection problems. This may subsequently improve the final decision (Wang and Zeng, 2010).
Numerous implemented redevelopment policies have often been ineffective (Kim et al., 2004), because of the difficulty of harmonizing everyone's opinions, the majority of problems addressed by urban renewal (Lee and Chan, 2008), neighborhood renewal (Fung and Yau, 2009), or the development of abandoned public buildings are complex. Additionally, in the urban regeneration process, city planning is an extremely difficult problem (Yau and Chan, 2008). Accordingly, the interests of numerous people are addressed. By contrast, the redevelopment of derelict public buildings is a case of single, independent architectural space or single, independent construction, with limited influence on private interests. In addition, the decision-making teams for the redevelopment of derelict public buildings are typically temporary and infrequently make optimal decisions during the assessment process.
This study combines Delphi's group decision-making technique (Murry Jr. and Hammons, 1995;Ziglio and Adler, 1996) with a fuzzy logic technique for processing quantitative values (Zadeh, 1983;Perng et al., 2005) as well as an AHP multicriteria decision-making technique (Saaty, 1980;Saaty and Takizawa, 1986) to develop a DFAHP (Delphi-Fuzzy-AHP) risk assessment model for redeveloping derelict public buildings. The DFAHP model has the implicit co-research characteristics of Delphi experts and can increase the reliability of the model. Additionally, the DFAHP model includes multicriteria quantitative processing functions, as well as fuzzy inference functions, and is an artificial intelligence model. Although the single AHP analysis method also has quantitative decision-making functions, it lacks inference functions and quantitative functions for processing natural human language. Related studies on applying the DFAHP method include Chen and Wang (2010), who suggested developing global business intelligence.

MODEL OVERVIEW
The U.S. RAND Corporation developed the Delphi method as a tool for assisting management in predicting the future; however, it is not restricted to this application (Ziglio and Adler, 1996). Obtaining the latest professional knowledge from expert groups (Hsueh and Yan, 2011) is the best method for increasing research reliability. Zadeh (1965Zadeh ( , 1987Zadeh ( , 1988 proposed fuzzy theory as a concept based on set theory. Fuzzy logic can accept the ambiguous information of human natural language, such as uncertainty, complexity, and the tolerance of imprecision (Zadeh, 1976(Zadeh, , 1996. Fuzzy set theory applies to a wide range of domains where information is incomplete or imprecise, such as the good, bad, like, dislike, in natural language. Moreover, membership functions help quantify the meaning of linguistic values, denoting the degree of membership of an element in a given set with values between 0 and 1 (Bingul et al., 2000). Various fields have successfully and comprehensively applied fuzzy logic theory. Previous studies have used it to investigate decision-making and evaluate new technology in the construction industry (Chao and Skibniewski, 1998), by selecting an architectureengineering team (Nguyen et al., 2008), selecting the most efficient maintenance approach (Al-Najjar and Alsyouf, 2003;Mechefske and Wang, 2003;Tahir et al., 2008), and evaluating industrial robotic systems (Kahraman et al., 2007). Fuzzy logic theory is suitable for assessing complicated and hard-to-quantify decision-making problems (Hsueh and Yan, 2011), especially those that involve group decision-making (Hadi-Vencheh and Mokhtarian, 2011;Li and Yang, 2004;Li, 2010;Chen and Lee, 2010;Chen and Niou, 2011).
Saaty was the first to propose AHP, which is currently and widely used in social policy and engineering decision-making (Saaty, 1980(Saaty, , 1990(Saaty, , 1994. Using AHP is considered suitable for solving complex multiobjective decisionmaking problems with multifactor conditions (Lee and Kim, 2000). Using AHP can investigate multi-criteria decision-making research concerns in the construction industry, such as managing projects (A1-Harbi A1-Subhi, 2001), selecting contractors (Fong and Choi, 2000), evaluating advanced construction technology (Skibniewski and Chao, 1992), and estimating and choosing building investments (Dziadosz, 2008).
Combining the Delphi method, fuzzy theory, and AHP is successful in investigating relevant research concerns, such as performing fuzzy hierarchical analysis (Buckley, 1985), selecting optimum maintenance strategies (Wang et al., 2007), selecting suitable bridge construction methods (Pan, 2008), planning large-scale projects (Chang et al., 1995), selecting managerial talent (Chang et al., 2000), and selecting maintenance strategies (Jafari et al., 2008). This study examined building operations relative to the pollution of the surrounding environment, by combining these three methodologies to develop a DFAHP multicriteria decision-making risk assessment model ( Figure 1) as the basis for choosing or assessing the redevelopment projects of derelict public buildings. After obtaining additional professional knowledge and appropriate criteria to understand the effect of each criterion on the hierarchy, a DFAHP figure or ratio can assist decision-making , is highly adaptive, and would be easy to maintain or revise in the future.
The Delphi experts assisting in this study have been practically engaged in relevant fields of industry, government, and academia for more than 15 years. Among these, five served at public departments, five were scholars, three were local public representatives, and three were CEOs of property development companies, comprising 16 Delphi experts. Group decision-making information obtained from these experts was essential in developing the DFAHP model for this study. Selecting the appropriate criteria from complicated affecting factors was necessary. The DFAHP is only effective after completing the hierarchy of each criterion, selecting the membership functions used to quantify natural language, determining the fuzzy sets, fuzzy scale, and linguistic values, and completing the IF-THEN rules base of the fuzzy logic inference system (FLIS).
This assessment model includes two major parts: (1) developing the model and (2) applying the model n ( Figure 1). Applying the Delphi-AHP and Delphi-fuzzy models requires four steps: Step 1: Investigate relevant previous studies and arrange the relevant criteria affecting the redevelopment of derelict buildings. Thereafter, use the Delphi group decision-making method to select the appropriate criteria.
Step 2: Use Delphi-AHP to establish the hierarchical framework of the cause-and-effect relationship among various criteria, confirm the main criterion and subcriterion, and complete the AHP questionnaire.
Step 3: Use Delphi-fuzzy to determine the fuzzy sets and fuzzy scale of the subcriterion, and choose appropriate membership functions to describe the linguistic values.
Step 4: Develop the IF-THEN rules required by the rules base to complete the FLIS.
Applying the model requires four calculation steps: Step 1: Assess one or several projects.
Step 2: Use AHP to calculate the weighting value (w i ) of the main criterion as the importance parameter for calculating decisionmaking.
Step 3: Use FLIS to calculate the fuzzy output value, and input the descriptions of uncertainty and ambiguity into the criteria (x i ) us- f Step 4: Calculate Σf(y i ) as the basis for choosing projects, and determine if the selected project is worthy of redevelopment.

THE FUZZY LOGIC INFERENCE SYSTEM
The fuzzy logic inference system (FLIS) involves two output systems, mamdani and sugeno. The output values of mamdani are continuous, whereas those of sugeno are discrete. To understand the change in continuous outputs, this study uses the mamdani system. The establishment process of FLIS requires: (1) inputting the selected criterion and the definition of fuzzy sets; (2)

Selecting initial criteria
Developing public buildings and redeveloping recreational facilities and derelict buildings are intended to serve the public. Effectively distributing and utilizing these services is another concern (Erkip, 1997). Inadequate development may easily lead to derelict buildings, affecting the appearance of cities and leading compromised security. Redeveloping derelict public buildings and abandoned sites is an example of a sustainable urban revitalization alternative. However, such an initiative includes complicated environmental, social, and economic concerns (Zavadskas and Antucheviciene, 2006).
Numerous complex factors may affect the redevelopment projects of derelict buildings. The AHP questionnaire data were completed with the assistance of 16 Delphi experts. Based on group decision-making, the Delphi experts assisting in this study suggest considering building conditions first, such as development convenience, high-quality public facilities, and rehabilitation costs. Attaching importance to enhancing sustainable development is necessary; therefore, energy consumption should be considered. Consequently, selected criteria include adopting multidesign, recycling building materials, and developing green buildings. Finally, Delphi experts follow the research of Van Herzele and Wiedemann (2003), who suggested that green spaces attract the public, maintaining that redevelopment projects must have attractive features. Additionally, Delphi experts cite the research of Grove-White (2005), who suggested the influence of the perspective of someone closely involved in society. In addition, Delphi experts cite Owen and Merna (1997) and Heald (2003) in presenting private finance initiative (PFI) projects, which use private funds to engage in public construction. Thus, based on harmonious consensus, the enthusiastic participation of the masses and harmonized opinions can be combined. This is beneficial to creating local characteristics. Therefore, selected criteria include cultural attractions, tourism, and the people closely involved. The model for reviewing the project should be as simple and comprehensible as possible, because professional teams will have discussed the details of derelict buildings (cost, design, the construction process and purpose of use) several times. Therefore, this study assesses the redevelopment process of derelict buildings, investigating the differences in time and space between the past and the present, and thus considers factors different from those for assessing development projects. This study also collected critical affecting factors from relevant studies. The experts in this study added other factors, amended them, and selected appropriate criteria to assess redevelopment of derelict public buildings (Table 1). Table 2 shows calculations of the weighing value of the main criteria. Because this study investigated the overall feasibility assessment of redevelopment, and FLIS can transform different entered scenario mapping into quantified output values, we omitted the subcriteria weighting value calculation. Figure 2 shows the hierarchical framework of the cause-and-effect relationship among various criteria.

Defining the fuzzy sets, fuzzy scale, and membership functions of the subcriteria
The researchers in this study calculated the fuzzy values of the three main criteria (building condition, sustainable development, and attractive features). Fuzzy sets and the membership functions of each criterion of the subcriteria quantified the assessed concerns. Because each factor's effect on redevelopment assessment varied, the researchers in this study defined the fuzzy sets and membership functions of each assessment factor to reflect the corresponding relationships among various scenarios and fuzzy output values.
The quantitative upper and lower values of the fuzzy sets and fuzzy scale of each criterion of the subcriteria and of the output values were defined by obtaining the Delphifuzzy experts' consistent approval (Tables 3 to  5). These relevant data result from the Delphi process. In addition, good, ordinary, and poor can be used as input values.The measurement scale defined in fuzzy logic is an artificially established fuzzy scale. Fuzzy logic accepts the complexity and imprecision of natural language. The multidesign criterion of the subcriterion of Table 4 indicates this, in which a score of 90 points and above denotes "very good", 80 points denotes "good", 70 points denotes "ordinary", 60 points denotes "poor", and 50 points and under denotes "very poor". A score of 75 points denotes "good" or "ordinary". In the fuzzy scale, membership functions were used to define a level of "good" or "ordinary". To operate FLIS normally, the rule base had to be completed. Although different calculation units and defined values were used in the fuzzy scale of each criterion, an appropriate figure or ratio presented the assessment result of the input scenario after defuzzifying FLIS to be assessed according to preference level.

Selection of membership function
A membership function characterizes a fuzzy linguistic term by giving its support value or degree of membership. The membership value varies from 0 to 1, representing none to full membership. Common membership functions include triangular and bell-shaped functions (Yu and Skibniewski, 1999). The researchers in this study selected applicable membership functions based on expert group decisionmaking. The experts in this study suggested that the Taguchi loss function could explain the phenomenon of customer satisfaction with a product. Customer satisfaction decreases when product quality fails to meet the customers' target value (Yacout and Boudreau, 1998). The Taguchi loss function explains individual preferences and feelings based on the changes in a curve. Because a bell-shaped curve can be used to simulate Taguchi loss functions, this study used bell-shaped functions to simulate membership functions. Exploiting the tolerance for imprecision is central to using words in computing (Zadeh, 1996).

Establishing the rules base of FLIS
The fuzzy logic inference system quantified the input scenario to be assessed according to the rule base this study established, and yielded distinct quantitative output values after defuzzification. The established rule base completed the systemic and logical mutually-corresponding relationships between the input criterion and the fuzzy output value to complete the definition of the IF-THEN rules.
There were a total of three input criteria: multidesign, recycling of building materials, and green buildings in sustainable development. The fuzzy sets of multidesign were composed of "very good", "good", "ordinary", "poor", and "very poor" using natural language, with five different scenarios. Moreover, three additional scenarios, good, ordinary, and poor, using natural language, represented the fuzzy sets of criteria input from the recycling of building materials and green buildings. Therefore, a total of 5*3*3 = 45 different input scenarios assessed the pros and cons of sustainable development. The rule base resembles a human brain in the overall FLIS. Therefore, FLIS could be used in an inference operation, after using it to complete the If-Then rule base. As long as a decision-maker input a value for each criterion, FLIS could automatically calculate the quantitative assessment value. Because the attractive-feature and sustainable-development criteria shared similar fuzzy sets, there were also 5*3*3 = 45 different input scenarios for attractive features. Therefore, there were three input criteria for building conditions, and three scenarios, "good", and "poor", presented the fuzzy sets of each criterion, using natural language. Therefore, there were a total of 3*3*3 = 27 compositions of the input scenarios.

INPUT AND OUTPUT MAPPING
For calculation of Σf(y i ), the weighing value w i of each main criterion and the fuzzy quantitative output value f(x i ) were calculated first. The values of Σf(y i ) were compared and used to select redevelopment projects of derelict public buildings. The larger the Σf(y i ) value is, the higher the quality of the assessed project. Figure 3 is a 3D diagram of the input and output mapping. Tables 4 and 6, respectively, show the  largest and smallest quantitative output values. The input scenarios in Table 6 could be either quantitative values or imprecise terms in natural language, such as "good" (high), "ordinary" (medium), and "bad" (low). This model could provide decision-makers with a scientific calculation to compare quantitative values as the basis for decision-making before assessing projects. The model improves the efficiency and effect of decision-making, and reduces the risk of inappropriate decision-making.

CASE STUDY
Local governments usually spend large amounts of money on development projects for derelict public buildings in cities, creating a financial burden. However, redevelopment and reuse of derelict public buildings promotes sustainable urban development, and improves the appearance of cities. Annual government budget restrictions make it difficult to choose appropriate development projects: inadequate development may waste budgets, increase future management and maintenance expenses, and arouse criticism. To reduce public construction investment risk, the government must use a fair, just, open, and efficient assessment procedure. The case study (Table 7) verifies the practicability and reliability of this assessment model. Redevelopment projects were selected based on scientific calculation. Results from the two cases (Table 7) explain how project selection was based on comparing quantitative values, allowing further analysis of whether the selected projects possessed high redevelopment value. For example, Project 1 in Table 7 was a newly-constructed public building that still failed after redevelopment.
Calculation of this assessment model demonstrated that the building no longer possessed value for redevelopment. After the project was completed, the usage rate of the building was extremely low. Moreover, although the total score Σf(y i ) of Project N was higher than that of Project 1, their corresponding fuzzy output values in the two criteria of sustainable development and attractive features were both ordinary. Therefore, the model assessed them both as projects with no redevelopment value. The previous case studies shows that this model is applicable in assessing the redevelopment of single derelict public buildings. It is also applicable in selecting assessments of redevelopment projects for multiple derelict public buildings. The output values for each criterion of the case studies listed in Table 7 can be the fuzzy linguistic terms of humans or quantified values, such as good, ordinary, or poor. For the convenient explanation, Table 7 lists numbers as input values.

CONCLUSIONS
Urban construction projects are a critical factor triggering economic development. However, inadequate development may lead to formidable problems, such as wasting land resources, governmental budgets, and energy, or environmental damage. However, public construction investment may easily lead to repeated mistakes, and may also lead to public disappointment with regular defects. An effective pre-development group decision-making model may affect assessments of public construction investments. Because reusing derelict public buildings is a positive strategy in sustainable urban development, the DFAHP group decision-making assessment model presented in this study belongs to the artificial intelligence category and can process the assessment of complex and high-risk derelict building redevelopment plans. Additionally, the proposed model has a high degree of objectivity, practicality, and adaptability and can aid in reducing the investment risk of derelict buildings. This study provides practical reference value for policy makers and key decision makers. The proposed model can bring economic benefit to communities and resolve potential problems in the urban environment.


Price Risk and Risk Management in Agriculture

This note studies the risk-management decisions of a risk-averse farmer. The farmer faces multiple sources of price uncertainty. He sells commodities to two markets at two prices, but only one of these markets has a futures market. We show that the farmer’s optimal commodity futures market position, i.e., a cross-hedge strategy, is actually an over-hedge, a full-hedge, or an under-hedge strategy, depending on whether the two prices are strongly positively correlated, uncorrelated, or negatively correlated, respectively.

Introduction
In today's economy, farmers and agribusiness firms face a high degree of risk because of certain new factors, such as the increased price volatility of inputs and outputs, climate change, international trade restrictions, new and more stringent food safety standards, and greater public concern about the environment, to name only a few. These developments coincide with major changes in the fundamentals of the agriculture market (UNCTAD, 2011). A critical issue in agriculture is adjusting supply and price risk. The role of economic risk is particularly important for pricing in commodity futures markets. In developed economies, farmers have access to commodity futures markets in which they can hedge the price risk.
Since 2006, there have been significant price fluctuations in major food commodities on international markets. Between early 2006 and mid-2008, grain and cereal prices more than doubled in real terms before falling sharply during the second half of 2008. From 2010 through 2012, prices again increased rapidly and generated fears that the global market was entering a phase of sustained commodity price volatility. Although short-term coping strategies are importantparticularly in economies that are negatively affected by rising food prices (Prakash, 2011;Prakash, & Gilbert, 2011) -an important part of the economic policy debate addresses the question of whether these recent price fluctuations are the result of speculation in the futures markets or whether they simply reflect the underlying economic fundamentals.
However, futures markets in the real world are far from complete. For example, less-developed countries and economies in transition -places in which risksharing markets are embryonic and markets are heavily controlled -are unlikely to have futures markets for agricultural goods. Farmers that are exposed to commodity price uncertainty must therefore rely on commodity futures contracts on related goods to indirectly hedge against their price-risk exposure (Allen and Lu-Price Risk and Risk Management in Agriculture eck, 2003;UNCTAD, 2011). Such a risk-management technique is referred to as cross hedging (see, e.g., Anderson and Danthine, 1981;Broll, Wong, & Zilcha, 1999;Chang, & Wong, 2003;Frechette, 2000;Haigh, & Holt, 2000;Hudson, 2007). An important part of the policy debate in agriculture addresses the question of whether commodity price volatility results from speculation in the futures market or whether it simply reflects the underlying economic fundamentals (e.g., Gilbert, 2010;Food and Agriculture Organization [FAO], 2011;Ziegler, 2012). In this context, there is growing concern that financial investment into commodity derivatives may have become an independent source of price behavior and is causing the recent volatility.
The purpose of this note is to provide theoretical insights into optimal cross-hedging strategies for farmers' contracts. To that end, we consider a riskaverse farmer who sells his output to two markets; however, only one of these markets has a futures market to which the farmer has access. We show that the farmer's optimal futures position hinges on the bivariate dependence of the random commodity prices in the separate markets. To derive concrete results, we propose the concepts of strong correlation. We show that the farmer can find an optimal solution through over-hedging, full-hedging, or under-hedging strategies, depending on whether the two random prices are strongly positively correlated, uncorrelated, or negatively uncorrelated, respectively.
The rest of this note is organized as follows. The next section develops the model of a farmer facing price risk and cross-hedging opportunities, and the section following that describes the farmer's optimal commodity futures hedging strategy. The final section concludes.

The Model
We consider a farmer who produces two final outputs, The farmer's profits are given by where h is the number of futures contracts sold (purchased, if negative). The farmer is risk averse and possesses a von Neumann-Morgenstern utility function, . For a given production, the farmer's decision problem is to choose his futures market position, h , to maximize the expected utility of its profits where ) ( E ⋅ is the expectation operator. The first-order condition for program (2) is given by where an asterisk ) ( * indicates an optimal level. Given the assumed properties of ) (Π U , the second-order condition for program (2) is satisfied.

Optimal Risk Management Policy
To examine the farmer's optimal futures position, * h , we write equation (3) as where ) , ( cov ⋅ ⋅ is the covariance operator. (Please note that for any two random variables, x and ỹ, we have Evaluating the lefthand side of equation (4) at  Hardy, Littlewood, and Pólya (1934) and Ingersoll (1987). An example of strongly correlated random variables is the following linear specification: , where α and β are scalars, and ε is a zero-mean random variable independent of 1 p . This linear specification is widely used in the hedging literature.
Proof: If 1 p and 2 p are strongly uncorrelated, then the covariance term of expression (5) vanishes. Thus, expression (5) is positive, zero, or negative, depending on whether f p 1 is greater than, equal to, or less than ) ( E 1 p , respectively, which implies that * h is greater than, equal to, or less than 1 x , respectively. If 1 p and 2 p are strongly positively (negatively) correlated, then the covariance term of expression (5) is positive (negative). Thus, expression (5) is positive The logic of Result 1 may be shown as follows.
Considering the variance on both sides of equation (1), we have where var ) (⋅ is the variance operator. Partially differentiating equation (6)

Conclusion
In today's economy, farmers and agribusiness firms face a high degree of risk because of certain new factors, such as greater price volatility for inputs and outputs, climate change, international trade restrictions, and new and more stringent food safety standards.
These developments coincide with major changes in the fundamentals of the agriculture market. A critical issue in agriculture is price risk.
An important topic in the policy debate in agriculture concerns the question of whether the volatility in commodity prices results from speculation in the futures market or whether this volatility simply reflects the underlying economic fundamentals. In this context, there is growing concern that financial investment into commodity derivatives based on the replication of futures indices has become an independent source of price behavior and is causing recent patterns of price volatility in these markets.
In this note, we have examined the optimal riskmanagement decisions of a risk-averse farmer who is facing multiple sources of commodity price uncertainty. The farmer sells commodities to two markets, but only one of these has a futures market. We have shown that the farmer's optimal forward position is an over-hedge, a full-hedge, or an under-hedge strategy, depending on whether the two random commodity prices are strongly positively correlated, uncorrelated, or negatively correlated, respectively.