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Top1. Introduction
The evaluation of a portfolio’s performance requires selecting an appropriate portfolio assessment method(s). As current methods have their own advantages and disadvantages, a constructive review and comparison of existing MCDM methods is required to identify the most suitable one(s) for PPM decision making.
The PT (Markowitz, 1952) is viewed as the premise of many existing assessment models used to choose portfolios in a broad range of applications. Many researchers have extended it by adding many different ideas and limitations as well as targets, such as the cardinality limit or operational expenses, to help it become even more practical (e.g., Arditti, 1975; Ho & Cheung, 1991; Kane, 1982). The principal method used to identify a portfolio’s functionality is the DEA which was presented by Charnes, Cooper, and Rhodes (1978) and used for only commercial banks taking into account risk and return procedures. Also, its diversification was evaluated and a way of dealing with it demonstrated (Lamb & Tee, 2012). However, no researchers have incorporated PT with DEA and AHP nor have studies addressed the normalisation of weighting scores.
Unlike the return, the variance as a variable in the PT model can adopt non-negative values which is not convenient for conventional DEA methods that presume positive values for both inputs and outputs. Therefore, these models cannot function if Decision Making Units (DMUs) consist of both positive and negative inputs and outputs. Many different techniques for managing non-positive information have been suggested. To determine the performances of DMUs with negative variables, Portela, Thanassoulis, and Simpson (2004) presented the Range Directional Model (RDM), Tone (2001) the slacks-based measure model (SBM), Sharp, Meng, and Liu (2007) a modified SBM based on the directional distance functionality of Portela et al. (2004) called the modified slacks-based measure model (MSBM), Emrouznejad, Anouze, and Thanassoulis (2010) the Semi-Oriented Radial Measure (SORM) and Cheng, Zervopoulos, and Qian (2013) the Variant of Radial Measure (VRM) Models.
Although the abovementioned methods might be employed as a way of dealing with negative data, they have shortcomings. Moreover, these models may sometimes not present total efficiency rankings for DMUs.
An integrated DEA/AHP method was beneficial and avoided each model’s limitations although using a basic DEA model led to the effective units not being reasonably distinguished. In turn, this justified incorporating a peer evaluation mode into the standard DEA model, with a cross-efficiency examination presented by Sexton, Silkman, and Hogan (1986) included. While applications of cross-efficiency in portfolio assessments have been reported to show significant advantages over approaches based on the standard DEA, some challenges have emerged.
The intention of this study is to build a reliable and operational model for examining the overall efficiency and success of a portfolio with regard to their comparative efficiencies influenced by the quality of efficiency outcome. A multi-objective model that applies the PT to identify the expected return and risk, and modifies the DEA-CE to properly score the efficiency of DMUs using AHP are proposed. Then, the portfolio’s performance is combined with the PT standard theory. Finally, a comparison table is produced to assist Decision Makers (DMs) to select the best assets characterised by the values of the expected return, risk, Sharpe ratio and efficiency scores obtained from the proposed model. Then, DMs can optimise the portfolio based on the outcomes of an examination and determine whether the modifications enhance the efficiency of original portfolio. The results obtained from the proposed model can assist organisations to understand their advantages and disadvantages, and the current possibilities and options, or threats, of their portfolios.