Abstract
Fuzzy sets theory is proposed as an alternative to the probabilistic approach for assessing portfolios of power plants, in order to capture the complex reality of decision-making processes. This paper presents different fuzzy portfolio selection models, where the rate of returns as well as the investor's aspiration levels of portfolio return and risk are regarded as fuzzy variables. Furthermore, portfolio risk is defined as a downside risk, which is why a semi-mean-absolute deviation portfolio selection model is introduced. Finally, as an illustration, the models presented are applied to a selection of power generation mixes. The efficient portfolio results show that the fuzzy portfolio selection models with different definitions of membership functions as well as the semi-mean-absolute deviation model perform better than the standard mean-variance approach. Moreover, introducing membership functions for the description of investors' aspiration levels for the expected return and risk shows how the knowledge of experts, and investors' subjective opinions, can be better integrated in the decision-making process than with probabilistic approaches.
Highlights
The purpose of the portfolio selection problem is to find combinations of investment possibilities which best meet the objectives of the investor
Considering power plants, we use the project’s net present value (NPV) as a proxy for portfolio selection, and risk is defined as the semi-mean-absolute deviation from the expected return
The calculations of efficient portfolios were made for three different fuzzy set models: Fuzzy Semi-Mean-Absolute Deviation (FSMAD)
Summary
The purpose of the portfolio selection problem is to find combinations of investment possibilities which best meet the objectives of the investor. This analysis needs various types of information and should be based on criteria which can provide some guidance about what is important and unimportant, or what is relevant and irrelevant. The weighting of these objectives and the criteria depend on the type of investor, the two that are common to all investors are expected return maximization and risk minimization. They want the return to be high and prefer certainty to uncertainty. The optimal portfolio enables the investor to mitigate risk and opportunities with respect to a wide range of alternatives.
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