# Efficiency and risk of investment projects – probability distribution or possibility distribution

## Author Info

• Bogdan Rebiasz

()

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## Abstract

Risk accompanies every economic decision. Investment decisions are burdened with particularly great risk. Quantification of risk belongs to most heaviest tasks in risk management of the investment project. Traditionally, probability distribution was being utilized for the description of the efficiency calculus parameters of the uncertainty. Difficulties in determining probability distribution and nature of uncertainty of some of the parameters caused that towards the end of the 1980’s some works were published, in which other methods of description of the efficiency calculus were applied. First of all, one should mention here the theory of fuzzy sets. So, at present two methods description of the uncertainty of efficiency calculus parameters are applied alternatively: probability distribution and fuzzy numbers. Depending on the parameter uncertainty description method we obtain possibility distribution or probability distribution of the effectiveness index for estimation of the investment project efficiency. In practice a situation most often occurs in which for one part of the efficiency calculus parameters we can determine probability distribution, and uncertainty of the other part may be described by the fuzzy number. Relations between theory of probability and theory of fuzzy sets is one of the most controversial issues in the area of uncertainty modelling. In the paper, methods of transforming the possibility distribution generated by a fuzzy set into probability distribution, and vice versa, transforming probability distribution into possibility distribution are discussed. It is shown that they may be effectively utilized for estimation of efficiency and risk of investment projects. In the paper, the estimation of efficiency and the risk of two investment projects has been made. For estimation purposes we alternatively used representation of the efficiency calculus parameters uncertainty in the form of fuzzy numbers and in the form of probability distributions. At first, part of the parameters were expressed in the form of fuzzy sets and part in the form of probability distributions. So, the distributions were subjected to transformation. Usefulness of the two methods for uncertainty representation of efficiency calculus parameters was compared.

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## Bibliographic Info

Article provided by Wroclaw University of Technology, Institute of Organization and Management in its journal Operations Research and Decisions.

Volume (Year): 3-4 (2006)
Issue (Month): ()
Pages: 113-131

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Handle: RePEc:wut:journl:v:3-4:y:2006:p:113-131

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## Related research

Keywords: risk analysis; fuzzy sets; computer simulation; capital budgeting;

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