Fuzziness and randomness in investment project risk appraisal

doi:10.1016/j.cor.2005.05.006

Computers & Operations Research

Volume 34, Issue 1, January 2007, Pages 199-210

https://doi.org/10.1016/j.cor.2005.05.006 Get rights and content

Abstract

Risk quantification is one of the most difficult tasks associated with investment project risk management, and computer simulation seems to be an especially effective tool for such risk appraisal. This article presents a method for quantification of project-specific risk. When assessing investment project risk it is very common to apply two analytical methods for describing parameter uncertainty: probability distribution and possibility distribution. This study discusses methods for integrating the above-mentioned approaches into a description of the uncertainty of parameters in calculations of effectiveness and investment project risk. The paper presents an example of a computer simulation used for the purpose of an investment project risk assessment. Uncertainty for some parameters of the effectiveness calculation is defined by a probability distribution and by fuzzy sets for others, and a transformation of possibility distributions into probability distributions is thus done. For comparison, the investment risk assessment is undertaken on the assumption that uncertainty distributions of the effectiveness calculation parameters are presented in the form of fuzzy numbers.

Introduction

Each decision of an economic nature is associated with risk. Investment decisions are especially burdened with risk. This is mostly due to the uniqueness of investment projects. Large dynamics of external and internal conditions of the company's development are such that in the investment profitability calculation there are fewer and fewer parameters, the values of which are known, but more and more uncertain parameters for which it is difficult to define the distribution using mathematical statistics methods [1], [2]. Many a times the type of uncertainty encountered in projects does not correspond to an axiomatic basis of probability theory, simply because uncertainty in these projects is usually caused by an inherent fuzziness of an estimate of a parameter rather than randomness [3]. Uncertainty involved in a situation of real risk is often epistemic (that is which relates to the knowledge of things) rather then alearotic things (that is which depends on a chance) [4]. Problems of risk evaluation in investment project are especially important in capital-intensive industries where the economic life of the project is long. In such cases, incorrect investment decisions can be both expensive and difficult to subsequently correct.

A risk in an investment project is commonly described in terms of the possibility of unfavourable occurrence of an effectiveness indicator. It is also identified with a range of variability for selected measures of the investment effectiveness [5]. A risk so defined results from the occurrence of uncertainty with regard to predicted quantity of sales, product prices, prices of raw materials, etc.

Quantification of investment projects risk is one of the most difficult tasks in managing a risk in an investment project. A fundamental problem in this phenomenon is the need to develop methods for estimation of the investment project risk and to improve methods for data gathering and processing with formal descriptions of uncertainty. An adequate mathematical description of parameter uncertainty is of course critical for assessment of project risk and a precondition for risk quantification.

Project risk can be thought of along several dimensions [5]:

$•$
As project-specific risk (a risk of a general nature in an investment project) which is dependent on particular features of a given investment project. It is assessed in isolation, independent of other effects.
$•$
As the risk of an investment project portfolio, which depends on mutual relationships between different portfolio members.
$•$
As an internal risk that a company bears when it is going to implement an investment project. This is measured by assessing the influence that the project exerts on the company's economic performance.
$•$
As market risk (or beta risk), which is project risk evaluated from the point of view of a shareholder with a diversified portfolio.

The method presented in this paper regards quantification of project-specific risk. A model was developed for the estimation of investment effectiveness and investment risk. Possibilities were discussed with a presentation of practical applications of integration methods of various ways in a description of uncertainty of parameters of the calculation of effectiveness in a computer simulation in order to estimate an investment project risk. In the presented example of the risk assessment, uncertainty for some parameters of the effectiveness measurement is defined by a probability distribution, and by a fuzzy set for the others. Thus, a transformation is done of possibility distributions into probability distributions used in the simulation. For comparison, the risk assessment of the analysed investment is carried out on the assumption that uncertainty distributions of the effectiveness measurement parameters are presented in the form of fuzzy sets.

Section snippets

A computer simulation applied to an appraisal of investment project risk

Several publications discuss the methods of quantification of risk in investment projects [1], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. At present, methods with quantitative risk assessments are preferred.

Computer simulation seems to be one of the most effective tools for risk appraisal. Simulation is based on repeated calculation of project effectiveness for randomly selected input parameters, and the probability distribution of the effectiveness measure thus

Fuzzy sets applied to an appraisal of investment project risk

Difficulties in estimating probability distributions have resulted in different forms of descriptions being used to describe parameter uncertainty in the calculation of effectiveness. One such form is that of fuzzy sets.

Tversky and Kahneman [8] show that heuristic methods applied to assess probabilities and predict values can sometimes lead to severe and systematic errors. Because people do not naturally think in probabilistic terms, they tend to find notions of fuzzy sets and their

Rearranging distributions of uncertainty of parameters in the calculation of effectiveness

As the above-mentioned considerations show, there are two alternative methods used as a description of uncertainty of parameters in the calculation of effectiveness: a probability distribution and possibility distribution. In the first case, risk is characterised by a probability distribution of the effectiveness indicator (most commonly, NPV). In the second case, risk is characterised by the possibility distribution of the indicator.

In practice, it is common in risk evaluations to use

Characteristics of investment project

The investment project under consideration is a modernisation of a HR (hot rolled) sheet mill. The process diagram for the production system under consideration is shown in Fig. 1.¹ Modernisation is proposed for an existing production unit that is technologically linked with other production units. The

Conclusions

These methods can be effective in estimating risk of investment projects. Simulation methods enable one to estimate risk with consideration of the total influence of all uncertain parameters of the effectiveness calculation. However, a fundamental practical problem with the application of simulation methods is determining the uncertainty distributions of forecasts of parameters of the calculation of effectiveness. This problem commonly arises in branches of industry which are characterised by

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Fuzziness and randomness in investment project risk appraisal

Abstract

Introduction

Section snippets

A computer simulation applied to an appraisal of investment project risk

Fuzzy sets applied to an appraisal of investment project risk

Rearranging distributions of uncertainty of parameters in the calculation of effectiveness

Characteristics of investment project

Conclusions

International Journal of Project Management

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Information Sciences

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

On replacement models via a fuzzy set theoretic framework

IEEE Transactions on Systems, Man, and Cybernetics-Part C, Applications and Reviews, UK

Risk management infrastructure

International Journal of Project Management

Fundamentals of financial management

Capital budgeting and long-term financing decisions

Incorporating risk into capital budgeting decision using simulation

Management Decision

Judgment under uncertainty: heuristic and biases

Science