- Email: [email protected]
Investment risk forecasting in a local energy market
Energy Conversion and Management 43 (2002) 515±522
www.elsevier.com/locate/enconman
Investment risk forecasting in a local energy market Waldemar Kamrat * Power Plants and Energy Economics Department, Faculty of Electrical and Control Engineering, Technical University of Gdansk, 11/12 Narutowicza Street, 80±952 Gdansk, Poland Received 9 October 2000; accepted 19 February 2001
Abstract The paper considers the general problems faced when evaluating the risk of investing in a local energy market by computer tools. The proposal formulated for the emerging local energy markets suggests broadening the method of evaluating investment risk so as to include elements of cluster analysis. The paper also discusses the signi®cance of estimating investment risk in market terms and the importance and range of the local energy market. Finally, the work formulates a method to estimate investment risk by a computer program and gauge its impact on the investment expenditure. The presented approach to estimating the cost of risk allows for identifying such cost in changing market conditions, with technical, economic and location parameters speci®c for a given investment in the power industry recognised. This is particularly crucial in planning the processes of investing in the regional power industry and local energy markets. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Local energy market; Investment risk; Risk evaluation
1. Introduction It is the authorÕs belief that the process of implementing structural and systemic transformations in the energy sector should recognise and take into account the phenomenon of investment risk. In general terms, for feasibility study calculations to be entirely reliable, such studies should consider the risk that accompanies the individual investments planned. This is usually achieved by way of: · Adjusting the interest rate by the so-called risk premium
*
Tel.: +48-58-343-1201; fax: +48-58-343-1170. E-mail address: [email protected] (W. Kamrat).
0196-8904/02/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 0 1 ) 0 0 0 2 9 - 2
516
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
· Employing probability calculus to estimate the anticipated cash ¯ow to be generated from an investment The interest rate plays a crucial role in feasibility studies that deal with investments in the energy market. It forms the base for calculations in the discounting methods of the economic calculus and re¯ects the (required) threshold rate of return on an investment project. By increasing this rate so as to include the so-called risk premium, the size of which depends on the degree of the risk run, we impose more stringent requirements on the project. The investor gains a certain safety margin, the width of which is determined by the size of the risk premium. Approval for construction is obtained only for such developmental ventures that oer a safety margin, since due to the approach, there is a chance that the enterprise involved should not generate losses even if the projected income on the investment is not fully achieved. The method of adjusting the interest rate oers the simplest way to account for risk when studying eectiveness. However, it also requires estimating the risk premium the investor might require. On the other hand, in order to conduct a feasibility study of a developmental project based on anticipated probable cash ¯ow, one needs to apply key statistical measures, such as the anticipated value, variance, standard deviation or variation ratio. Unfortunately, not always is it possible to use them in assessing an investment project. There is no simple or unambiguous de®nition of investment risk. One of the possible de®nitions says the risk is the conviction that in a long run, one investment option will generate a higher or lower income (net pro®t) than another. Since there is no precise or formal de®nition of investment risk, studies adopt it as the so-called hidden system variable. This, in turn, means that it does not yield itself to direct analysis and can only be studied indirectly, using other variables that well describe the hidden variable when employed in econometric calculations. This paper drafts a method of recognising the investment risk based on elements of comparative cluster analysis that allows the risk to be rated precisely and the cost of risk to be estimated on an annual basis. 2. General problems encountered when estimating the investment risk in the local energy market The authorÕs suggestion is that the investment risk inherent in a given venture can be gauged with the so-called risk rate identi®ed based on a taxonomic variable, the construction of which can be found in earlier works [1±4]. A synthetic scale of the investment risk is constructed by employing the comparative cluster analysis method that enables ranking individual entities along the synthetic scale under the socalled model method [5]. Selecting the diagnostic variables is an important step in the suggested risk assessment method. Described by using a set of diagnostic variables, the analysed energy market investment strategies can be treated as real, multi-feature objects. Such objects can be analysed for the risk involved under appropriate methods of comparative cluster analysis. The methods put numerical representations of the input variables in the centre of the studies, i.e. treat them as the objects of study. This makes it possible to obtain information on uniformity within the set of objects considered, i.e. uniformity within the considered set of numerical data. When numerical representations of the
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
517
input variables are used to study dierent strategies, the set of data analysed is found nonhomogenous, as it groups entities that dier in size, technology and/or technical equipment. Therefore, to study the regularities occurring in investment strategies, the non-homogeneous data set should be split into relatively uniform subsets, which can then be studied using methodologies and techniques of comparative cluster analysis [5,6]. We suggest two types of basic data should be adopted for the purpose of synthetic studies of the risk inherent in investing in local energy markets, i.e.: · A set of possible objects X fxi g; i 1; 2; . . . ; m · A set of diagnostic data U fuj g; j 1; 2; . . . ; n where the diagnostic data can represent both physical, technical and/or economic variables. The notions of the object, xi , and the features, uj , are considered to be prime in nature, hence need not be de®ned. The features, uj , can be interpreted to be the result of transformation of the object set X into a set of real numbers, i.e.: uj : X ! nj R1 Hence, each xi 2 X element has an xij 2 nj value assigned. In this natural way one arrives at the following data matrix: 2 3 x11 x12 x1n X 4 5 1 xm1 xm2 xmn where xij represents feature ``j'' in object ``i''. The rows, Xi , of the matrix, or the so-called vectors, xi1 ; xi2 ; . . . ; xin , can be considered representations or visual pictures of the xi objects. This should be understood as the following mapping: X ! Gn1 Rn , where each xi 2 X element has an Xi xi1 ; xi2 ; . . . ; xin 2 Gn1 vector, i.e. a row in the X matrix, assigned. The above notions should, thus, be understood as a process of transformation: U ! Gm2 Rm , where each /j 2 U element has an Xj x1j ; x2j ; . . . ; xmj T 2 Gm2 vector assigned. The Gn1 and Gm2 sets are thus called: the space of object graphic representations and the space of feature graphic representations, respectively. Studies do not deal directly with the objects or features but with numerical representations of the features. In other words, objects are compared with one another via their assigned numerical representations. Analysis of this kind very much relies on securing the base for comparisons. This is achieved by dierentiating between the notions of a stimulant and destimulant [1,2,5]. For example, feature /j will function as a stimulant for objects x1 and x2 when the numerical representation of feature ``j'' of the object x2 , i.e. x2j , is greater than the respective x1j value of object x1 . To arrive at a general de®nition for objects xr and xs , feature /j is said to be a stimulant when: ^ xsj P xrj ) xs xr
xrj ;xsj
2
518
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
The same /j feature is said to be a destimulant when: ^ xsj P xrj ) xs xr
xrj ;xsj
3
where · xrj , xsj denote numerical relations of feature ``j'' · denotes ``domination'' of the object over another object. To continue into further considerations, we need to adopt the following two assumptions: · Set U U1 [ U2 ; U1 \ U2 £; where U1 is the set of stimulants and U2 is the set of destimulants. · For each destimulant, there is a transformation that changes it into a stimulant. This indicates that upon transformation, sets U and U1 can be considered identical, i.e. U U1 or U2 £. The simplest way of transforming a destimulant into a stimulant is to reverse its numerical representation. The procedure of assessing the investment risk is based on the assumption that the representations of the features included in the observation matrix constitute representations of one (and the same) chance variable, all of which refer to individual elements of the object set. A comparative cluster analysis of the risk inherent in investment strategies will be performed using diagnostic variables of the characteristic features of a speci®c project planned. One of the key issues is to compile a correct set of diagnostic variables. In practice, such sets are compiled based on familiarity with the objects studied. Cluster analysis proves useful also when the studied objects are not very well known, however, then it is bound to be based on a large set of features. These are initially hard to rank in terms of their priority for the purposes of the conducted comparative studies. All things considered, using a cluster and spatial measure to assess risk has the advantage of enabling the positioning of relatively uniform features along individual axes of the spatial model. In addition, this kind of measure can be easily interpreted in its simple graphic representation. Its disadvantage, compared to the synthetic (unilateral assessment measure), is the unavailability of a simple way to rank objects against a single, synthetic ratio. Furthermore, it is easy to end up with a set including non-diagnostic features, which will hinder identi®cation of characteristic types and increase the amount of work needed to complete the calculations. The latter argument is used to justify use of the so-called reduction of the description of the studied space. The purpose here is to eliminate doubled information (e.g. closely correlated space constituents), data of low informative value (low information capacity) and little dierentiation between features of the objects grouped in the studied set. Comparative cluster analysis serves as a tool for comparing variables (re¯ecting the features and speci®cs of processes) that can be expressed in identical or dierent measurement units. It also allows for implementing the following analytical computer procedure: · Stage I · Stage II
preliminary variable selection identifying the co-relations between the variables
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
519
· Stage III identifying the factors that underlie the co-relations · Stage IV forming synthetic variables to re¯ect the factors · Stage V arriving at aggregate variables that will allow objects to be ranked along the scale of investment risk. The presented comparative procedure involves employing a set of statistical methods sequenced so that the results obtained under one method, used at one stage of the analysis, serve as the starting point for the subsequent stage that uses a dierent method. The stages meet the requirements of the above-mentioned tasks that comparative cluster analysis is expected to achieve. The process of identifying the risk usually involves three basic methods: · Co-relation analysis ± stages I, II · Main constituent method ± stages III, IV · Taxonomic methods ± stage V. Variable selection is conducted in several steps. Step one consists of analysing the contents of the variables on the preliminary list, which gathers all the available variables related to the aim and scope of the study. The variables should be precisely and unambiguously de®ned. A formal analysis performed at step two aims at excluding all the variables whose informative signi®cance is minor (i.e. are irrelevant) or which double the information contained in other variables from the preliminary list. The starting point for the analysis proper is the Bo xij matrix of ``t n'' size, where ``t'' stands for the number of observations and ``n'' for the number of variables. The Bo matrix must be complete, i.e. must include information on the variables of each investment strategy. The described procedure eliminates those variables whose variation ratio (relation of the standard variation to the mean) is smaller than the adopted threshold value e. Such data is insigni®cant, or quasi-stable. To reduce the number of variables, the present work seeks to incorporate a method once developed by Hellwig [5]. The literature mentioned is under the concept of the ``developmental model method'' used to rank energy market investment strategies in terms of risk. A description of the above can be found further in the paper.
3. A measure of the risk inherent in investing in the energy market constructed For the present purposes an investment process is understood only to denote construction, development or modernisation of the sources of energy produced. Further on, this is called an investment strategy. Observations are positioned along a synthetic scale of investment risk under the previously mentioned model method. Here, the Euclid distance (in multi-dimensional space, the borders of which are determined by the number of variables) is calculated for all values of the factor objects from the factor values of the hypothetical ``model'' object de®ned based on ``the most desirable'' values of the variables found in the entire set of investment strategies.
520
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
The objects ``closest'' to the model have the most favourable parameters in terms of the adopted criterion, i.e. represent the lowest investment risk. For formal reasons, it is more convenient to use a standardised scale (between 0 and 1) to depict the positioning of the objects. The ``best'' object is represented by the highest value, the ``worst'' by the lowest. Thus, in the present study, strategies involving the lowest risk are found at the beginning of the synthetic investment risk scale, while those burdened with the highest risk come at the end. The investment risk is measured with a synthetic risk rate calculated according to the following formula: ep 1
dp k Dk
4
where
v u k uX 2 xpj qj dp t
5
j1
· xpj is the sequentially numbered value of the technical and economic variable of feature ``p'' of the investment strategy ``j'', · kDk d P ; Q is the distance between the ``extremes'' (maximum, minimum) of the features characterising the strategies of investing in the energy market. A block diagram of the algorithm for identifying the investment risk is presented in Fig. 1. An important fact is that the risk can be subdivided into several categories along the synthetic scale. Such subdivision is not only possible, but also recommendable. It seems reasonable to identify the following ®ve investment risk categories: · · · · ·
Low risk ± for strategies with a ratio above h0, 0.1) Medium risk ± for strategies with a ratio between h0.1, 0.2) Increased risk ± for strategies with a ratio between h0.2, 0.3) High risk ± for strategies with a ratio between h0.3, 0.4) Extreme risk ± for strategies with a ratio below h0.4, 1.0i
The above procedure allows for ranking the degree of risk from the ``lowest'' to the ``highest''. With the risk rates de®ned this way, we can now multiply them by the Knd expenditure ¯ow and, in eect, determine the annual cost of risk Kryz represented in the following formula: Kryz ep Knd where · ep is the risk rate · Knd , the discounted ¯ow of investment expenditure (common discounting methods).
6
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
Fig. 1. Block diagram of the algorithm of identifying the investment risk.
521
522
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
Thus, the identi®ed annual cost of the investment risk allows one to assess the impact the risk will have upon the total annual expenditure. This can be calculated as follows: Kr Ks Kz Kryz
7
where · Ks is the indirect cost per annum · Kz , the direct cost per annum. An additional bene®t gained here is the possibility to compare the cost of risk to the installed power. In this way, we calculate the unit risk cost for a speci®c investment strategy. The values of the risk rates range between h0, 1i. The closer the ep value is to 1, the higher is risk involved in a given investment strategy.
4. Conclusions The presented approach to estimate the cost of risk allows for identifying such cost in changing market conditions, with the technical, economic and location parameters characteristic for a given investment in the power industry recognised. This is particularly crucial in planning the processes of investing in the regional power industry and local energy markets.
References [1] Kamrat W. Synthetic measure of the eectiveness of industrial heat and power generating plants. Arch Energ 1988:(1);87±91 (in Polish). [2] Kamrat W. Application of the comparative cluster analysis in studying eectiveness. Doctorate Dissertation, Gdansk, 1989 (in Polish). [3] Kamrat W. Methodology of investment eectiveness evaluation in case of local energy market in Poland. Proceedings of 4th European Conference IAEE/GEE, Berlin, 9±10th September 1998 (in English). [4] Kamrat W. Methodology of investment eectiveness evaluation in the local energy market. Energy Department Report, EN D-65, Lappeenranta University of Technology, Finland, July 1999 (in English). [5] Hellwig W. Taxonomic method applied to arrive at state typological categorisation with reference to their development level. Polish Stat Rev Warsaw, 1968:(4) (in Polish). [6] Pluta W. Comparative cluster analysis in econometric modelling. PWN, Warsaw, 1986 (in Polish).
www.elsevier.com/locate/enconman
Investment risk forecasting in a local energy market Waldemar Kamrat * Power Plants and Energy Economics Department, Faculty of Electrical and Control Engineering, Technical University of Gdansk, 11/12 Narutowicza Street, 80±952 Gdansk, Poland Received 9 October 2000; accepted 19 February 2001
Abstract The paper considers the general problems faced when evaluating the risk of investing in a local energy market by computer tools. The proposal formulated for the emerging local energy markets suggests broadening the method of evaluating investment risk so as to include elements of cluster analysis. The paper also discusses the signi®cance of estimating investment risk in market terms and the importance and range of the local energy market. Finally, the work formulates a method to estimate investment risk by a computer program and gauge its impact on the investment expenditure. The presented approach to estimating the cost of risk allows for identifying such cost in changing market conditions, with technical, economic and location parameters speci®c for a given investment in the power industry recognised. This is particularly crucial in planning the processes of investing in the regional power industry and local energy markets. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Local energy market; Investment risk; Risk evaluation
1. Introduction It is the authorÕs belief that the process of implementing structural and systemic transformations in the energy sector should recognise and take into account the phenomenon of investment risk. In general terms, for feasibility study calculations to be entirely reliable, such studies should consider the risk that accompanies the individual investments planned. This is usually achieved by way of: · Adjusting the interest rate by the so-called risk premium
*
Tel.: +48-58-343-1201; fax: +48-58-343-1170. E-mail address: [email protected] (W. Kamrat).
0196-8904/02/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 0 1 ) 0 0 0 2 9 - 2
516
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
· Employing probability calculus to estimate the anticipated cash ¯ow to be generated from an investment The interest rate plays a crucial role in feasibility studies that deal with investments in the energy market. It forms the base for calculations in the discounting methods of the economic calculus and re¯ects the (required) threshold rate of return on an investment project. By increasing this rate so as to include the so-called risk premium, the size of which depends on the degree of the risk run, we impose more stringent requirements on the project. The investor gains a certain safety margin, the width of which is determined by the size of the risk premium. Approval for construction is obtained only for such developmental ventures that oer a safety margin, since due to the approach, there is a chance that the enterprise involved should not generate losses even if the projected income on the investment is not fully achieved. The method of adjusting the interest rate oers the simplest way to account for risk when studying eectiveness. However, it also requires estimating the risk premium the investor might require. On the other hand, in order to conduct a feasibility study of a developmental project based on anticipated probable cash ¯ow, one needs to apply key statistical measures, such as the anticipated value, variance, standard deviation or variation ratio. Unfortunately, not always is it possible to use them in assessing an investment project. There is no simple or unambiguous de®nition of investment risk. One of the possible de®nitions says the risk is the conviction that in a long run, one investment option will generate a higher or lower income (net pro®t) than another. Since there is no precise or formal de®nition of investment risk, studies adopt it as the so-called hidden system variable. This, in turn, means that it does not yield itself to direct analysis and can only be studied indirectly, using other variables that well describe the hidden variable when employed in econometric calculations. This paper drafts a method of recognising the investment risk based on elements of comparative cluster analysis that allows the risk to be rated precisely and the cost of risk to be estimated on an annual basis. 2. General problems encountered when estimating the investment risk in the local energy market The authorÕs suggestion is that the investment risk inherent in a given venture can be gauged with the so-called risk rate identi®ed based on a taxonomic variable, the construction of which can be found in earlier works [1±4]. A synthetic scale of the investment risk is constructed by employing the comparative cluster analysis method that enables ranking individual entities along the synthetic scale under the socalled model method [5]. Selecting the diagnostic variables is an important step in the suggested risk assessment method. Described by using a set of diagnostic variables, the analysed energy market investment strategies can be treated as real, multi-feature objects. Such objects can be analysed for the risk involved under appropriate methods of comparative cluster analysis. The methods put numerical representations of the input variables in the centre of the studies, i.e. treat them as the objects of study. This makes it possible to obtain information on uniformity within the set of objects considered, i.e. uniformity within the considered set of numerical data. When numerical representations of the
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
517
input variables are used to study dierent strategies, the set of data analysed is found nonhomogenous, as it groups entities that dier in size, technology and/or technical equipment. Therefore, to study the regularities occurring in investment strategies, the non-homogeneous data set should be split into relatively uniform subsets, which can then be studied using methodologies and techniques of comparative cluster analysis [5,6]. We suggest two types of basic data should be adopted for the purpose of synthetic studies of the risk inherent in investing in local energy markets, i.e.: · A set of possible objects X fxi g; i 1; 2; . . . ; m · A set of diagnostic data U fuj g; j 1; 2; . . . ; n where the diagnostic data can represent both physical, technical and/or economic variables. The notions of the object, xi , and the features, uj , are considered to be prime in nature, hence need not be de®ned. The features, uj , can be interpreted to be the result of transformation of the object set X into a set of real numbers, i.e.: uj : X ! nj R1 Hence, each xi 2 X element has an xij 2 nj value assigned. In this natural way one arrives at the following data matrix: 2 3 x11 x12 x1n X 4 5 1 xm1 xm2 xmn where xij represents feature ``j'' in object ``i''. The rows, Xi , of the matrix, or the so-called vectors, xi1 ; xi2 ; . . . ; xin , can be considered representations or visual pictures of the xi objects. This should be understood as the following mapping: X ! Gn1 Rn , where each xi 2 X element has an Xi xi1 ; xi2 ; . . . ; xin 2 Gn1 vector, i.e. a row in the X matrix, assigned. The above notions should, thus, be understood as a process of transformation: U ! Gm2 Rm , where each /j 2 U element has an Xj x1j ; x2j ; . . . ; xmj T 2 Gm2 vector assigned. The Gn1 and Gm2 sets are thus called: the space of object graphic representations and the space of feature graphic representations, respectively. Studies do not deal directly with the objects or features but with numerical representations of the features. In other words, objects are compared with one another via their assigned numerical representations. Analysis of this kind very much relies on securing the base for comparisons. This is achieved by dierentiating between the notions of a stimulant and destimulant [1,2,5]. For example, feature /j will function as a stimulant for objects x1 and x2 when the numerical representation of feature ``j'' of the object x2 , i.e. x2j , is greater than the respective x1j value of object x1 . To arrive at a general de®nition for objects xr and xs , feature /j is said to be a stimulant when: ^ xsj P xrj ) xs xr
xrj ;xsj
2
518
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
The same /j feature is said to be a destimulant when: ^ xsj P xrj ) xs xr
xrj ;xsj
3
where · xrj , xsj denote numerical relations of feature ``j'' · denotes ``domination'' of the object over another object. To continue into further considerations, we need to adopt the following two assumptions: · Set U U1 [ U2 ; U1 \ U2 £; where U1 is the set of stimulants and U2 is the set of destimulants. · For each destimulant, there is a transformation that changes it into a stimulant. This indicates that upon transformation, sets U and U1 can be considered identical, i.e. U U1 or U2 £. The simplest way of transforming a destimulant into a stimulant is to reverse its numerical representation. The procedure of assessing the investment risk is based on the assumption that the representations of the features included in the observation matrix constitute representations of one (and the same) chance variable, all of which refer to individual elements of the object set. A comparative cluster analysis of the risk inherent in investment strategies will be performed using diagnostic variables of the characteristic features of a speci®c project planned. One of the key issues is to compile a correct set of diagnostic variables. In practice, such sets are compiled based on familiarity with the objects studied. Cluster analysis proves useful also when the studied objects are not very well known, however, then it is bound to be based on a large set of features. These are initially hard to rank in terms of their priority for the purposes of the conducted comparative studies. All things considered, using a cluster and spatial measure to assess risk has the advantage of enabling the positioning of relatively uniform features along individual axes of the spatial model. In addition, this kind of measure can be easily interpreted in its simple graphic representation. Its disadvantage, compared to the synthetic (unilateral assessment measure), is the unavailability of a simple way to rank objects against a single, synthetic ratio. Furthermore, it is easy to end up with a set including non-diagnostic features, which will hinder identi®cation of characteristic types and increase the amount of work needed to complete the calculations. The latter argument is used to justify use of the so-called reduction of the description of the studied space. The purpose here is to eliminate doubled information (e.g. closely correlated space constituents), data of low informative value (low information capacity) and little dierentiation between features of the objects grouped in the studied set. Comparative cluster analysis serves as a tool for comparing variables (re¯ecting the features and speci®cs of processes) that can be expressed in identical or dierent measurement units. It also allows for implementing the following analytical computer procedure: · Stage I · Stage II
preliminary variable selection identifying the co-relations between the variables
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
519
· Stage III identifying the factors that underlie the co-relations · Stage IV forming synthetic variables to re¯ect the factors · Stage V arriving at aggregate variables that will allow objects to be ranked along the scale of investment risk. The presented comparative procedure involves employing a set of statistical methods sequenced so that the results obtained under one method, used at one stage of the analysis, serve as the starting point for the subsequent stage that uses a dierent method. The stages meet the requirements of the above-mentioned tasks that comparative cluster analysis is expected to achieve. The process of identifying the risk usually involves three basic methods: · Co-relation analysis ± stages I, II · Main constituent method ± stages III, IV · Taxonomic methods ± stage V. Variable selection is conducted in several steps. Step one consists of analysing the contents of the variables on the preliminary list, which gathers all the available variables related to the aim and scope of the study. The variables should be precisely and unambiguously de®ned. A formal analysis performed at step two aims at excluding all the variables whose informative signi®cance is minor (i.e. are irrelevant) or which double the information contained in other variables from the preliminary list. The starting point for the analysis proper is the Bo xij matrix of ``t n'' size, where ``t'' stands for the number of observations and ``n'' for the number of variables. The Bo matrix must be complete, i.e. must include information on the variables of each investment strategy. The described procedure eliminates those variables whose variation ratio (relation of the standard variation to the mean) is smaller than the adopted threshold value e. Such data is insigni®cant, or quasi-stable. To reduce the number of variables, the present work seeks to incorporate a method once developed by Hellwig [5]. The literature mentioned is under the concept of the ``developmental model method'' used to rank energy market investment strategies in terms of risk. A description of the above can be found further in the paper.
3. A measure of the risk inherent in investing in the energy market constructed For the present purposes an investment process is understood only to denote construction, development or modernisation of the sources of energy produced. Further on, this is called an investment strategy. Observations are positioned along a synthetic scale of investment risk under the previously mentioned model method. Here, the Euclid distance (in multi-dimensional space, the borders of which are determined by the number of variables) is calculated for all values of the factor objects from the factor values of the hypothetical ``model'' object de®ned based on ``the most desirable'' values of the variables found in the entire set of investment strategies.
520
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
The objects ``closest'' to the model have the most favourable parameters in terms of the adopted criterion, i.e. represent the lowest investment risk. For formal reasons, it is more convenient to use a standardised scale (between 0 and 1) to depict the positioning of the objects. The ``best'' object is represented by the highest value, the ``worst'' by the lowest. Thus, in the present study, strategies involving the lowest risk are found at the beginning of the synthetic investment risk scale, while those burdened with the highest risk come at the end. The investment risk is measured with a synthetic risk rate calculated according to the following formula: ep 1
dp k Dk
4
where
v u k uX 2 xpj qj dp t
5
j1
· xpj is the sequentially numbered value of the technical and economic variable of feature ``p'' of the investment strategy ``j'', · kDk d P ; Q is the distance between the ``extremes'' (maximum, minimum) of the features characterising the strategies of investing in the energy market. A block diagram of the algorithm for identifying the investment risk is presented in Fig. 1. An important fact is that the risk can be subdivided into several categories along the synthetic scale. Such subdivision is not only possible, but also recommendable. It seems reasonable to identify the following ®ve investment risk categories: · · · · ·
Low risk ± for strategies with a ratio above h0, 0.1) Medium risk ± for strategies with a ratio between h0.1, 0.2) Increased risk ± for strategies with a ratio between h0.2, 0.3) High risk ± for strategies with a ratio between h0.3, 0.4) Extreme risk ± for strategies with a ratio below h0.4, 1.0i
The above procedure allows for ranking the degree of risk from the ``lowest'' to the ``highest''. With the risk rates de®ned this way, we can now multiply them by the Knd expenditure ¯ow and, in eect, determine the annual cost of risk Kryz represented in the following formula: Kryz ep Knd where · ep is the risk rate · Knd , the discounted ¯ow of investment expenditure (common discounting methods).
6
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
Fig. 1. Block diagram of the algorithm of identifying the investment risk.
521
522
W. Kamrat / Energy Conversion and Management 43 (2002) 515±522
Thus, the identi®ed annual cost of the investment risk allows one to assess the impact the risk will have upon the total annual expenditure. This can be calculated as follows: Kr Ks Kz Kryz
7
where · Ks is the indirect cost per annum · Kz , the direct cost per annum. An additional bene®t gained here is the possibility to compare the cost of risk to the installed power. In this way, we calculate the unit risk cost for a speci®c investment strategy. The values of the risk rates range between h0, 1i. The closer the ep value is to 1, the higher is risk involved in a given investment strategy.
4. Conclusions The presented approach to estimate the cost of risk allows for identifying such cost in changing market conditions, with the technical, economic and location parameters characteristic for a given investment in the power industry recognised. This is particularly crucial in planning the processes of investing in the regional power industry and local energy markets.
References [1] Kamrat W. Synthetic measure of the eectiveness of industrial heat and power generating plants. Arch Energ 1988:(1);87±91 (in Polish). [2] Kamrat W. Application of the comparative cluster analysis in studying eectiveness. Doctorate Dissertation, Gdansk, 1989 (in Polish). [3] Kamrat W. Methodology of investment eectiveness evaluation in case of local energy market in Poland. Proceedings of 4th European Conference IAEE/GEE, Berlin, 9±10th September 1998 (in English). [4] Kamrat W. Methodology of investment eectiveness evaluation in the local energy market. Energy Department Report, EN D-65, Lappeenranta University of Technology, Finland, July 1999 (in English). [5] Hellwig W. Taxonomic method applied to arrive at state typological categorisation with reference to their development level. Polish Stat Rev Warsaw, 1968:(4) (in Polish). [6] Pluta W. Comparative cluster analysis in econometric modelling. PWN, Warsaw, 1986 (in Polish).