**4. Methodology**

In order to decide which business risks are the most important to natural gas trading companies, we employed an expert survey. The obtained results were processed by applying the Analytic Hierarchy Process (AHP) model, which is highly recommended for solving complex, interconnected, hierarchical problems that cannot be solved using purely quantitative methods [76]. Initially, more than ten business risks were identified during the scientific literature analysis, which is more than the maximum number of alternatives that AHP is capable of processing. Therefore, we performed an initial survey, during which we eliminated the less important business risks (according to the potential impact on a gas trading company) and identified nine of the most significant business risks, which were the subject of our research: operating volume risk, purchase price risk, product competition risk, alternative energy risk, risk of customers' default, risk of supplier default, technological risk, reputation risk, and personnel risk.

In the pursuance of obtaining more reliable results and following the principle of triangulation, we employed three di fferent scales of an AHP: balanced, Koczkodaj and adaptive, representing all three scale groups. After obtaining the results of each scale, the eigenvector of each risk was normalized.

GET Baltic has 77 registered natural gas trading companies, though four of the biggest market players control over 87% [77] of the market share. In 2018, GET Baltic was responsible for 15.3% of all natural gas sold in Lithuania. Lithuanian gas trading companies received more than 130 mln. EUR of revenues from gas retailing in a first half of 2018, showing an increase of 6.5% compared to the first half of 2017 [77].

The following criteria were employed for selecting the experts: (a) all biggest market players must be represented in a survey; (b) at least 10% of the rest natural gas trading companies, registered in GET Baltic, must be represented in the survey; (c) the expert must hold a Master of Science or equal degree (in fact, all the respondents hold a Master of Science; no MBAs or similar degree holders participated in the survey), have at least 5 years of experience in gas trading business sector and occupy a position no lower than manager. In total, 12 experts participated in our survey.

In AHP, the chosen experts evaluated the presented alternatives (business risks of natural gas trading companies) {θ\_1, ... , θ\_*<sup>n</sup>*}, by filling individual pairwise comparison matrices, which were being calculated as follows:

$$\mathbf{M} = \begin{pmatrix} \frac{m\_1}{m\_1} & \frac{m\_1}{m\_2} & & \frac{m\_1}{m\_n} \\ \frac{m\_2}{m\_1} & \frac{m\_2}{m\_2} & \dots & \frac{m\_2}{m\_n} \\ & \frac{m\_n}{m\_1} & \frac{m\_n}{m\_2} & & \frac{m\_n}{m\_n} \end{pmatrix} = \begin{pmatrix} b\_{11} & b\_{12} \dots & b\_{1n} \\ b\_{12} & b\_{21} \dots & b\_{2n} \\ b\_{n1} & b\_{n2} \dots & b\_{nn} \end{pmatrix}.$$

Here: *bij*—Pairwise comparison matrix element; *mi mj* —A priority vector of the *i*-th factor with the respect to *j*-th factor.

$$m\_{ij} = \frac{1}{m\_{ji}} \,\,\forall \, i, j = 1, 2, \dots, n.$$

After the experts made a pairwise comparison of the criteria presented, all responses (evaluations) were recorded in the form of standardized matrices.

A multiplication of the *i*-th line elements was being computed to every *M* matrix:

$$
\Pi\_i = \Pi\_{j=1}^n m\_{ij\prime} \ (i = 1, \dots, n).
$$

The obtained values were being normalized using the formula:

$$k\_i = \frac{\sqrt[n]{\prod\_i}}{\sum\_{i=1}^n \sqrt[n]{\prod\_i}} = \frac{\sqrt[n]{\prod\_{j=1}^n i\_j}}{\sum\_{i=1}^n \sqrt[n]{\prod\_{j=p^{a\_{ij}}}^n}}, \ (i = 1, \dots, n; \sum k\_1 = 1)$$

A priority rank of each expert was obtained in such a way. After that, a procedure of consistency of matrices was being undertaken. Matrix was considered consistent, when *mik* = *mijmjk*, ∀ *i*, *j*, *k* and a priority vector was existent, which satisfied the equation: *w* = (<sup>ω</sup>1, ... , <sup>ω</sup>*n*), where *mij*= ω*i* , ∀ *i*, *j*.

<sup>ω</sup>*j* After that, the consistency index (CI) of each standardized matrix was being calculated. In order to obtain CI, an eigenvalue (λ*max*) of each standardized matrix was calculated using formula:

$$
\lambda\_{\text{max}} = \sum\_{j=1}^{n} \frac{(\mathbf{P} \cdot \mathbf{v})\_j}{n \cdot v\_j}.
$$

Here λ*max*—the largest eigenvalue of each research standardized matrix; *n*—Number of independent rows in matrix; *j*—Eigenvalue of a matrix. All these steps were represented in *Mq* matrix:

$$M\_{\boldsymbol{q}} = \begin{array}{ccccc} b\_{11} & b\_{12} \dots & b\_{1n} \\ & b\_{12} & b\_{21} \dots & b\_{2n} \\ & & b\_{n1} & b\_{n2} \dots & b\_{nn} \\ \end{array} \left( \begin{array}{ccccc} q\_{1} \\ & q\_{2} \\ & q\_{n} \\ \end{array} \right) = \left( \begin{array}{ccccc} b\_{11}q\_{1} + & b\_{12}q\_{2} + & \cdots & +b\_{1n}q\_{n} \\ b\_{12}q\_{1} + & b\_{21}q\_{2} + & \cdots & +b\_{2n}q\_{n} \\ b\_{m1}q\_{1} + & b\_{m2}q\_{2} + & \cdots & +b\_{mn}q\_{n} \\ \end{array} \right) = \lambda\_{\text{max}} \left( \begin{array}{ccccc} q\_{1} \\ & q\_{2} \\ & q\_{n} \\ \end{array} \right) = \left( \begin{array}{ccccc} \lambda\_{\text{max}} q\_{1} \\ \lambda\_{\text{max}} q\_{2} \\ \end{array} \right) = \left( \begin{array}{ccccc} \lambda\_{\text{max}} q\_{1} \\ \lambda\_{\text{max}} q\_{2} \\ \end{array} \right) = \left( \begin{array}{ccccc} \lambda\_{\text{max}} q\_{1} \\ \lambda\_{\text{max}} q\_{2} \\ \end{array} \right) = \left( \begin{array}{ccccc} \lambda\_{\text{max}} q\_{1} \\ \lambda\_{\text{max}} q\_{2} \\ \end{array} \right)$$

An expert comparison matrix *Mq* was considered absolutely consistent when λ*max* = *n*, although in reality it almost never happens. In the case of small *mij* changes, matrix *M* satisfied the pre-selected compatibility condition (in this case 0.1 was selected), the λ*max* value became close to *n*.

After calculating the eigenvalue λ*max*, the CI was calculated using formula:

$$\text{CI} = \frac{\lambda\_{\text{max}} - n}{n - 1}.$$

Here *n*—number of possible alternatives.

If CI met the pre-selected compatibility condition (our case: 0.1), the aggregated expert evaluation was being calculated using formula [78]:

$$p\_{ij}^P = \sqrt[n]{p\_{ij}^1} \times p\_{ij}^2 \times \dots \times p\_{ij}^n$$

Here *pAij*– aggregated evaluation of element, belonging to *i* row and *j*-column;

*n*—number of matrices of the pairwise comparison of each expert.

After obtaining new aggregated matrixes, a consistency validation procedure was once again performed. If matrix was consistent, then preferred ranks of alternatives were being calculated using formula [79]:

$$w\_{\vec{j}} = \frac{\sqrt[i]{\prod\_{j=1}^{i} p\_{ij}^P}}{\sum\_{j=1}^{i} \sqrt[i]{\prod\_{j=1}^{i} p\_{ij}^P}}$$

Here <sup>ω</sup>*j* —Weight of alternative *j*.

In order to check, whether the experts' opinions were consistent and valid, and they actually reflected the realistic picture, the index of expert mutual agreemen<sup>t</sup> (S\*) was calculated [80]:

$$\mathcal{S}^\* = \frac{\frac{1}{\exp\left(H\_\beta\right) - \frac{\exp\left(H\_{\text{armin}}\right)}{\exp\left(H\_{\text{YM}}\right)}}}{1 - \frac{\exp\left(H\_{\text{armin}}\right)}{\exp\left(H\_{\text{YM}}\right)}}$$

Here *H*α—Shannon alpha diversity; *<sup>H</sup>*β—Shannon beta diversity; *<sup>H</sup>*γ—Shannon gamma diversity. Goepel's index varies between 0% and 100% and shows the agreemen<sup>t</sup> level of the experts involved. Afterthenoticedthattwoofthedidnotmeetthe

 completing survey, we questionnaires survey predefined consistency ratio of 0.1. In order to solve this issue, we employed S-Method [81], following the steps:


Only after these steps can the results be considered robust and be analyzed further.

#### **5. Results and Discussion**

The calculated aggregated index of expert mutual agreemen<sup>t</sup> S\* equals to 0.64631, meaning that the level of expert compatibility is 65%. Such a result corresponds to the requirements of the data reliability for scientific articles; therefore, expert evaluation is acknowledged to be appropriate and the conclusions based on them are reliable. After additional procedures were taken to increase compatibility, all of the surveys were recognized as acceptable and eigenvectors of each business risk were calculated applying balanced, Koczkodaj and adaptive scales. The achieved results are presented in Table 2.



The achieved research results allow classifying business risks that affect gas trading companies into two groups: substantial risks that have a grea<sup>t</sup> impact on the activity of natural gas trading companies, or primary risks (i.e., operating volume risk, purchase price risk, risk of customers' default, risk of supplier default), for the managemen<sup>t</sup> of which gas trading companies have to pay grea<sup>t</sup> attention; and less substantial, or secondary risks (such as personnel risk, product competition risk, technological risk, alternative energy risk, reputation risk).

Referring to the achieved results, it becomes clear that volume risk is the most important for natural gas trading companies. Namely, in gas trading activity, extremely grea<sup>t</sup> attention should be given to an especially precise forecasting of the demand. It is a di fficult task due to the rapidly changing climate when the average winter temperature of two years in a row in Lithuania may di ffer by 2.5 degrees Celsius. This a ffects the natural gas demand by 13%, since the largest amount of natural gas, 77%, is consumed in winter. Even greater fluctuations (up to 21%) are observed when analyzing monthly consumption, which makes the prognostication of a precise operating volume even more challenging.

Second in importance is the purchase price risk. Such a high position of this risk is not surprising since gas is an especially homogeneous product, completely undistinguished in its features and sold having converted it to MWh of energy. As a result, there are no other attributes of this commodity that could portray its distinctiveness in respect to other products (such as appearance, physical features, brand, country of origin), and so it is chosen only depending on the price. Therefore, if the gas trading company purchases the product (natural gas) at a higher price than competitors in the market do, there is a grea<sup>t</sup> likelihood that it will lose consumers and work at a loss.

The importance of customers' default risk was likely determined by its direct role in a ffecting the operating volume risk, described in the theoretical section of this research paper. In fact, in pursuance of simplifying the analysis, eigenvectors of these two business risks could be summed. This would reduce the total number of business risks, as well as their interrelations, that a ffect natural gas trading companies.

The risk of supplier default stands in the fourth place for the gas trading companies operating in the liberalized market, whereas in non-liberalized markets it is the most important risk [70]. This is so because, given the liberalized market, in pursuance to conform to contract responsibilities, natural gas trading companies can rather promptly purchase the deficient quantity of natural gas in the spot market. In the closed natural gas market dominant by one supplier, which usually is also the owner of the natural gas supply and distribution system (i.e., if the requirements of the EU Third Energy Package are not implemented) and if the gas supplier fails in fulfilling the contract obligations, there is no possibility to purchase the lacking quantity of natural gas. This potentially determines the bankruptcy of the natural gas trading company and leaves the customers' a ffected. To make matters worse, this can lead to the consumers' business failure and cause a marked impairment of citizens' living conditions, given the risk manifested in winter.

Analyzing secondary risks a ffecting natural gas trading companies, we notice personnel risk being at the top. Even though it can cause plenty of negative outcomes to natural gas trading companies, this risk is not assessed to be very hazardous, because its manifestation to natural gas trading companies would not be direct. It cannot directly cause the risk of technology failure, since the balancing data has to be approved by the transmission system operator (in Lithuania's case, AmberGrid). The operating volume is prognosticated and approved by more than one person; therefore, this risk is assumed to be more theoretical, however, due to the damage that could be caused if it manifested, the risk is assessed to be the fifth in importance.

Product competition risk and alternative energy risk, in the context of Lithuania and other Baltic States, should be assessed jointly. Even though the product competition risk covers more factors than just the development of alternative energy (which caused its higher place on the list), it is only the development of alternative energy that can a ffect the competitiveness of natural gas as a commodity in the Baltic States.

Technological risk, when transmitting and distributing natural gas, is rather widely discussed in the scientific literature [82–84], thus it is perceived to be inexpedient to elaborate it in this research paper. It is noteworthy to mention that such a low importance of this risk means the market participants highly trust in the reliability of physical natural gas transportation infrastructure.

A low place of the reputation risk indicates that the company's prestige in Lithuania is not assumed to be an important part of the enterprise's intangible assets that could significantly a ffect the

company's results. Such findings contradict the supposed assumptions regarding the importance of this risk in the scientific literature [85] and identify a negative aspect evidencing that the country's market is not su fficiently matured yet.
