## 3 Sample, Dataset and Methods
The distance between the objects is calculated using the Euclidean norm:  
\[d_{i,j}=\left\{\sum_{k=1}^{m}\left(x_{ik}-x_{jk}\right)^{2}\right\}^{1/2}\ \ \ for\ i\
eq j \tag{1}\]  
where:  
\(x_{ik}\)--value of the k variable in the \(i\)-th object;  
\(x_{jk}\)--value of the k variable in the \(j\)-th object;  
\(k\)--number of characteristics examined;  
\(m\)--number of diagnostic variables. The clustering is based on a criterion that summarises the scope of disclosed information on the bank's direct environmental and climate impacts reported in the banks' annual reports for 2020. All disclosed categories of the bank's direct environmental and climate impact as reported in the audited institutions' annual reports for 2020 are selected for the analysis. They are assigned to three criteria (Table 3). Information sharing is a dummy variable that equals 1 if the factor occurs directly in the respective bank's reporting and 0 otherwise. A bank's direct environmental and climate impacts, divided into 3 categories, were used to classify and separate homogenous subsets of objects in the analysed sample of banks. Based on the analysis of data derived from audited annual reports of the sampled banks as of 31 December 2020, the authors performed a qualitative evaluation of particular variables. \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{2}{c}{**Absolute Quantities (w)**} \\ \hline w1 & Electricity, heat and fuel consumption \\ w2 & Water consumption \\ w3 & Quantity of waste or materials \\ w4 & CO\({}_{2}\) emission \\ \hline \hline \multicolumn{2}{c}{Intensity (i)} \\ \hline i1 & Electricity consumption per employee \\ i2 & Water consumption per employee \\ i3 & Waste or materials consumption per employee \\ i4 & CO\({}_{2}\) emission per employee \\ i5 & Emission of CO\({}_{2}\) or electricity consumption per 1 client or per assets of PLN 1 million \\ \hline \hline \multicolumn{2}{c}{Initiatives to reduce negative environmental impacts (in)} \\ \hline in1 & Reduction of CO\({}_{2}\) emission \\ in2 & Reduction of water consumption \\ in3 & Recycling \\ in4 & Reduction of electricity, heat and fuel consumption \\ in5 & Reduction of paper consumption and digitisation \\ in6 & Reduction of plastics consumption \\ in7 & Limitation of business traveling \\ in8 & Pro-ecological education of employees \\ in9 & Production or purchase of electricity from renewable energy sources \\ in10 &conducting business in energy-efficient real estate \\ in11 &Replacement of gasoline vehicles for electric fleet \\ in12 &Energy-saving lighting \\ in13 &Responsible purchasing \\ in14 &Optimisation of office space \\ in15 &Facilities for employees using public transport or bicycles \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Bank’s direct environmental and climate impacts considered in the study. Two methods are used for the hierarchical concentration analysis of quantitative weights for the attributes:  
A system of \(w_{1}\) representing equal weighting for all variables:  
\[w_{k}=\frac{1}{m}\,\ \text{where}:\ k\text{--indicator's number}\ (k=1,\ 2,\ \ldots,\ \text{m});\]  
A system of \(w_{2}\) representing particular weights which are determined according to the expert method, where the highest weights are assigned to diagnostic features (in) \(-0.50\), and the other characteristics, (\(w\)) and (\(i\)). are assigned weights of 0.25 and 0.20, respectively. This approach is assumed according to the following formulae:  
\[IBRK=(0.25w+0.25i+0.50 in)\times 100 \tag{2}\]  
\[w=\sum_{i=1}^{4}0.25\ w_{i} \tag{3}\]  
\[i=\sum_{i=1}^{5}0.20\ i_{i} \tag{4}\]  
\[in=0.5 in_{1}+\sum_{i=2}^{15}0.0357\ in_{i} \tag{5}\]  
The proposed index includes all categories of the bank's direct environmental and climate impacts as reported in the audited institutions' annual reports for 2020 (the latest available audited figures). They are grouped into three criteria, giving priority to initiatives announced by the banks aimed at reducing the given bank's negative impact on the environment.