Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
38
The application of correlation models for the analysis of market
risk factors in KGHM capital group
Łukasz Bielak & Paweł Miśta
KGHM, Lubin, Poland
Anna Michalak
Faculty of Geoengineering, Mining and Geology, Wrocław University of Science and Technology,
Wrocław, Poland
Agnieszka Wyłomańska
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology,
Wrocław, Poland
ABSTRACT: Mining companies to properly manage their operations and be ready to make
business decisions are required to forecast potential scenarios for main market risk factors.
Regardless of the typical uncertainty related to asset price projections, the main challenge is to
properly quantify dependencies/relations among main risk factors and its stability over time.
From the KGHM perspective, Polish copper and silver mining company, main market risks
can be divided into four baskets: base metals (copper, nickel), precious metals (gold, silver),
exchange rates (EURUSD, Dollar Index, USDPLN) and interest rates (LIBOR). Detailed
studies of the risk factors dependency structure and finding proper correlation models may
enable building more adequate forecasts, especially for stress test scenarios. In the literature
one can find different approaches in the considered issue. In this paper we concentrate on the
relations between mentioned factors and using mathematical/statistical methods we propose
a models that takes under consideration the dependences between them.
1 INTRODUCTION
Risk measurement is an integral and very important part of market risk management process.
Proper determination of market risk exposure and exposure change dynamics allows for
the selection and application of appropriate tools, by means of which this risk can be properly shaped and managed. KGHM as a mining company is exposed on significant market
risk driven by mainly metals prices and exchange rates. For planning and sensitivity analysis
purposes there are prepared several potential price deck scenarios which are based on certain given correlations between main risk factors. Confirmation of dependence between risk
factors or improvement of used methodology to reflect dynamic characteristic of such relations may help in improving of the usability of the price deck scenarios that are prepared.
In the literature there are known many measures that can help to describe the dependence
between variables and indicate the strength of the relationship between them. One of the
most classical one is the Pearson correlation coefficient which indicates the linear relationship between variables. The classical measure was introduced in 1895 and it is the most often
used in the problem of the data dependence description because of its simple form. However,
this measure indicates only the linear dependence between data and might be misleading in
case of the nonlinear relation [1]. Thus one can find different alternative measures used in
this context. Among all measures of association between data the Kendall’s rank correlation
seems to be the most popular. It can be used in the nonlinear relationship between variables,
it does not depend on their scale and is robust of outliers. Especially the last feature of the
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
38
The application of correlation models for the analysis of market
risk factors in KGHM capital group
Łukasz Bielak & Paweł Miśta
KGHM, Lubin, Poland
Anna Michalak
Faculty of Geoengineering, Mining and Geology, Wrocław University of Science and Technology,
Wrocław, Poland
Agnieszka Wyłomańska
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology,
Wrocław, Poland
ABSTRACT: Mining companies to properly manage their operations and be ready to make
business decisions are required to forecast potential scenarios for main market risk factors.
Regardless of the typical uncertainty related to asset price projections, the main challenge is to
properly quantify dependencies/relations among main risk factors and its stability over time.
From the KGHM perspective, Polish copper and silver mining company, main market risks
can be divided into four baskets: base metals (copper, nickel), precious metals (gold, silver),
exchange rates (EURUSD, Dollar Index, USDPLN) and interest rates (LIBOR). Detailed
studies of the risk factors dependency structure and finding proper correlation models may
enable building more adequate forecasts, especially for stress test scenarios. In the literature
one can find different approaches in the considered issue. In this paper we concentrate on the
relations between mentioned factors and using mathematical/statistical methods we propose
a models that takes under consideration the dependences between them.
1 INTRODUCTION
Risk measurement is an integral and very important part of market risk management process.
Proper determination of market risk exposure and exposure change dynamics allows for
the selection and application of appropriate tools, by means of which this risk can be properly shaped and managed. KGHM as a mining company is exposed on significant market
risk driven by mainly metals prices and exchange rates. For planning and sensitivity analysis
purposes there are prepared several potential price deck scenarios which are based on certain given correlations between main risk factors. Confirmation of dependence between risk
factors or improvement of used methodology to reflect dynamic characteristic of such relations may help in improving of the usability of the price deck scenarios that are prepared.
In the literature there are known many measures that can help to describe the dependence
between variables and indicate the strength of the relationship between them. One of the
most classical one is the Pearson correlation coefficient which indicates the linear relationship between variables. The classical measure was introduced in 1895 and it is the most often
used in the problem of the data dependence description because of its simple form. However,
this measure indicates only the linear dependence between data and might be misleading in
case of the nonlinear relation [1]. Thus one can find different alternative measures used in
this context. Among all measures of association between data the Kendall’s rank correlation
seems to be the most popular. It can be used in the nonlinear relationship between variables,
it does not depend on their scale and is robust of outliers. Especially the last feature of the