Document Type : SPECIAL ISSUE


1 Department of Economic Cybernetics, The National University of Water and Environmental Engineering, Rivne, Ukraine

2 Department of Management, Institute of Economy and Management, National University of Water and Environmental Engineering


Grain production is one of the Ukrainian agro-industrial complex main branches. An indicator of the grain production efficiency is its profitability. It is characterized by significant annual fluctuations that induce risk. Redistribution of existing grain crops areas taking into consideration their profitability can bring to increase of production efficiency. The paper observes Markowitz’s optimal portfolio theory appliance to grain branch. The central aim of this work is the development and justification of a new technique of sown areas portfolio risk evaluating. In this study, the annual profitability of four cereal crops cultivated in the Rivne region: wheat, barley, corn, and oats, have been analyzed. It is shown that the profitability of the cereals is not normally distributed. Under these conditions, the portfolio variance loses part of its informativity and can not serve as a good risk measure. It has been determined that the profitability of crops with good precision follows Laplace distribution (double exponential distribution). The analytical expression for Value-at-Risk measures has been obtained using the Laplace distribution function. Numerical risk assessments performed. Using a modified Markowitz model and obtained risk estimates the efficient frontiers of cereal sown areas portfolios in the Rivne region were constructed. Obtained results allow indicating ways for optimization the region grain industry structure.


Balakrishnan, N., (2010). Methods and applications of statistics in business, finance, and management science. A John Wiley and Sons, Inc.

Bjornson, B.; Innes, R., (1992). Risk and return in agriculture: evidence from an explicit-factor arbitrage pricing model. J. Agric. Resour. Econ., 17(2): 1-21 (21 pages).

Bollerslev, T., (1990). Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev. Econ. Stat., 72(3): 498–505 (8 pages). 

Corder, G.W.; Foreman, D.I., (2014). Nonparametric statistics: a step-by-step approach, 2nd. Ed. John Wiley and Sons, Inc.

Downey, A.B.,  (2011). Think stats: probability and statistics for programmers. Green Tea Press.

Emmer, S.; Kratz, M.; Tasche, D., (2015). What is the best risk measure in practice? A comparison of standard measures. J. Risk, 18(2): 31-60 (30 pages).

Engle, R.F., (1995). ARCH: selected readings. Oxford University Press.

Härdle, W.; Simar, L., (2015). Applied multivariate statistical analysis. 4th. Ed. Springer.

Holton, G. A., (2014). Value at risk. Theory and practice. 2nd. Ed. Glyn A. Holton.

Hrytsiuk, P. M.; Babych, T. Yu., (2017). Optimization of crop industry structure in Ukrane taking into account risks, in: Sustainable development goals of Ukraine: monograph. Sciemcee Publishing, London.

Jian, W.;  Rehman, A., (2016). Risk management in agriculture: theories and methods. Science Publishing Group.

Kay, R. D.; Edwards, W. M., (1999). Farm management, 4th. Ed. WCB McGraw-Hill.

Kisiala, J.,  (2015). Conditional Value-at-Risk: theory and applications. Ph.D. dissertation, University of Edinburgh, Scotland.

Khokhlov, V.Yu., (2012). VaR and the problem of "large tails" of the profitability distribution. Risk Manage. Credit Inst., 2: 35-49 (15 pages).

Ma, W., (2011). Research on portfolio optimization of agricultural intellectual property promotion engineering projects. Syst. Eng. Procedia, 2: 324-330 (7 pages).

Markowitz, H. M., (1952). Portfolio Selection. J. Fin., 7 (1): 77–91 (15 pages).

Markowitz, H., (1991). Foundations of portfolio theory. J. Fin., 46(2): 469–477 (8 pages).

Mechler, R., (2013). Modeling aggregate economic risk: an introduction. In: Integrated catastrophe risk modeling: supporting policy processes. Springer, Dordrecht.

Mitter, H.; Heumesser, Ch.; Schmid, E., (2014). Crop production portfolio optimization in managing climate-induced risks in Austria. Erschienen im Jahrbuch der Österreichischen Gesellschaft für Agrarökonomie, 23: 121–130 (10 pages).  

Pepelyaev, V. A.; Golodnikova, N. A.,  (2014). Mathematical methods for crop losses risk evaluation and account for sown areas planning. Cybern. Sys. Anal., 50(1): 60-67 (8 pages).

Sharpe, W.  F.; Alexander G.  J.; Bailey, J. V., (1998). Investments, 6th. Ed. Prentice Hall.

State Statistic Service of Ukraine, (2010)

Tóth, M.; Holúbek, I.; Serenčéš, R., (2016). Applying Markowitz portfolio theory to measure the systematic risk in agriculture. In Conference: International Scientific Days 2016. The Agri-Food Value Chain: Challenges for Natural Resources Management and Society. Nitra, the Slovak Republic 19-20 May. Slovak University of Agriculture in Nitra.

Zabolotskyy, T., (2016). Modeling in the management of the portfolio of financial assets: monograph. Publishing LNU, Lviv. 

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