# Indirect Estimation of Farm’s Risk Aversion: Mathematical Programming Approach

J. ZGAJNAR and S. KAVCIC

*University of Ljubljana, Biotehnical Faculty, Dept. of Animal Science, SI - 1230 Domzale, Slovenia*

### Abstract

ZGAJNAR, J. and S. KAVCIC, 2011. Indirect estimation of farm’s risk aversion: mathematical programming approach.* Bulg. J. Agric. Sci.*, 17: 218-231

In the paper we present an approach how farmer’s risk aversion could be estimated indirectly. This is particularly beneficial if one analyses hypothetical farms with absence of decision makers, as for example in the case of representative farms that are usually used for systematic studying. Applied approach is based on mathematical programming methods. The main idea is to use current farm practice as a baseline and to calculate missing data with partial optimization process. Non-interactive procedure based on expected value-variance framework and quadratic programming paradigm minimising variance has been applied to locate current farms’ plans in expected value - variance space and to estimate their risk aversion. To demonstrate applicability of the approach, three representative dairy farms were analysed. Obtained results indicate high relative risk aversion in all three cases. More intensive dairy farm in flat area is less risk averse as smaller, still intensive farm with similar production

conditions or farm with less intensive farming typical for hilly area. The study illustrates also discrepancy between

optimal solutions considering or neglecting farmers risk aversion.

*Key words*: risk aversion, quadratic programming, livestock farms, mathematical programming

*Abbreviations*: CAP - Common Agricultural Policy; CARA - Constant Absolute Risk Aversion; CE- Certainty Equivalent; DARA - Decreasing Absolute Risk Aversion; E - Expected value; E(U(X)) - expected utility of final wealth; EUMV - Expected Utility Mean Variance; FADN - Farm Accountancy Data Network; IARA - Increasing Absolute Risk Aversion; k - capitalization factor; LP - Linear Program; MAUT - Multi Attribute Utility Theory; MCDM - Multi Criteria Decision Making; r_{A} - absolute risk aversion; r_{R} - relative risk aversion; SD - Standard Deviation; V - Variance; W - Wealth; Y - short period income

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