# Efficiency of Risk Reduction on Slovenian Livestock Farms: Whole-Farm Planning Approach

J. ZGAJNAR and S. KAVCIC

*University of Ljubljana, Biotehnical Faculty, Dept. of Animal Science, Groblje 3, SI-1230 Domzale, Slovenia*

### Abstract

ZGAJNAR, J. and S. KAVCIC, 2010. Efficiency of risk reduction on Slovenian livestock farms: whole-farm planning approach.* Bulg. J. Agric. Sci.*, 16: 500-511

This paper deals with whole farm planning problem under stochastic conditions caused by production and price risk. Exposition to risk and efficiency of risk reduction was studied on five livestock farms in Slovenia. For this purpose linear and quadratic risk programming modeling paradigm has been applied. Linear program assumes that farmer maximizes expected gross margin subject to a set of constraints related to farm’s limited resources, while quadratic risk programming is based on E,V efficient rule, minimizing total variance. Risk performance of livestock case farms has been analyzed in E-V efficient set. Efficiency of diversification strategies for all farms has been estimated with risk gradient value.

*Key words*: risk modeling, linear programming, quadratic risk programming, diversification.

*Abbreviations*: CAP common agricultural policy; CE certainty equivalent; CV_{A,f} coefficient of variation per activity per farm; DM decision maker; E expected income; EGM_{A} vector of expected gross margins per activities; EGM_{A,f} vector of expected gross margins per activities per farm; EGM_{f} scalar of expected maximum gross margin per farm; E-V expected value variance; GM_{A,k} matrix of gross margins per activities at each state of nature; GMmax_{f} maximal gross margin per farm; GMmin_{f} minimal gross margin per farm; k states of nature; LP linear programming; maxEGM_{f} maximal expected gross margin at the farm level; MOTAD minimization of total absolute deviation; MP mathematical programming; p_{k} vector of probabilities’ per states of nature; QRP quadratic risk programming; ra absolute risk aversion coefficient; R_{f} vector of resource stocks and other constraints; RGV risk gradient value; RHS right hand side; SD (ˆ) standard deviation expressed in euro; SD(GM_{f}) scalar of standard deviations of total gross margins for a farm *f*; SD(GMmax_{f}) maximal standard deviation of gross margin per farm; SD(GMmin_{f}) minimal standard deviation of gross margin per farm; TCf matrix of technical coefficients for the analyzed farm; V total variance of income; VAR_{A,f} variance of gross margin per activity per farm; VARCOV(GM_{A,i,j})_{f} variance-covariance matrix of activities gross margins per farm; X_{f} activities decision vector; λ - (lambda) fixed coefficient for parameterisation.

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