Asseldonk, M.A.P.M., van

Huirne, R.B.M.

Kobzar, O.

Wageningen Yield 

 1
Whole-farm planning under risk: Application of alternative risk 
programming techniques to support portfolio-decisions in Dutch 
agriculture. 
 
O.A. Kobzar1,2,* 
M.A.P.M. van Asseldonk1  
R.B.M. Huirne1,2 
1 Institute for Risk Management in Agriculture, Hollandseweg 1, 6706 KN, Wageningen University, The 
Netherlands 
2 Business Economics, Wageningen University, The Netherlands 
*Corresponding author. Contact information: 
Business Economics 
Hollandseweg 1  
6706 KN Wageningen 
tel: +31 317 48 34 88 
fax: +31 317 48 27 45 
e-mail: oxana.kobzar@wur.nl  
 
Introduction 
In order to balance risk and return of alternative crop production plans, portfolio-modelling 
approaches are often used. Portfolio analysis requires the inclusion of the normal range of 
risky cropping activities. Risks (i.e. joint stochastic distribution) comprise the probability 
distribution for each cropping activity and stochastic dependencies between cropping 
activities. A number of studies have shown that a farm-specific approach of risk management 
is very important. Due to the lack of data-, a lot of studies have been done on basis of 
aggregated data (Heifner and Coble, 1996; Kobzar et al, 2004; Lien, 2002; Rasmussen, 1997). 
However each of these authors stressed the importance of farm-level optimisations, since the 
difference between aggregated and farm-specific approaches can be considerable. Each 
farmer is forced to cope with his or her own specific risks. Surely only an individual farm 
study can only give a custom-made answer about their specific problems.  
 
Most decision problems involve multiple risks whereby, in practice, complete stochastic 
independence may be the exception rather than the rule (Hardaker et al., 2004, pp. 74-86). 
Getting the joint distribution of the cropping activities adequately specified is nearly always a 
difficult job in portfolio analysis. Capturing the joint distribution not adequately will produce 
results that are significantly in error and perhaps seriously misleading. Another problem of 
specifying the joint probability distribution is how it can be included in a farm-specific 
 2
portfolio analysis. Usually, the forms of continuous joint distributions used in risk analyses 
have often been limited to the few relatively tractable cases, such as the multivariate normal – 
the joint distribution of several underlying normally distributed variables. The joint 
distribution is therefore assumed to be appropriately described by means of the variance-
covariance matrix of the possible cropping activities. Quadratic risk programming (QRP), 
developed by Markowitz (1959) and the even earlier work of Freund (1956), is based on these 
multivariate normal assumptions. Subsequently, the expected utility of a risk averse decision 
maker subject to a set of resource and other constraints is maximised. However, correlation 
coefficients measure the overall strength of the association, but give no information about 
how that varies across the distribution. As an alternative, a non-parametric risk-programming 
method is free of distribution assumptions and includes the joint distribution by means of 
states of nature (i.e. specific combinations and probabilities of possible outcomes).  
 
In this study the impact of alternative ways to capture the joint stochastic distribution is tested 
within a portfolio context. For the analysis two different approaches to specify the joint 
distributions are used: non-parametric and parametric. The impact of specifying the joint 
distribution in alternative ways was quantified by expected gross margins and their standard 
deviations. To compare these approaches, as an additional measure, the risk gradient value is 
used as well.  
 
Materials and methods  
Data – materials 
Input data concerning yields and costs were obtained from the Farm Accounting Data 
Network (FADN) data set. The FADN data is a unique panel data set consisting crop 
information at farm level. For the analysis farms were selected from the 718 available arable 
farms according to the following selection criteria: 
• The farms are 100% specialised arable farms;  
• The total land area cultivated did not change considerably over the observed period; 
• The land is 100% owned property of the farmer; 
• The soil type is sea clay; 
• The farms grew a particular stable crop set every year during period observed. 
Applying these criteria to the data set, 218 farms were left for the analysis and ten farms were 
randomly selected. An overview of the selected farms is presented in Table 1. All the farms 
had different sizes and locations (Figure 1).  
INSERT TABLE 1, FIGURE 1 
 3
 
Gross margin components de-trending  
The costs and prices were de-trended by applying the Paasche equation (Mas-Colell et al, 
1995, p.37) with the consumer price index and the cost index used as deflators (CBS, 1993-
2002). Yields were de-trended by a linear or multiplicative time-series model. In the case 
where heteroskedasticity was present in the linear model, the multiplicative variation was 
applied (Verbeek, 2002, p. 80). In this approach, each model consists of three different 
functional forms: linear, second and third-degree polynomial (Kobzar, et al, 2004). This 
method allows for differences in the systematic changes during the period (Oskam, 1991) and 
provides the best data fit.  
 
Model optimisation 
This paper overviews the differences between non-parametric and parametric approaches. The 
non-parametric optimisation is based on a state programming model. In the non-parametric 
approach the states of nature are based on the de-trended gross margins of each cropping 
activity observed in the consecutive years. The (discrete) parametric optimisation is based on 
a state programming model as well. However, the 100 states were derived by means of 
stochastic simulation from a multivariate normal distribution (thus 100 iterations).  The 
multivariate normal distribution was parameterised with the mean values and variance-
covariance matrixes of the de-trended gross margins. The logical structure of the analysis is 
shown in Figure 2.  
INSERT FIGURE 2 
 
For each of the approaches two alternative gross margin parameters have been estimated: 
maximum (GMmaxn) and minimum (GMminn) gross margins. They both are formulated 
(GMTOTn) as follows: 
(1)    
⎭⎬
⎫
⎩⎨
⎧ = ∑∑
= =
Q
q
qns
S
s
qnsnTOT GMpE(GMoptimise
1 1
)  
where ( )qnsqnsqnsqnsqns CPYAGM −=  
where GMTOTn states for gross margin values on farm n; pqns is probability value that for crop 
q state s occurs on farm n; GMqns is a gross margin of crop q on farm n in state of nature s; 
Aqns  is the cultivated area for crop q on farm n for state s; Yqn, Pqn and Cqn is the yield, price 
and variable cost respectively for crop q at the farm n for state s. 
 
 4
GMmaxn is the maximum expected gross margin of farm and this value is obtained without 
any constraints with respect to risk aversion and reflects the optimal plan for risk-neutral 
decision-makers. GMminn is the expected gross margin when the standard deviation of total 
gross margin is minimised (Equation 2), under the condition that all land area is used for 
production. Thus this optimisation reflects the optimal cropping plan for decision-makers 
aversive to risk (i.e. minimising standard deviation of total gross margin).  
(2)    ⎪⎭
⎪⎬⎫⎪⎩
⎪⎨⎧ ⎟⎟⎠
⎞
⎜⎜⎝
⎛= ∑∑
==
S
s
qnsqns
Q
q
n GMASDSD(GMminimise
11
)  
Optimisation constraints  
Some additional normative assumptions based on literature (KWIN, 2001) were made in order 
to perform these calculations. Cereal crops (winter wheat and summer barley) were restricted 
to maximum one-third of the cultivated area and tuberous crops (sugar beet, onion seed, table 
potato, potato for processing, seed potato and carrot) were restricted to a maximum three-
fourth of the cultivated area. With regard to the area cultivated in tuberous, the rotation 
restriction for all kinds of potato could not be more than one-thirds of the total area; onions 
and carrots were restricted to a maximum of one-fifth of total area. Due to the quota 
limitation, the maximum amount of sugar beet was based on individual farm observations. 
The individual rotation rate was also applied for grass seed.  
 
Most field operations have to be performed during a certain period. To take into account the 
peaks in labour and machine use, the year is divided into periods of one month (Kobzar, 
2005). The amount of fixed labour is assumed to be 1.1 labour units (Wossink, 1993). A 
farm’s total area is one more limiting resource factor. As noted above, farm size is different 
for each farm studied (Table 1). 
 
Risk Gradient Value 
As an additional measure to compare and analyse the differences between in the impact of 
alternative modelling approaches the risk gradient value (RGV) is included (Kobzar et al, 
2005). The RGV is calculated per farm (equation 3) reflecting the gradient of the efficiency 
line. In this paper the risk gradient is defined as the difference between GMmax and GMmin 
then divided by the difference between the corresponding standard deviations of gross margin. 
It represents the farm-specific trade-off between expected gross margin and standard 
deviation. 
(3)    
)SD(GMmin)SD(GMmax
GMminGMmax
RGV
nn
nn
n −
−=  
 5
 
Analysis of results  
Gross margin components de-trending 
To demonstrate the results of current analysis, one farm has been chosen for further 
description in detail. The de-trended gross margin components of farm I are presented in 
Table 2. This farm has following production activities: winter wheat, sugar beet, seed potato 
and summer barley.  
INSERT TABLE 2 
 
Model optimisation 
Table 3 contains the detail results of different optimisation approaches for farm I. As 
presented in this table, maximum and minimum values of cultivated area size stay stable for 
all approaches. That concerns for all farms, only in few cases it was a slight difference in 
maximum and minimum land values between parametric and non-parametric approaches (this 
results are not presented). 
INSERT TABLE 3 
 
Maximum expected gross margins of farm I does not differ considerably in both of the 
approaches. The same concerns almost all of the farms (Table 4). Maximum expected gross 
margin values stay the same or almost the same. There is no considerable difference in 
minimum gross margins for all of the farms between different approaches. For instance, on 
farm I it is €80 000 for non-parametric approach and €79 000 for parametric one. Minimum 
expected gross margins differ considerably only for farm VI. Minimum gross margin for non-
parametric approach equals €197 000 and for parametric approach it equals €248 000. More 
differences in values between approaches are observed for standard deviations. Thus for farms 
III, VI and VIII the maximum standard deviation differed from €5 000 till €35 000. Minimum 
standard deviations differ on farms VI (non-parametric SD(GMmin)=99 and parametric 
SD(GMmin)=70) and VIII (non-parametric SD(GMmin)=208 and parametric 
SD(GMmin)=213).  
INSERT TABLE 4 
 
The additional RGV measures to compare the non-parametric and parametric approaches are 
approximately similar (Table 4). Only on farm VI the RGV differs considerably. For non-
parametric approach it equals 1.67 and for parametric it is 1.11.  
 
 6
Conclusions and discussion  
This paper compares different approaches (non-parametric and parametric) of whole-farm 
optimisation. One of the outcomes of the optimisation results is that independently what 
approach is chosen the gross margin values do not differ from each other that much. Only for 
one of the farms (farm VI) considerable difference as in gross margins as in RGV were 
observed. More differences between approaches were observed for standard deviations 
values. The results show that RGV is a good indicator of farm-specific risk response. Lower 
RGV indicates a farm with more effective gross margin change with respect to change in 
standard deviation of gross margin. Farms with less efficient diversification have higher RGV 
values. In this paper the RGV ranged from XXX to XXX. This shows that there are 
considerable differences between farms, which should be recognised in advising farms on 
portfolio selection. 
 
References 
CBS, Agricultural Economic Research Institute and Central Bureau of Statistics. The Division of Agricultural 
Areas (in Dutch). The Hague, 1991. 
CBS, Agricultural Economic Research Institute and Central Bureau of Statistics. Agricultural Figures, several 
volumes (in Dutch). The Hague, 1993-2002. 
Freund, R.J. “The Introduction of Risk into a Programming Model”. Econometrica 24 (1956): 253-63. 
Markowitz, H. M. Portfolio Selection. Efficient diversification of investments. 2nd ed. Malden: Blackwell 
Publishers Ltd., 1959. 
Mas-Colell A., M.D. Whinston, and J.R.Green. Microeconomic Theory. New York: Oxford University Press 
Inc., 1995. 
Hardaker, J.B., R.B.M. Huirne, J.R. Anderson, and G. Lien. Coping with Risk in Agriculture. 2nd ed. 
Oxfordshire: CABI Publishing, 2004. 
Kobzar O.A, van Asseldonk M.A.P.M., and R.B.M. Huirne. “Farm level yield, price and cost variations”. 86th 
EAAE Seminar Farm Income Stabilisation: what role should public policy play? Anacapri, Italy - 21-22 October 
2004. 
Kobzar O.A, van Asseldonk M.A.P.M., and R.B.M. Huirne. “Analysing the Efficiency of Farm Diversification”. 
PREBEM 8th PhD Conference, Business Economics, Management & Organisation Science, Amersfoort, the 
Netherlands, 26 January 2005. 
KWIN. Quantitative Information of Agriculture and Vollegrondsgroenteteelt (in Dutch). W.A. Dekkers. 
Wageningen: Practical Research Plant & Environment Ltd, 2001. 
Lien, G. “Non-parametric estimation of decision makers’ risk aversion”. Agricultural Economics 27 (2002): 75-
83.  
Oskam, A.J. “Weather indices of agricultural production in The Netherlands 1948-1989.1. General methodology 
and the arable sector”. Netherlands Journal of Agricultural Science 39 (1991): 149-64.  
Verbeek, M. Modern Econometrics. West Sussex: John Wiley&Sons Ltd, 2002. 
Wossink, G.A.A., T.J. de Koeijer, and J.A. Renkema. “Environmental policy assessment: a farm economic 
approach”. Agricultural System 39 (1993): 421-38. 
 7
TABLE 1: Short overview of the selected farms 
Farm 
number 
Number of 
observed states 
of nature 
Location and 
cultivated area Activities 
I  5 A, 40 ha Winter wheat, sugar beet, seed potato, summer barley 
II  5 A, 156 ha Winter wheat, potato industrial, sugar beet, table 
potato, seed potato 
III  8 E, 57 ha Winter wheat, sugar beet, table potato, onion seed, 
grass seed 
IV  5 E, 22 ha Winter wheat, sugar beet, table potato, summer 
barley, grass seed 
V  4 A, 101 Winter wheat, sugar beet, grass seed, seed potato, 
summer barley, onion seed 
VI  3 A, 100 ha Winter wheat, sugar beet, table potato, seed potato, 
summer barley, onion seed 
VII  5 A, 125 ha Winter wheat, sugar beet, seed potato, summer 
barley, onion seed 
VIII  6 A, 78 ha Winter wheat, sugar beet, carrot, seed potato, 
summer barley 
IX  5 C, 36 ha Winter wheat, sugar beet, onion seed, table potato, 
carrot 
X  9 C, 78 ha Winter wheat, sugar beet, table potato, summer 
barley 
 
TABLE 2: Example of input data for farm I 
Approach Non-parametric  Parametric 
State of nature   1 2 3 4 5 Mean SD
Probability 0.20 0.20 0.20 0.20 0.20     
yield 6626 9707 7359 7907 8626 8045 1184
price 0.26 0.16 0.18 0.16 0.15 0.18 0.05
cost 490 602 543 465 650 550 77
Winter 
wheat 
GM 1254 974 748 800 651 886 237
yield 69414 53600 52064 55243 51618 56388 7420
price 0.05 0.05 0.06 0.06 0.06 0.05 0.01
cost 265 321 314 301 443 329 67
Sugar 
beet 
GM 2990 2182 2875 2780 2571 2680 318
yield 25922 30404 33835 27865 33011 30207 3351
price 0.03 0.10 0.65 0.21 0.04 0.21 0.26
cost 2479 3672 2689 3061 3964 3173 633
Potato 
seed 
GM -1790 -627 19385 2922 -2722 3433 9170
yield 4737 6001 4513 6493 6808 5710 1035
price 0.25 0.16 0.16 0.14 0.16 0.18 0.04
cost 265 321 314 301 443 329 67
Summer 
barley 
GM 941 661 424 620 616 653 186
 
 
 8
TABLE 3: Default results from farm I studied 
Model Non-parametric Parametric 
Optimisation  max min max min
SD (€‘1000) 95 80 94 79
E(GM) (€‘1000) 124 62 124 62
Activity  Cultivated area (ha) 
Winter wheat 10.0 0.0 10.0 0.0
Sugar beet 16.7 20.0 16.7 20.0
Seed potato 13.3 6.7 13.3 6.7
Summer barley 0.0 13.3 0.0 13.3
RGV 0.25 0.24 
 
TABLE 4: Default results of different approaches from all farm studied  
  Non-parametric Parametric  
 Farm   max min max min 
I  E(GM)* 95 80 94 79 
  SD* 124 62 124 62 
  RGV 0.25 0.24 
II  E(GM) 708 205 709 205 
  SD 718 59 717 59 
  RGV 0.76 0.77 
III E(GM) 432 103 434 103 
  SD 437 11 442 11 
  RGV 0.77 0.77 
IV E(GM) 45 31 45 31 
  SD 36 15 36 15 
  RGV 0.66 0.67 
V  E(GM) 372 145 372 145 
  SD 465 26 465 27 
  RGV 0.52 0.52 
VI E(GM) 330 197 330 248 
  SD 179 99 144 70 
  RGV 1.67 1.11 
VII E(GM) 570 457 573 459 
  SD 643 434 644 436 
  RGV 0.54 0.55 
VIII E(GM) 385 358 385 358 
  SD 246 208 252 213 
  RGV 0.69 0.68 
IX E(GM) 304 108 304 108 
  SD 204 56 206 56 
  RGV 1.32 1.31 
X E(GM) 432 384 432 383 
  SD 419 358 419 355 
  RGV 0.79 0.77 
E(GM) and SD values are in €‘1000. 
 9
FIGURE 1: Agricultural regions in The Netherlands 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
FIGURE 2: Comparing of different approaches 
       
       
       
       
       
  NON-PARAMETRIC  PARAMETRIC 
       
Programming State programming  State programming 
       
Input De-trended observed data  Simulated input based on 
Mean and Variance-
Covariance Matrix of de-
trended observed data (100-
iterations) 
       
Output GMmax, GMmin  GMmax, GMmin 
  SD(GMmax), SD(GMmin)  SD(GMmax), SD(GMmin) 
  optimal plans  optimal plans 
  RGV  RGV 
       
 
 
 
Panel data: 
farm-level de-trended yields, 
prices and cost


Whole-farm planning under risk : application of alternative risk programming techniques to support portfolio-decisions in Dutch agriculture

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