ASSESSMENT OF MARKET RISK IN HOG PRODUCTION USING VALUE-AT-RISK AND EXTREME VALUE THEORY



Application to hog production

4.1 Model and data

Following Manfredo and Leuthold (1999), who investigate the market risks in US cattle feeding, we now use the
VaR approach to quantify the market risk in hog production under German market conditions. Our target is the
determination of a 12-week-VaR for three types of producers: firstly, a specialized farrow producer, secondly, a
farmer, who is specialized on hog finishing and purchases feeder farrows, and thirdly a farmer, who feeds his self-
produced farrows. We assume that prices of farrows and hogs are not fixed by forward contracts; inputs and
products are rather bought and sold at current spot market prices. The gross margin (cash flow) at time
t associated
with these production activities is defined as

CFt = a Pt -Y biZt

(26)


t t it

i=1

Formally the gross margin can be considered as a portfolio consisting of a long-position (the product price P) and
several short-positions (the factor prices
Zi). Thus (5) can be applied directly. The portfolio weights a and bi now
have to be interpreted as technical coefficients (slaughtering weight, fodder consumption etc.). Empirical
investigations of Odening and Musshoff (2002) indicate that the market risk in hog production is mainly caused by
the prices of farrows and hogs. Other items, e.g. fodder costs, have an impact on the level of the gross margins, but
they do not contribute to the fluctuations of the cash flow and therefore we decided to ignore them. Due to this the
VaR calculation simplifies considerably in the present case. In what follows we display the VaRs for the farrow
prices (the perspective of the specialized farrow producer), for the hog prices (the perspective of the joint production
of farrows and hogs) and for the residual of revenues from hog sales and expenses for feeder farrows (the
perspective of the specialized hog finishing farm). The weights of feeder farrows and fattened hogs are assumed to
be 20 kg and 80 kg, respectively.

Note, that in a strict sense we do not display a Value-at-Risk, but rather a Cash-Flow-at-Risk (CFaR) (Dowd 1998,
p. 239 f.)3. Despite the formal analogy of both concepts one should have in mind the differences when it comes to an
economic interpretation of the figures: VaR quantifies the loss of value of an asset, whereas CFaR addresses a flow
of money. The knowledge of a CFaR is presumably valuable in the context of a risk-oriented medium-term financial
planning. However, conclusions about the financial endangerment of the farm should be drawn carefully, since the
initial cash flow level as well as the duration of the cash flow drop should be taken into account. Experience shows
that specialized livestock farms are able to endure losses, if such a period does not persist too long and appropriate
profits have been earned before.

3 Nevertheless we continue to speak of VaR (in a broader sense) below.

10



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