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

The last step consists of extrapolating the 1-week-VaRs derived from figure 4 to the target horizon of 12 weeks. In
the case of HS and VCM this is done with the square-root-rule, i.e. via multiplication with the factor 3.464. In
contrast the quantiles of the extreme value distribution are projected with the alpha-root-rule, i.e. using the
respective tail indices a. Table 2 contains the results for different confidence levels. To allow a better comparison
the values of the extreme value distributions are also depicted for a 95% confidence level although they already lie
to the right of the order statistics X_k+1 and thus should be taken from HS according to the proposal of Danielsson &
De Vries (2000).

Table 2:     1- and 12-week-VaRs for the three time series and for different confidence levels (95%, 99%,

99,9%)

Compared to the EVT estimator the VCM shows an underestimation of VaR for a short term forecast. The
underestimation, which increases with the confidence level, is a result of the assumed normality of the VCM and the
actual leptocurtosis of the distributions. The 1-week-VaR of the VCM for the farrows (hogs and margin) amounts to
0.197 Euro (0.153 and 10.571) on the 99.9% level. The respective figure of the EVT is 0,27 Euro (0.230 and
11.653). The difference should be related to the average price of 1.938 Euro (1.399 and 73.192).

HS and EVT differ only slightly on the 99% level, i.e. the distribution functions of the EVT and the HS intersect in
that region (see figure 4). The VaR of the farrows derived from HS is with 0.182 Euro even higher than that the
EVT with 0.176 Euro. On the 99.9% level quantiles can not be determined with HS, because losses of this size did
not occur during the observation period.

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