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

Summary and conclusions

The previous section exemplifies that the EVT can be applied to problems in agribusiness, what is basically not
surprising. It has to be qualified now if and when such an application appears necessary and should be
recommended. In order to do so costs and benefits of EVT have to be pondered. Undeniably, computational burden
of EVT increases compared to VCM or to HS. The reason for this is not the tail estimation itself, but the bootstrap
procedure, which turned out to be necessary for the determination of an optimal sample fraction. However, this
disadvantage is weakened, since a tail index estimation will be executed less frequently compared with short-term
financial applications, where a permanent updating of VaR forecasts is required when new price information drops
in. Regarding the information gain of a EVT based VaR calculation three points have to be emphasized:

1. Short-term VaR is underestimated in particular by the VCM when the return distributions are leptocurtic.

2. Using the alpha-root-rule instead of the common square-root-rule leads to a substantially smaller VaR for
longer forecast horizons.

3. The accuracy of the estimation increases compared to HS.

To summarize, the benefits of displaying extreme quantiles depend on the specific problem. Apparently, the
informational needs concerning risk differ largely e.g. between a hog producer, a broker trading with hog futures
and an insurance company insuring against animal diseases. In some cases the inclusion of additional sources of risk
seems more important than to push the confidence level of VaR from 95% to 99.9%. For example, the production
risks emanating from foot and mouth disease or BSE for a individual producer, are not echoed by aggregated market
prices. However, if a calculation of extreme quantiles (e.g. 99% or higher) appears desirable then EVT should be
used as a supplement. Additional cost of computation are overruled by a higher accuracy of the tail estimates as well
as by significant differences in the temporal aggregation of VaR whenever leptocurtic distributions are involved.

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