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

The time series of hog prices and farrow prices, which form the basis for our computations, consist of weekly
quotations for East Germany spanning the period from January 1994 until October 2001⁴. Prices are measured in
euro per kg live weight and slaughtering weight for farrows and hogs, respectively and refer to an average
commercial quality. The original data series are presented in figure A1 in the appendix. Note, that in what follows
not the prices themselves, but price changes are considered.⁵

4.2 Empirical results

In line with the discussion in section 2.2 the first step in VaR calculation is to clarify, what kind of distributions
underlie the market factors, i.e. hog prices, farrow prices and the feeding margin. This task breaks down into two
questions: Firstly, should a conditional or an unconditional model be used and secondly, are the respective
distributions fat tailed or thin tailed? To answer the first question a Lagrange Multiplier test to test the presence of
conditional heteroscedasticity is employed (Greene 2000, p. 808). This test rejects the null hypothesis of the
homoscedasticity for the weekly hog prices changes and for the weekly changes of the hog finishing margin.
Thereupon a GARCH(1,1) model for all three time series is estimated⁶.

The estimated parameter values are summarized in table 1.

Table 1: Parameters of the GARCH (1,1)-Models

* level of significance 95% ** level of significance 99%; t-values in parentheses

All estimated parameters are significant. The standardized residuals ɛ_t / σ_t indicate no autocorrelations on a 1%
level of significance. This applies also to the squared standardized residuals with exception of the farrow price
series. Thus the inclusion of further lags into the GARCH model does not appear necessary. Inserting the parameters

⁴ The data have been made available to us by the German Price Reporting Agency (Zentrale Markt- und Preisberichtstelle,
Berlin).

⁵ In financial applications it is common to analyze log returns instead of absolute changes. Their advantage is to be independent
of the price level. However, problems occur if values become negative. While this is impossible for prices it may happen with
the hog finishing margin.

⁶ We refrain from estimating a Bi-GARCH-model for the farrow prices and pig prices to estimate the volatiliy and the VaR of
the hog finishing margin. Instead, a univariate GARCH model for the margin is estimated. This corresponds to the procedure,
that is used later for the EVT application. It takes into account that EVT at its present stage is only applicable to univariate
distributions.

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