Assessment of Market Risk in Hog Production
using Value-at-Risk and Extreme Value Theory
Martin Odening and Jan Hinrichs
1 Introduction
In the last quarter in 2000 German hog and cattle producers have been exposed to tremendous price fluctuations due
to the BSE crisis and the foot and mouth disease. Many farmers suffered severe liquidity problems and the EU was
forced to stabilize markets by massive intervention. These events in conjunction with the anticipation that price
volatility on agricultural markets will rise according to the intended liberalization of the CAP increased the demand
for indicators showing the risk exposition of farms. A concept discussed in this context is Value-at-Risk (VaR). VaR
has been established as a standard tool in financial institutions to depict the downside risk of a market portfolio. It
measures the maximum loss of the portfolio value that will occur over some period at some specific confidence level
due to risky market factors (Jorion 1997). Though VaR has been primarily designed for the needs in financial
institutions it also has been successfully applied in agriculture (Manfredo and Leuthold 1999). However, some well
known problems have to be overcome when utilizing VaR. First, the time horizon in agricultural applications will in
general be longer than in financial applications and hence the question of extrapolating, let’s say, a week-to-week
volatility forecast arises. The usual way to achieve this is to use the square-root-rule. Unfortunately this method
presumes iid returns and little is known about its properties if returns are not independent (for instance if they follow
a GARCH process or a mean reverting process). Secondly, common VaR models have difficulties in estimating the
left tail of the return distribution in particular if long time series of historical prices are not available. However, in
the case of the livestock crisis described above the prediction of extreme events is of particular interest. Diebold et
al. (1998) suggest the use of Extreme Value Theory (EVT) to improve the estimation of extreme quantiles.
The objective of this paper is to investigate the performance of different VaR models in the context of risk
assessment in hog production. Potential pitfalls of traditional VaR models are pinpointed and proposals to solve
them are analyzed. After a brief description these methods are used to calculate the VaR of the hog finishing margin
under German market conditions. In particular we apply EVT to our data and compare the results with historical
simulation and the variance-covariance method. Hill’s estimator is used to determine the tail index of the extreme
distribution of the gross margin in hog finishing and farrow production. It turns out that the results are sensitive with
respect to the choice of the sample fraction. To overcome this problem we adopt a bootstrap method proposed by
Danielsson et al. (1999).