PriceVariation module¶
Summary¶
Notwithstanding weather variation, agricultural commodity price is a major source of farm risk. There are two main methods to include price variation in whole farm LP.
Expected price variation (e.g. Kingwell, 1994): Expected price variation represents price variation by applying a discrete distribution to cashflow items after management decisions have been made. This method of representing price variation assumes that there is no knowledge of the price state, prior to purchasing or selling a commodity. The only known information is the expected price (i.e. a farmer does not know if they are in a high or low price year until they purchase or sell). Therefore, price variation has no impact on farm management for a risk neutral farmer. However, for a risk averse farmer price variation can alter their management. For example, if the grain price is more variable than livestock prices, it may be optimal for a risk averse farmer to have a higher livestock focus because it will reduce the variation in farm profit between years.
Forecasted price variation (Apland and Hauer, 1993): Forecasted price variation is a more realistic method achieved by including discrete states based on forecast information, allowing decision-making to change based on the forecasted conditions. The forecasted states are adjusted using a discrete distribution to reflect the actual prices received at purchase or sale. This requires a stochastic programming approach that increases model size and complexity.
AFO currently uses method 1 because price variation has not been a major focus as yet. Nonetheless, a likely valuable future improvement for AFO would be to include forecasted price variation. AFO’s flexible structure would facilitate inclusion of such price variation.
Currently, price variation is approximated in AFO using a range of discrete price states for meat, wool and grain. The need to form discrete approximations of a continuous distributions is a necessary requirement for developing a LP model of farm management responses to price and weather-year states. By their nature, discrete stochastic programming models cannot consider all possible price states as described by continuous distributions. Rather continuous variables such as price need to be approximated by discrete states.
Price scalars have two main purposes:
To account for variations in the price received for a given year due to external market conditions (c1 axis).
To account for variation in prices due to season type.
Within year price cycles are accounted for in AFO for products such as sale sheep that can be sold at different times during the year. Including the within year price cycles ensures that optimisation of the nutrition of sale sheep represents that sale data has an effect on expected price. Representing the annual price cycle also ensures that strategic management such as time of lambing is also evaluated correctly given the impact of time of lambing on likely turn-off dates.
Generation of discrete price states¶
The price state scalars and their probabilities are calculated by fitting a multivariate normal distribution to historical prices, then summarises as discrete states by dividing the multi-dimensional probability density distribution into segments. A multivariate distribution is used so that correlations between commodities are accurately represented in the resulting price states. Grain and wool prices are better represented by log-normal distributions [Kin96]. Thus, before fitting the distribution, grain and wool data were subject to a log transformation. Additionally, the historical prices were CPI adjusted and detrended using a long-term moving average. The reason for detrending the price data was that the price states represented in AFO serve the purpose of capturing yearly price variation (i.e. variations around the expected price for that year) rather than capturing within year price cycles.
To reduce model size and simplify input calibration, all meat classes (lamb, shipper, mutton, etc) receive the same meat price scalar. The same thing happens for classes of wool and types of grain. This simplification should not compromise the accuracy of the results because subclasses of a given commodity tend to have a high correlation (e.g. between 2000 and 2021 the correlation between light lamb and mutton was 96%). A further simplification was excluding price variation for input costs because input costs tend to vary less [Kin96] and therefore the additional model size was not justified. The resulting assumptions are that all animal classes are 100% correlated, all wool microns are 100% correlated, all grains are 100% correlated and all input commodities have no variation. This assumption is not entirely accurate (e.g. canola and wheat prices are not 100% correlated) however, if in future analysis, price variation is of high importance this can easily be rectified by expanding the inputs.
The c1 axis is averaged for both the asset constraint and the working capital. This saves space without losing much/any information.