Copula-based agricultural conditional value-at-risk modelling for geographical diversifications in wheat farming portfolio management

Abstract

An agricultural producer's crop yield and the subsequent farming revenues are affected by many complex factors, including price fluctuations, government policy and climate (e.g., rainfall and temperature) extremes. Geographical diversification is identified as a potential farmer adaptation and decision support tool that could assist producers to reduce unfavourable financial impacts due to the variabilities in crop price and yield, associated with climate variations. There has been limited research performed on the effectiveness of this strategy. This paper proposes a new statistical approach to investigate whether the geographical spread of wheat farm portfolios across three climate broad-acre (i.e., rain-fed) zones could potentially reduce financial risks for producers in the Australian agro-ecological zones. A suite of popular and statistically robust tools applied in the financial sector based on the well-established statistical theories, comprised of the Conditional Value-at-Risk (CVaR) and the joint copula models were employed to evaluate the effectiveness geographical diversification. CVaR is utilised to benchmark the losses (i.e., the downside risk), while the copula function is employed to model the joint distribution among marginal returns (i.e., profit in each zone). The mean-CVaR optimisations indicate that geographical diversification could be a feasible agricultural risk management approach for wheat farm portfolio managers in achieving their optimised expected returns while controlling the risks (i.e., target levels of risk). Further, in this study, the copula-based mean-CVaR model is seen to better simulate extreme losses compared to the conventional multivariate-normal models, which underestimate the minimum risk levels at a given target of expected return. Among the suite of tested copula-based models, the vine copula in this study is found to be a superior in capturing the tail dependencies compared to the other multivariate copula models investigated. The present study provides innovative solutions to agricultural risk management with advanced statistical models using Australia as a case study region, also with broader implications to other regions where farming revenues may be optimized through copula-statistical models.