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

An agricultural producer's crop yield and 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 variabilities in crop price and yield, associated with climate variations. There has been limited research performed on the effectiveness of this strategy. The paper proposed 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 Australian agro-ecological zones. A suite of popular and statistically robust tools applied in finance based on well-established statistical theories, comprised of the Conditional Value-at-Risk (CVaR) and the joint copula model were employed to evaluate the effectiveness geographical diversification. CVaR is utilised to benchmark the loss (i.e., downside risk), while the copula function is employed to model 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., targeting 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