Conservation agriculture practices are promoted to increase productivity, profitability, and sustainability across diverse cropping systems. Many studies have used these goals in decision support frameworks to identify the most effective treatment among those examined. While this approach is valuable, it lacks actionable guidance for farmers regarding maximizing return, while minimizing risk. It does not provide specific recommendations on how to allocate land across various cropping systems and tillage practices to achieve such objectives. This would require another long-term experiment exploring various combinations of treatments. To address this challenge, we propose the application of modern portfolio theory, specifically leveraging mean-variance and conditional value at risk optimization models. Using these models has enabled us to identify the optimal cropping system combinations with different tillage practices that maximized yield and net returns with minimal associated risk. The proposed approach allows for recommendations involving combinations of treatments that may not have been previously tested in a geography. In a 14-year long-term conservation agriculture study involving twelve combination of tillage and cropping systems, we showed how different combination of treatments differ in risk-return profile using mean-variance and conditional value-at-risk models that trace out a frontier of options—combinations of treatments that give highest returns at minimal risk. For example, we find that across risk neutral (most profitable) and most risk averse (lowest risk) farmers, the optimal treatments on the frontier encompass of maize-mustard-mungbean (MMuMb) under zero tillage and maize-wheat-mungbean (MWMb) under bed planting (which offer high returns and associated risk), maize-maize-Sesbania (MMS) under zero tillage (providing a balance of moderate returns and risk), and MMS under conventional tillage (yielding lower returns and risk). Additionally, risk-averse farmers stand to gain by diversifying their land allocation. For instance, they could allocate 54 % of their land to MMuMb under zero tillage and 46 % to MWMb under bed planting to target net returns of INR 1,32,000, with downside risk of INR 56,000, otherwise they can allocate 44 % and 56 % of their land to MMS under zero tillage and MWMb under bed planting, respectively, with a targeted net return of INR 1,22,000 and downside risk of INR 43,540. This highlights the nuanced trade-off between risk and return in maize based diversified cropping systems under different tillage practices. Leveraging mean-variance and conditional value at risk optimization models in the analysis of long-term experiments can yield novel treatment combinations that hold promise and can be recommended to farmers for implementation.

中文翻译：

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保护性农业下多样化种植系统的风险回报权衡——来自印度西北部 14 年长期田间试验的证据


推广保护性农业实践，以提高不同种植系统的生产力、盈利能力和可持续性。许多研究在决策支持框架中使用了这些目标，以确定在接受检查的受试者中最有效的治疗方法。虽然这种方法很有价值，但它缺乏为农民提供关于最大化回报和最小化风险的可行指导。它没有就如何在各种种植系统和耕作实践中分配土地以实现这些目标提供具体建议。这将需要另一项长期实验，探索各种治疗方法的组合。为了应对这一挑战，我们建议应用现代投资组合理论，特别是利用风险优化模型的均值-方差和条件值。使用这些模型使我们能够确定具有不同耕作方法的最佳种植系统组合，从而以最小的相关风险最大限度地提高产量和净回报。拟议的方法允许涉及以前可能未在某个地区测试过的治疗组合的建议。在一项涉及 12 种耕作和种植系统组合的 14 年长期保护性农业研究中，我们使用均值方差和条件风险值模型展示了不同的治疗组合在风险回报概况上有何不同，这些模型追踪了一系列选择——以最小风险提供最高回报的治疗组合。 例如，我们发现，在风险中性（最有利可图）和最厌恶风险（风险最低）的农民中，前沿的最佳处理包括免耕玉米-芥菜-绿豆 （MMuMb） 和苗床种植玉米-小麦-绿豆 （MWMb）（提供高回报和相关风险），免耕玉米-玉米-塞斯巴尼亚 （MMS）（提供中等回报和风险的平衡）， 以及传统耕作下的 MMS（收益和风险较低）。此外，规避风险的农民可以通过实现土地分配的多样化而受益。例如，他们可以将 54% 的土地分配给免耕 MMuMb，将 46% 的土地分配给苗床种植的 MWMb，以实现 1,32,000 印度卢比的目标净回报，下行风险为 56,000 印度卢比，否则他们可以将 44% 和 56% 的土地分配给零耕 MMS 和苗床种植下 MWMb，目标净回报率为 1,22,000 印度卢比，下行风险为 43,540 印度卢比。这凸显了在不同耕作方式下，以玉米为基础的多元化种植系统在风险和回报之间的微妙权衡。在长期实验分析中利用均值-方差和风险条件值优化模型可以产生有前途的新型处理组合，并可以推荐给农民实施。