：Land management strategies often prioritize agricultural supply services at the expense of other ecosystem services. To achieve a high and steady supply of multiple ecosystem services, it is essential to optimize land management practices in areas suitable for agriculture. However, many studies on land management tend to focus on their benefits to ecosystem service delivery without adequately considering the potential risks to other services that might be involved. Here we use modern portfolio theory to quantitatively measure benefits and risks from land management strategies to enhance ecosystem services. We create seven land management scenarios that balance different kinds of ecosystem services in different ways in the agricultural production area of Maoming, Guangdong Province, China. The method yielded optimal portfolios of land management patterns that enhanced ecosystem services while reducing risk as much as possible. This includes a scenario delivering a 22% increase in agricultural production service, while simultaneously increasing the provision of nature-related ecosystem services by 2%. However, no optimization scenario was perfect, and there was always a trade-off between gaining certain ecosystem service benefits and creating a risk of losing others. Our portfolio theory approach reveals that it is essential to consider both the benefits and risks of land management strategies.

Resource allocation for land acquisition is a common multiobjective problem that involves complex trade-offs. The National Wildlife Refuge System (NWRS) of the U.S. Fish and Wildlife Service currently uses the Targeted Resource Acquisition Comparison Tool (TRACT) to allocate funds from the Migratory Bird Conservation Fund (MBCF; established through the Migratory Bird Hunting and Conservation Act of 1934) for land acquisition based on cost-benefit analysis, regional priority rankings of candidate land parcels available for acquisition, and the overall biological contribution to duck population objectives. However, current policy encourages decision makers to consider societal and economic benefits of lands acquired, in addition to their biological benefits to waterfowl. These decisions about portfolio elements (i.e., individual land parcels) require an analysis of the difficult trade-offs among multiple objectives. In the last decade the application of multicriteria decision analysis (MCDA) methods has been instrumental in aiding decision makers with complex multiobjective decisions. In this study, we present an alternative approach to developing land-acquisition portfolios using MCDA and modern portfolio theory (MPT). We describe the development of a portfolio decision analysis tool using constrained optimization for land-acquisition decisions by the NWRS. We outline the decision framework, describe development of the prototype tool in Microsoft Excel, and test the results of the tool using land parcels submitted as candidates for MBCF funding in 2019. Our results indicate that the constrained optimization outperformed the traditional TRACT method and ad hoc portfolios developed using current NWRS criteria.

Investments in forestry are long-term and thus subject to numerous sources of risk. In addition to the volatility from markets, forestry investments are directly exposed to future impacts from climate change. We examined how diversification of forest management regimes can mitigate the expected risks associated with forestry activities in New Zealand based on an application of Modern Portfolio Theory. Uncertainties in the responses of Pinus radiata (D. Don) productivity to climate change, from 2050 to 2090, were simulated with 3-PG, a process-based forest growth model, based on future climate scenarios and Representative Concentration Pathways (RCPs). Future timber market scenarios were based on RCP-specific projections from the Global Timber Model and historical log grade prices. Outputs from 3-PG and the market scenarios were combined to compute annualized forestry returns for four P. radiata regimes for 2050-2090. This information was then used to construct optimal forestry portfolios that minimize investment risk for a given target return under different RCPs, forest productivity and market scenarios. While current P. radiata regimes in New Zealand are largely homogenous, our results suggest that regime diversification can mitigate future risks imposed by climate change and market uncertainty. Nevertheless, optimal portfolio compositions varied substantially across our range of scenarios and portfolio objectives. The application of this framework can help forest managers to better account for future risks in their management decisions.

This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

Climate change and urban growth impact habitats, species, and ecosystem services. To buffer against global change, an established adaptation strategy is designing protected areas to increase representation and complementarity of biodiversity features. Uncertainty regarding the scale and magnitude of landscape change complicates reserve planning and exposes decision makers to the risk of failing to meet conservation goals. Conservation planning tends to treat risk as an absolute measure, ignoring the context of the management problem and risk preferences of stakeholders. Application of risk management theory to conservation emphasizes the diversification of a portfolio of assets, with the goal of reducing the impact of system volatility on investment return. We use principles of Modern Portfolio Theory (MPT), which quantifies risk as the variance and correlation among assets, to formalize diversification as an explicit strategy for managing risk in climate-driven reserve design. We extend MPT to specify a framework that evaluates multiple conservation objectives, allows decision makers to balance management benefits and risk when preferences are contested or unknown, and includes additional decision options such as parcel divestment when evaluating candidate reserve designs. We apply an efficient search algorithm that optimizes portfolio design for large conservation problems and a game theoretic approach to evaluate portfolio trade-offs that satisfy decision makers with divergent benefit and risk tolerances, or when a single decision maker cannot resolve their own preferences. Evaluating several risk profiles for a case study in South Carolina, our results suggest that a reserve design may be somewhat robust to differences in risk attitude but that budgets will likely be important determinants of conservation planning strategies, particularly when divestment is considered a viable alternative. We identify a possible fiscal threshold where adequate resources allow protecting a sufficiently diverse portfolio of habitats such that the risk of failing to achieve conservation objectives is considerably lower. For a range of sea-level rise projections, conversion of habitat to open water (14-180%) and wetland loss (1-7%) are unable to be compensated under the current protected network. In contrast, optimal reserve design outcomes are predicted to ameliorate expected losses relative to current and future habitat protected under the existing conservation estate.

Modern Portfolio Theory is a well-established method in economic research for considering the risks and returns in asset allocations and the potential benefits of diversification for risk averse agents. Thus, it is a useful tool for guiding sustainability discourse under uncertain future states. Existing discussions around the method\'s use in environmental research have evolved during over the 75 years of its application, leading to a continued renewal of perspectives on utilising it. We classify the environmental questions where portfolio theory has been applied, and critically discuss the methodological approaches taken; providing a stepping stone for future use of the method. This article provides a framework for its application in environmental research using the following questions: 1) what is the type of research or management question and objective(s) of the decision-maker(s); 2) what are the definitions of the assets to be included in the portfolio; 3) what are the ways that returns are valued, discounted, distributed and weighted; 4) what is the most appropriate way for risks to be accounted for and managed, including the selection of the appropriate model and taking into account risk preferences; and 5) what are the definitions of constraints in the programming problem.

Groundwater management in China has been facing challenges from both climate change and urbanization and is considered as a national priority nowadays. However, unprecedented uncertainty exists in future scenarios making it difficult to formulate management planning paradigms. In this paper, we apply modern portfolio theory (MPT) to formulate an optimal stage investment of groundwater contamination remediation in China. This approach generates optimal weights of investment to each stage of the groundwater management and helps maximize expected return while minimizing overall risk in the future. We find that the efficient frontier of investment displays an upward-sloping shape in risk-return space. The expected value of groundwater vulnerability index increases from 0.6118 to 0.6230 following with the risk of uncertainty increased from 0.0118 to 0.0297. If management investment is constrained not to exceed certain total cost until 2050 year, the efficient frontier could help decision makers make the most appropriate choice on the trade-off between risk and return.