A non-stochastic portfolio model for optimizing the transformation of an even-aged forest stand to continuous cover forestry when information about return fluctuation is incomplete

Abstract

Key messageNon-stochastic portfolio optimization of forest stands provides a good alternative to stochastic mean-variance optimization when available statistical data is incomplete. The suggested approach has a theoretical background in the areas of robust optimization, continuous multicriteria decision-making, and fuzzy theory. Resulting robust portfolios only show slight economic losses compared to the efficient frontier of a stochastic optimization.ContextEconomic optimization addressing diversification in mixed uneven-aged forest stands is a useful tool for forest planners.AimsThe study aims to compare two approaches for optimizing rotation age cohort portfolios under risk. Rotation age cohorts emerge from age-based regeneration-harvesting operations simulated for two tree species: Picea abies and Fagus sylvatica.MethodsThe first optimization approach is a stochastic mean-variance approach. The second is a non-stochastic optimization approach, which has rarely been applied to optimize tree species composition and the distribution of harvested timber over many periods. It aims at relatively good solutions, even if the deviation from the initially assumed return is very high. The objective function for both approaches is sensitive to the selection of various harvesting periods for different parts of the stand. For the stochastic approach, the objective function maximizes the annuitized net present value (economic return) for specific levels of risk by allocating area proportions to harvesting periods and tree species. In the non-stochastic approach, the allocation of area proportions instead minimizes the maximum deviation from the greatest possible economic return among many uncertainty scenarios (non-stochastic approach).ResultsPortfolios from both approaches were diverse in rotation age cohorts. The non-stochastic portfolios were more diverse when compared with portfolios from the efficient frontier, which showed the same standard deviation. However, P. abies clearly dominated the non-stochastic portfolios, while stochastic portfolios also integrated beech to a greater extent, but only in very low risk portfolios. The economic losses of the non-stochastic portfolios compared to the efficient frontier of the mean-variance approach lay between 1 and 3% only for different levels of accepted risk.ConclusionThe non-stochastic portfolio optimization over a large uncertainty space is so far uncommon in forest science, yet provides a viable alternative to stochastic optimization, particularly when available data is scarce. However, further research should consider ecological effects, such as increased resistance against hazards of conifers in mixed stands.