Timber harvest scheduling with price uncertainty using Markowitz portfoliooptimization

Harvest scheduling models need to account for uncertain revenue predictions when minimizing risk of financial loss is an important management objectiv e. In this paper, we present methods for estimating the means and covarianc es of stumpage prices and incorporating them in harvest scheduling models. We approached the estimation problem by fitting time-series models to loblo lly pine sawtimber and pulpwood stumpage prices in Georgia, USA, and derivi ng formulas for means and covariances of price predictions. Statistical evi dence supported integrated autoregressive models, which caused covariances of price predictions to increase with time. The means and covariances of pr ice predictions were combined with timber yield and land value predictions to give exact formulas for the revenue means and covariances of timber mana gement activities. Sawtimber regimes dominated pulpwood regimes by providin g higher mean revenues across a wide range of revenue variances. Harvest sc heduling results for a hypothetical forest of pine plantations showed that the forest plan that maximized mean income without concern for risk (expres sed as the standard deviation of income) involved sawtimber production with a 35-year rotation age. Risk was reduced 30% with little effect on mean in come by using shorter-rotation sawtimber regimes. Risk was reduced 80% by u sing a mix of short-rotation sawtimber and pulpwood regimes because pulpwoo d price was only weakly correlated with sawtimber price. The latter risk-re duction came at the expense of mean income, which was reduced by as much as 50%. The risks and compositions of optimal forest plans were extremely sen sitive to assumptions about the range of future prices that were inherent i n different prediction models. This sensitivity emphasizes the importance o f carefully determining the decision maker's beliefs about stumpage price b ehavior.