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Timber harvest scheduling with price uncertainty using Markowitz portfolio optimization

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  • Laurence Reeves
  • Robert Haight

Abstract

Harvest scheduling models need to account for uncertain revenue predictions when minimizing risk of financial loss is an important management objective. In this paper, we present methods for estimating the means and covariances of stumpage prices and incorporating them in harvest scheduling models. We approached the estimation problem by fitting time-series models to loblolly pine sawtimber and pulpwood stumpage prices in Georgia, USA, and deriving formulas for means and covariances of price predictions. Statistical evidence supported integrated autoregressive models, which caused covariances of price predictions to increase with time. The means and covariances of price predictions were combined with timber yield and land value predictions to give exact formulas for the revenue means and covariances of timber management activities. Sawtimber regimes dominated pulpwood regimes by providing higher mean revenues across a wide range of revenue variances. Harvest scheduling results for a hypothetical forest of pine plantations showed that the forest plan that maximized mean income without concern for risk (expressed as the standard deviation of income) involved sawtimber production with a 35-year rotation age. Risk was reduced 30% with little effect on mean income by using shorter-rotation sawtimber regimes. Risk was reduced 80% by using a mix of short-rotation sawtimber and pulpwood regimes because pulpwood price was only weakly correlated with sawtimber price. The latter risk-reduction 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 sensitive to assumptions about the range of future prices that were inherent in different prediction models. This sensitivity emphasizes the importance of carefully determining the decision maker’s beliefs about stumpage price behavior. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Laurence Reeves & Robert Haight, 2000. "Timber harvest scheduling with price uncertainty using Markowitz portfolio optimization," Annals of Operations Research, Springer, vol. 95(1), pages 229-250, January.
  • Handle: RePEc:spr:annopr:v:95:y:2000:i:1:p:229-250:10.1023/a:1018974712925
    DOI: 10.1023/A:1018974712925
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    Cited by:

    1. Kanieski da Silva, Bruno & Tanger, Shaun & Marufuzzaman, Mohammad & Cubbage, Frederick, 2022. "Perfect assumptions in an imperfect world: Managing timberland in an oligopoly market," Forest Policy and Economics, Elsevier, vol. 137(C).
    2. Busby, Gwenlyn M. & Binkley, Clark S. & Chudy, Rafal P., 2020. "Constructing optimal global timberland investment portfolios," Forest Policy and Economics, Elsevier, vol. 111(C).
    3. Miguel A. Lejeune & Janne Kettunen, 2017. "Managing Reliability and Stability Risks in Forest Harvesting," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 620-638, October.
    4. Bernardo K. Pagnoncelli & Adriana Piazza, 2017. "The optimal harvesting problem under price uncertainty: the risk averse case," Annals of Operations Research, Springer, vol. 258(2), pages 479-502, November.
    5. Ran Wei & Alan Murray, 2015. "Spatial uncertainty in harvest scheduling," Annals of Operations Research, Springer, vol. 232(1), pages 275-289, September.
    6. Adriana Piazza & Bernardo Pagnoncelli, 2014. "The optimal harvesting problem under price uncertainty," Annals of Operations Research, Springer, vol. 217(1), pages 425-445, June.
    7. Veli-Pekka Heikkinen, 2003. "Timber Harvesting as a Part of the Portfolio Management: A Multiperiod Stochastic Optimisation Approach," Management Science, INFORMS, vol. 49(1), pages 131-142, January.
    8. Rakotoarison, Hanitra & Loisel, Patrice, 2016. "The Faustmann model under storm risk and price uncertainty: A case study of European beech in Northwestern France," MPRA Paper 85114, University Library of Munich, Germany.
    9. Couture, Stéphane & Cros, Marie-Josée & Sabbadin, Régis, 2016. "Risk aversion and optimal management of an uneven-aged forest under risk of windthrow: A Markov decision process approach," Journal of Forest Economics, Elsevier, vol. 25(C), pages 94-114.
    10. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    11. Restrepo, Héctor I. & Orrego, Sergio A., 2015. "A comprehensive analysis of teak plantation investment in Colombia," Forest Policy and Economics, Elsevier, vol. 57(C), pages 31-37.
    12. V.-P. Heikkinen & & Timo Kuosmanen, 2002. "Stochastic Dominance Portfolio Analysis of Forestry Assets," Finance 0210002, University Library of Munich, Germany.
    13. Newman, D.H., 2002. "Forestry's golden rule and the development of the optimal forest rotation literature," Journal of Forest Economics, Elsevier, vol. 8(1), pages 5-27.
    14. Buongiorno, Joseph & Zhou, Mo, 2011. "Further generalization of Faustmann's formula for stochastic interest rates," Journal of Forest Economics, Elsevier, vol. 17(3), pages 248-257, August.
    15. Guo, Christopher & Costello, Christopher, 2013. "The value of adaption: Climate change and timberland management," Journal of Environmental Economics and Management, Elsevier, vol. 65(3), pages 452-468.
    16. Müller, Fabian & Hanewinkel, Marc, 2018. "Challenging the assumptions of a standard model: How historical triggers in terms of technical innovations, labor costs and timber price change the land expectation value," Forest Policy and Economics, Elsevier, vol. 95(C), pages 46-56.

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