Predicting the financial return from a forest plantation investment
Date
2009-09-04T18:17:53Z
Authors
Reed, W.J.
Haight, R.G.
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Abstract
In order to predict the financial return from a forestry plantation one must predict both the price of timber and the volume growth of the plantation many years into the future. In this article plausible statistical models based on stochastic differential equations are fitted to historical time-series data on stumpage prices and to data on volume growth. In particular geometric Brownian motion is used to model stumpage price evolution. Extrapolations into the future are made using these models and various cutting rules. The simple forecasts of financial return are based on "certainly-equivalence" deterministic models. However because of the skewness of the price distribution, which arises as a consequence of the geometric Brownian motion specification, a distinction between a "mean certainty equivalence" and a "median certainty equivalence" arises. Feedback harvest rules based on stochastic dynamic programming and the heuristic "myopic-look-ahead" procedure are considered. However in order to include the statistical sampling error in parameter estimates along with the system error in price and volume evolution, simulation methods are required. It is demonstrated how the sampling error in parameter estimates results in a great deal of uncertainty concerning financial return. Also some consequences of the geometric Brownian motion specification for the price process are discussed. In particular it is demonstrated how this price model (which seems to fit the historical data very well) leads to an extremely skewed distribution of financial return, with the expected value often falling above the 90th percentile of the distribution. The median and quartiles of the distribution of the present value provide a better indication of the possible financial return, than do the mean and variance.
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Keywords
timber price series, stochastic growth, geometric Brownian motion, harvesting rules, system and sampling error, certainty equivalence