Optimization of Decision Tree and Simulation Portfolios: A Comparison

Abstract

Abstract This paper compares the results of carrying out portfolio analysis and optimization of a collection of exploration projects that have been modelled using both decision tree and stochastic simulation approaches. The collection of exploration projects comprises the opportunity set for the portfolio. In the decision tree approach, selecting a few scenarios from the full distribution and assigning probabilities to those scenarios approximates the range of possible project outcomes. In contrast to the decision tree method, stochastic simulation proceeds by assigning probability distributions to key input variables. In a single iteration of the simulation each of these variables is randomly sampled, with allowances for dependencies, in order to calculate cash flow and economic parameters such as net present value. This process is repeated many times for each exploration project to produce a distribution of economic outcomes. Earlier studies have shown the difficulty of adequately characterizing projects with large uncertainty using the decision tree approach. In this paper we take the comparison between decision tree and simulation methodologies to the next stage by looking at the effect on portfolio selection of the differing evaluation methodologies. The portfolio analysis is carried out using the optimization methodology pioneered by Markowitz to estimate the combination of projects, which produces the maximum NPV for a given level of risk. Comparison of the project selections made for the decision tree and stochastic simulation portfolios shows significant differences between the project selections required to produce an efficient portfolio for the two different evaluation methodologies. This result implies that, even if a decision tree model could be constructed which adequately characterized the uncertainty in a project, the optimization of a collection of projects modelled using decision trees may not yield an efficient portfolio if the full range of uncertainty were to be considered.