Short-term shocks, reversion, and long-term decision-making

Many observers claim that discounted cash-flow methods lead to a neglect of long-term and strategic decision-making. Using modern asset pricing methods, we examine one possible reason for this problem. If the cash-flows being discounted have an increasing dependence on an uncertain variable that tends to revert to a long-term equilibrium path in the face of short-term shocks, and if this reversion is ignored, then the uncertainty in the cash-flows will be overestimated. If this uncertainty causes risk discounting, then the amount of risk discounting that is appropriate will also be overestimated, which will tend to result in a relative undervaluation of long-term alternatives. We examine the implications of such an error for the comparative analysis of decision alternatives, including some involving an initial timing option. We use, as examples, decisions about production projects where the output price is the reverting variable.Where applicable, we look at two measures of what is meant by long-term: the operating duration of the project and the length of an initial timing option. For the projects without options, the analysis is based on the relatively straightforward "risk discounting effect" already mentioned. Reversion tends to decrease long-term uncertainty, and, with it, long-term risk discounting, which increases the relative value of long-term alternatives. Options complicate matters. The long-term decrease in uncertainty due to reversion tends directly to decrease long-term option values. Moreover, in addition to the original risk discounting effect and this "variance effect," there can be direct "future reversion effects" if the options involve a timing component or payoffs generated by cash-flows over a period of time. The overall influence can be a complicated mixture of the three different types of effects.We use this classification scheme to analyze two sets of examples: investment timing options on an instantaneous production project (equivalent to at-the-money American options on the project output price), and "now-or-never" options, as well as investment timing options, on projects that differ in their operating lives. We find that a neglect of reversion leads to an undervaluation of at- or in-the-money options on projects with longer operating lives. This is primarily due to the risk discounting effect. Longer timing options on the same project tend to be relatively overvalued by a neglect of reversion if the operating life of the project is moderately long, and undervalued if the project is instantaneous and currently at the money. The first is primarily due to variance and future-reversion effects. The second is primarily due to risk-discounting and future-reversion effects.Because parts of the economy may be influenced by short-term shocks in the presence of long-term equilibrium, these results suggest a reexamination of those aspects of analyses in the "real options" literature that depend on the use of non-reverting models.Supported by the Natural Science and Engineering Research Council of Canada, Imperial Oil University Research Grants, Interprovincial Pipeline Co., Saskoil, Exxon Corp., and the Social Science and Humanities Research Council of Canada, and by the Central Research Fund, a Nova Faculty Fellowship, the Muir Research Fund and the Institute for Financial Research of the University of Alberta, and by the Finance, Investment and Contracts Program of the MIT Center for Energy and Environmental Policy Research

Project evaluation : a practical asset pricing method

This paper presents a practical approach to project evaluation using techniques of modern financial economics, with a sample application to oil development under a complex tax system. The method overcomes shortcomings of conventional DCF methods which are either imprecise about the relation between economic value and uncertainty, or are rigid and unrealistic in the required assumptions about how a project's risks (and therefore its value) are influenced by market conditions, the project physical structure, and tax and contract provisions. It is based on the formulation and estimation of an "information model" which represents the resolution over time of uncertainties underlying a project (oil prices in the examples shown). Oil prices are the underlying uncertainty in the examples shown. The project can then be valued using derivative asset valuation, which replicates the consequences of a complex asset by a traded portfolio of simpler assets (in our case, riskless bonds and future claims on oil). For ease of implementation, the method is designed to resemble current industry practice. The information model can be estimated using analysis and judgment similar to that applied in conventional evaluation. The formulation of decision alternatives, the selection of underlying uncertainties, and the design of a cash-flow model are the same as in standard DCF methods. Simulation and valuation results also can be represented in a familiar format. Restrictions must be placed on the "best" current asset pricing theory to achieve this convenient framework: the expected returns on the basic assets, which comprise the portfolios traded to replicate project cash flows, must be assumed to be known with certainty at the time of an evaluation.Supported by the MIT Center for Energy Policy Research, the Social Science and Humanities Research Council of Canada, the Natural Science and Engineering Research Council of Canada, the Imperial Oil University Research Grants Programme, the Central Research Fund, a Nova Faculty Fellowship, the Muir Research Fund and the Institute for Financial Research of the University of Alberta

A two-method solution to the investment timing option

Within the realm of derivative asset valuation, two types of methods are available for solving the investment timing option, each with a serious limitation for practical projects. Methods that use Monte Carlo simulation of risk-adjusted probability measures allow consideration of the complicated cash flow models typical of real projects, in the face of prespecified operating policies, but they do not provide an adequate way to determine what the optimal policy is. Formulation of the problem as an American option in the vein of Black-Scholes and Merton permits calculation of an optimal start policy, but only in situations with drastically simplified cash flow models. The solution to this dilemma is the development of an approach which applies the two methods in tandem. The rights to explore and develop an oil field are used as an example, and Monte Carlo simulation is used to calculate the value of these rights as a function of start time and contemporaneous oil price. This payoff function is then input to a Black-Scholes-Merton option calculation. The resulting optimal start policy is then reinserted to the Monte Carlo model for further analysis of project and individual cash-flow magnitudes and risks. Also, possible bias because of numerical-analysis errors are checked by direct search of start policies in the vicinity of the calculated optimum.Supported by the Social Science and Humanities Research Council of Canada, the Natural Science and Engineering Research Council of Canada, Imperial Oil and various research funds of the University of Alberta and the M.I.T. Center for Energy Policy Research

A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.Comment: 37 pages, 15 figures, 5 tables, submitted to Computer Methods in Applied Mechanics and Engineering, revision

Exploration in competitive nonrenewable resource markets : an extension of Pindyck's perfect foresight model

Pindyck's model of exploration for, and production of, a non-renewable resource (Pindyck 1978) is extended so that the production cost function may depend separately on concurrently available reserves and on the total amount of past production. A method for obtaining the optimal trajectory of parameterised specifications of the model is tested on elaborations of a corrected version of the parameterised specification used by Pindyck in his paper. The initial price for each simulation is tabulated.SSHRC Canada and the Sloan School of Management, MI

Rapid nano-gram scale screening method of micro-arrays to evaluate drug-polymer blends using high-throughput printing technology

A miniaturized, high-throughput assay was optimized to screen polymer-drug solid dispersions using a 2-D Ink-jet printer. By simply printing nanoliter amounts of polymer and drug solutions onto an inert surface, drug:polymer micro-dots of tunable composition were produced in an easily-addressable micro-array format. The amount of material printed for each dried spot ranged from 25 ng to 650 ng. These arrays were used to assess the stability of drug:polymer dispersions with respect to recrystallization, using polarized light microscopy. One array with a panel of 6 drugs formulated at different ratios with Poly (vinylpyrrolidone-vinyl acetate) copolymer (PVPVA) was developed to estimate a possible bulk (gram-scale) approximation threshold from the final printed nano amount of formulation. Another array was printed at a fixed final amount of material to establish a literature comparison of one drug formulated with different commercial polymers for validation. This new approach may offer significant efficiency in pharmaceutical formulation screening, with each experiment in the nano-micro-array format requiring from 3 up to 6 orders of magnitude lower amounts of sample than conventional screening methods