A Simple Way of Developing a Probability Distribution of Present Value
Authors: Davidson L.B. , Cooper D.O. 
Published: December 2007

Uncertainty in present value can be computed relatively easily and quickly. To do so, all that is needed is an algebraic model of the investment and a modest helping of statistics. The key to the approach is a focus on the parameters of the probability distributions involved. parameters of the probability distributions involved. Introduction

A discomforting fact about tomorrow is that it seldom turns out as expected. Sometimes our hopes are exceeded, but all too often they are not realized. So it is when we bid on an exploration prospect, set a platform, begin a waterflood, or build a gas processing plant. Many investments in the oil business involve a relatively high risk that the investment will not achieve "most-likely" results. On the other hand, many such investments also have an element of "romance" in the possibilities for better results or even a bonanza. possibilities for better results or even a bonanza. In many cases, the final decision on whether to proceed with a petroleum investment is based on trade-offs proceed with a petroleum investment is based on trade-offs of the risk of loss vs the romance of potential large gains. To aid this comparison of risk with reward, a number of techniques have been developed over the past 20 years. The product of these techniques is past 20 years. The product of these techniques is usually a distribution of the probabilities associated with possible values of some investment measure. This possible values of some investment measure. This provides information such as "the chances are 80 percent provides information such as "the chances are 80 percent this prospect will lose money - that is, it will not achieve a 0 percent rate of return," or "there is a 15-percent probability that this exploration play could exceed a present value of $200 million."

Monte Carlo simulation is perhaps the most comprehensive of these techniques. In theory, one can use it to consider risk as thoroughly as desired. However, Monte Carlo simulation, like tomorrow, has not turned out as well as expected. Its drawbacks are (1) it can be expensive to use; (2) the time and effort required to get an answer can be excessive; and (3) it can be too "black-boxish." Moreover, given normal corporate behavior, promotion of Monte Carlo simulation can lead to business practices that ultimately work counter to the intended purpose of fostering better risk analysis. This is not to say that Monte Carlo simulation is useless. It is a valuable tool for risk analysis when applied under appropriate circumstances and applied wisely.

An approach termed the "parameter method" has been developed for quick results when Monte Carlo simulation is too slow and cumbersome or requires more information than is available. The parameter method provides approximate results with a minimum of effort. Also, all steps of the calculation are "visible," avoiding the black-box stigma that sometimes makes Monte Carlo simulation discomforting, particularly to decision makers for whom the results are particularly to decision makers for whom the results are developed.

The parameter method is so named because it deals with the parameters of the probability distributions involved, rather than the distributions in their entirety. Usually, only two parameters, the mean and variance, are used. These parameters are estimated for each uncertain quantity affecting the investment measure of interest. With these parameter values, the mean and variance of the investment measure itself may be computed.

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