### James L. Smith and Rex Thompson

James L. Smith and Rex Thompson, January 2004

We consider the impact of sequential investment and active management on the value of a portfolio of real options. The options are assumed to be interdependent, in that exercise of any one is assumed to produce, in addition to some intrinsic value based on an underlying asset, further information regarding the values of other options based on related assets. We couch the problem in terms of oil exploration, where a discrete number of related geological prospects are available for drilling, and management’s objective is to maximize the expected value of the combined exploration campaign. Management’s task is complex because the expected value of the investment sequence depends on the order in which options are exercised. A basic conclusions is that, although dependence increases the variance of potential outcomes, it also increases the expected value of the embedded portfolio of options and magnifies the value of optimal management. Stochastic dynamic programming techniques may be used to establish the optimal sequence. Given certain restrictions on the risk structure, however, we demonstrate that the optimal dynamic program can be implemented by policies that are relatively simple to execute. In other words, we provide sufficient conditions for the optimality of intuitive decision rules, like “biggest first,” “most likely first,” or “greatest intrinsic value first,” and we develop exact analytic expressions for the implied value of the portfolio. This permits the value of active management to be assessed directly. Finally, the sufficient conditions we identify are shown to be consistent with plausible exploration risk structures.