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

Abstract

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.