The effect of mean reversion on investment under uncertainty

Abstract

Mean-Reverting processes are appropriate for most “real option” investment models, yet Geometric Brownian Motion (GBM) processes are generally used for tractability. Hassett and Metcalf (J. Econom. Dyn. Control 19 (1995) 1471–1488) argue that using a GBM process is justified because mean-reversion has two opposing effects—it brings the investment trigger closer, and also reduces the conditional volatility (thereby lowering the likelihood of reaching the trigger)—and the overall effect on investment should be negligible for most reasonable parameter values. This paper extends the Hassett and Metcalf model by incorporating a third factor, the effect of mean-reversion on systematic risk. The main result is that mean reversion, in general, does have a significant impact on investment. Moreover, this effect could be either positive or negative, depending on various factors such as project duration, cost of investing, interest rate, etc. Thus it is generally inappropriate to use the GBM process to approximate a mean-reverting process.