Certainty equivalent and uncertainty premium of time-to-build

Speaker: Haejun Jeon 
Affiliation:  Tokyo University of Science

Abstract

Time-to-build of an investment project induces a discrepancy between the timing of investment and that of revenue generation. Jeon (2024) showed that uncertainty in the time-to-build always accelerates investment and enhances pre-investment firm value, regardless of its distribution. This study examines the extent to which the uncertainty advances the timing of investment and improves firm value. Specifically, we show that there always exists a unique certainty equivalent of uncertain time-to-build and derive it in an analytic form. This enables us to derive the investment strategy with uncertain time-to-build in the form of the one that would have been adopted in the absence of such uncertainty. Even without full knowledge of the uncertainty, the firm can approximate the optimal investment strategy using only the mean and variance of time-to-build. We also clarify the positive impact of entropic risk measure of time-to-build on investment and derive the dual representation of the certainty equivalent of time-to-build based on relative entropy. Furthermore, we show that there always exists an uncertainty equivalent of fixed time-to-build. This implies that the firm can deduce the equivalent risk that its investment strategy, established without considering uncertainty in time-to-build, implicitly assumes. Lastly, we illustrate the practical application of our findings using some representative probability distributions and analyze the effects of the variance of time-to-build. In particular, we contrast the effects of uncertainty in demand with those of uncertainty in time-to-build, deriving the level of variance in time-to-build that offsets the negative impact of increased demand volatility on investment.  Joint work with Michi Nishihara (Osaka University).