Determining the Generalized Discount Rate for Risky Projects
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Determining the Generalized Discount Rate for Risky Projects Lanlan Luo1 · Shou Chen1 · Ziran Zou1 Accepted: 9 July 2020 © The Author(s) 2020
Abstract It is widely recognized that the evaluation of risky projects critically depends on how the riskiness of future benefits is treated. Standard discounting theories are based on the assumption that risks that are uncorrelated with aggregate risk are diversified, so that projects’ idiosyncratic risk is not priced. However, this may not be true for long-term risky projects, such as those with persistent idiosyncratic shocks. In this study, we investigate the impact of both aggregate risk and nondiversifiable idiosyncratic risk on the discount rate for risky projects. We extend the generalized discount rate to the case of persistent shocks. A particular advantage of the generalized discount rate is that it can be applied in the setting of incomplete markets. We show that nondiversifiable idiosyncratic risk reduces the discount rate, and increases the present value of projects’ future uncertain benefits. We further apply our findings to the evaluation of emissions reduction projects. Keywords Generalized discount rate · Term structure · Idiosyncratic risk · Cost–benefit analysis · Emissions reduction projects JEL Classification H43 · D61 · G12
1 Introduction The choice of an appropriate discount rate is a critical and contentious issue in environmental and resource economics, as it determines whether a project passes the cost-benefit test. This is especially true for projects with long time horizons and uncertain benefits (Arrow et al. 2013, 2014). The discount rate for risky projects is critically dependent upon the riskiness of future benefits. Classical discounting models implicitly assume that a project’s idiosyncratic risk can be diversified, and therefore, this risk is not priced (Gollier 2014, 2016b; Dietz et al. 2018). However, public projects are not arbitrarily divisible (Traeger 2013), and idiosyncratic risk should be incorporated into the discount rate of climate change investments (Weitzman 2013). In this study, we investigate the impact of * Shou Chen [email protected] * Ziran Zou [email protected] 1
Business School of Hunan University, Changsha 410082, Hunan, China
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both aggregate risk and nondiversifiable idiosyncratic risk on the discount rate for risky projects. In our model, we assume that risky projects’ benefits are affected by both uncertainties of consumption growth and project productivity. Traeger (2013) initially defines a generalized discount rate (GDR) that is determined by the joint distribution of an uncertain consumption growth rate and project productivity rate. The GDR, as a devaluation rate, measures the present value consumption loss due to a future shift to productive consumption. Motivated by Traeger (2013), we use the GDR framework to evaluate risky projects. We relax the assumption of perfect serial correlation in Traeger (2013)1 and assume that both consumption growth and project p
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