Investment decisions in situation of risk

This text links two research fields. The first one is cost-bene fit analysis (CBA) of investment projects. CBA has received a lot of attention in the economics literature, from both the conceptual and practical standpoints. Many scient ific books and articles, as well as practical guidelines, have been devoted to this subject. Similarly, almost all countries have issued guidelines on how to implement cost–benefit anal ysis. However, while these texts pay great attention to how to estimate yearly benefits, to take into account consumers’ surplus or externalities, they do not insist much on how thes e yearly benefits can be used to derive prioritisation rules. The basic criterium is the N t Present Value; but little is said on how to use NPV to choose among several alternatives or to de cide when to implement a project. Another field of research is the inclusion of risk in economic calculus. This very vivid field has put a lot of light on taking into account the systemic risk, according to which the surpluses generated by the project are correlated with t he economic growth. Important insights have been given to the way of reckoning the average e xp ctation of NPV of a project, and one of the basic results is that discounting sho uld be made according to the so-called extended Ramsey rule, the extensions of it lead to many debates and progress. But this field of research has almost not addressed the abovementioned practical issue of the rules of decision for a project. The communication aims at filling this gap, and trying to asse s decision rules about when, and whether, to implement a project in presence of syst ematic risk. Using methods derived of real options theory, we find that, in the case of Brownian stochastic processes, the decision rule can be expressed as a threshold value of the First Year Advantage/Cost ratio, and that this threshold value is depending on each of the parameters appearing in the relations defining those Brownian processes. This threshold can be expressed in a closed form including the means, standard d eviations and correlations of the stochastic variables. Simulations with sensible curre nt values of these parameters show that the most important ones are the three standard values of the processes, and especially the parameter of the construction cost of the project. Some e xtensions are explored. Other are suggested for further research. JEL : C61, D61, D81, D92, G12, H54. Cermics, Ecole des Ponts ParisTech Paris Scool of Economics, Ecole des ponts ParisTech 1 This text aims at providing a stone in the field of investment d ecision rules under risk 1. Its specific input is to build a bridge between two streams up t o now without much contact: CBA and its traditional criteria which pay little attention to risk, especially systematic risk, and modern theory of discount rate which focuses on systemic ris k in its recent developments but has up to now no large input in CBA practice. CBA mainly aims at estimating monetary values of the effects of an investment. In its major developments, and even more in its implementation directiv s, the bulk of the effort is directed towards how to reckon the benefits but there has been little at ention to the indicators able to hierarchize the projects, and even less on how to take into co nsideration situations of risk and uncertainty, though, everybody agrees, are of paramount im portance. On the other side, risk is having an increasing consideratio n in modern theories of discounting. But it is striking that the main results deal on how to com pare effects taking place at various instants of time, and how to estimate correctly a Net Present Value (NPV) in presence of risk, but not to set rules for decision making. This text should be a first step in the direction of putting tog ether these up to now rather separate fields. A first section briefly recalls the condition in which CBA is im plemented and stresses on the poor role of hierarchization rules in general and risk in the se rules. The second section reminds the main basic lines of discounting in presence of uncertain ty. The third one shows how it is possible to fill this gap and presents in a simple case a clos ed formula giving the decision rule for the implementation of an investment. The fourth one presents simulations drawn from the previous formula, using sensible parameters in the rang e of what is encountered in current transport infrastructure projects, and shows that some up t o now not noticed play an important role. The fifth one concludes by presenting possible further research directions. CBA practice misregards uncertainty CBA has received a lot of attention in the economics literature, from both the conceptual and practical standpo ints. Many scientific books and articles, as well as practical guidelines, have been devoted t o this subject. Some books deal exclusively with this topic 2, and all textbooks devoted to transport economics 3 the sector that will be taken as an example in this paper have a chapter on it. Similarly, almost all countries, at least in Europe, have issued guidelines on how to implement c ost-benefit analysis (CBA). However, while these texts pay great attention to how to estimat e yearly benefits, to take into account consumers’ surplus or externalities, they do not insist muc h on how these yearly benefits can be used to derive prioritisation rules. On the theoretical gro unds, the most evoked criteria are: • the net present value (NPV):