Risk-adjusted Social Discount Rates.

• Author: Cherbonnier, Frederic

1. INTRODUCTION

The necessity to decarbonize our economies confronts the energy sector to an immense transitional challenge. Huge investment efforts will have to be made over a relatively short period of time. Deep uncertainties affect the outcomes of these investments, from the evolution of energy demand, the ability to capture CO2 in the atmosphere, the capacity to store electricity, the timing of the phasing out of coal and natural gas, the carbon price in the next decades, to the role of biofuels and the architecture of electricity production and of the electricity transmission grid. Because of the long duration of most investment projects in the sector, the discounting rule that is used to value them plays a key role in the decision process, in the allocation of capital in the sector, and eventually in the speed and efficiency at which the energy transition will materialize. Modern asset pricing theory reminds us that it is desirable to adjust project-specific discount rates to the riskiness of the project. According to the Consumption-based Capital Asset Pricing Model (CCAPM), this is measured by its "consumption beta" which is, under proper assumptions recalled in section 3 of this document, obtained from the covariance of the project's return with aggregate consumption growth.

Although the private sector has long been using risk-adjusted discount rates to value investment projects, this practice is much less prevalent in the public sector. This is probably due to difficulties faced by evaluators to measure the social beta of the public investments under scrutiny. Even now, most recovery plans from the COVID-19 crisis contain vast sources of public funding to green our economies, without a proper risk-adjusted assessment.

In this context, our paper makes two main contributions. First, it refines the methodology for estimating project-specific betas, by showing how to take into account the economic characteristics of the supply and demand. Second, it illustrates the importance of the risk-adjustment of discount rates for decision-making by considering specific types of investment (capacity investment, cross-border link) where the betas vary considerably from one project to another. We use a partial equilibrium approach by focusing on each specific project and on its relation to aggregate consumption. We first provide an explicit formula for the beta directly derived from the characteristics of the supply and demand for the flow of goods or services that are generated by the investment. In particular, we clarify the intuitive link that exists between the risk-adjustment coefficient beta and the income-elasticity of the demand for the goods and services generated by the investment under scrutiny. Inferior (superior) goods are associated to assets with a negative (positive) beta. This characterization of betas to the intrinsic economic characteristics of the investment leaves the evaluators with the easier and more classical task of estimating parameters such as the price and income elasticities.

This result is general and is not related to the energy sector specifically. However, this research project was triggered by a social demand originating from various stakeholders active in the French electricity sector. This is due to the fact that public evaluators in France have recently been obliged to adjust discount rates to their project's beta, without any clear guideline. The illustrations presented in this paper come from our interactions with these stakeholders. We first estimated the beta of the electricity sector in France. We obtain a fairly small order of magnitude (

The elasticity of supply also affects the beta of the underlying asset. It implies that the CCAPM beta is also affected by the capacity utilization ratio of the asset, which typically vary in a predictable way through the lifetime of the investment. This suggests that risk premia, and their associated betas, have a non-flat term structure. (1) To examine this question, we consider a more specific class of investments in transportation infrastructures (such as a railway infrastructure or an electricity network). We show that their social betas vary greatly, exhibiting a decreasing term structure starting from a surprisingly large value ([beta]> 10) at short maturities (when capacity is under-utilized) and possibly negative value (when the infrastructure is used to export). As an illustration, we use data provided by the French operator of electricity transmission infrastructure to estimate the beta of an investment in a France-Spain electric cross-border link, which provides, to our knowledge, the first real-case based example of a negative beta. These estimations are based on two polar scenarios designed by the European Network of Transmission Systems Operators for Electricity (ENTSO-E), a relatively conservative one and a second scenario more ambitious with respect to the development of renewable energies.

Those results show how the adjustment of the social beta to risk can radically change the allocation of capital in the public sector. We help decision-makers to identify the investments that provide some form of insurance for our economies (as is the case for projects with negative beta). We know since Aschauer (1989) that investments in "core infrastructure" (i.e. transportation and public utilities) can have a strong and positive impact on private output. (2) Institutions in charge of those infrastructures must constantly anticipate the growth in demand. They must allocate investments accordingly between maintenance, renewal and extension of their networks. The decreasing term structure highlighted in our work can play a crucial role in determining the optimal timing of an increase in the size of such infrastructures. The last example considered here is all the more important as it concerns countries belonging to an imperfect monetary union with significant asymmetric shocks that traditional adjustment mechanisms via labor mobility are not enough to mitigate. We know since Frankel and Rose (1998) that the optimal currency area criteria are partly endogeneous. Our work shows that estimating project-specific betas is a valuable means of prioritizing investments that can play an attenuating role in the event of an adverse asymmetric shock.

This paper is part of the attempts to reach academic consensus on these topics and to convince public decision-makers to adopt more efficient discounting rules. As shown by Drupp et al. (2018), there is an emerging consensus among researchers on the risk-free discount rate and, in particular, on the fact that declining discounting rates should be used for risk-free projects. (3) Further work is needed to estimate the risk premia associated with long term projects and to convince public authorities to use risk-adjusted discount rates. Most governments use a much simplified system in which a single discount rate is used independent of the investments' risk profle. This is the case for the UK (Treasury, 2018) for which a constant premium of 1% may be added to the discount rate in order to take account of unpredictable risks both 'catastrophic' and 'systemic'. (4) The United States have also adopted such an approach by selecting a single "risk-adjusted" discount rate of 7%, which is assumed to be the average cost of capital in that country. (5) In the same way as the WACC fallacy observed by Krueger et al. (2015) for the private sector, (6) this is likely to severely distort public investment, leading to under-investment in safe projects and over-investment in riskier ones. (7)

The paper proceeds as follows. Section 2 reviews the literature and section 3 presents a detailed reformulation of the CCAPM discounting system. In section 4, we provide an explicit formula for social betas for projects in which the consumers' willingness to pay and the variable production cost are Cobb-Douglas in aggregate income and quantity. Section 5, 6 and 7 deals with two specific categories of public investment--core infrastructure or cross-border trade infrastructure. Section 8 concludes.

(2.) RELATED LITERATURE

Regarding the choice of the social discount rate, the theory has often been misleading. For example, the celebrated Arrow-Lind theorem (Arrow and Lind, 1970) prevailed over decades among public institutions on both sides of the Atlantic to support the use of a single discount rate to evaluate all public investment projects. The idea was that the mutualization capability of the public sector is so large that the risk of individual projects are washed out by diversification, so that it should evaluate them assuming risk-neutrality. But many economists and most evaluation experts overlooked the fact that Arrow and Lind implicitly assumed that the net benefit of the public projects are statistically independent from each other, so that consumption per capita is certain (Baumstark and Gollier, 2014). In reality, most investment projects, public or private, have benefits that are statistically related to aggregate consumption. This implies that diversification does not fully eliminate risk, and evaluators should be concerned with the impact of public actions on the collective risk eventually borne by the risk-averse citizens.

The right reaction to the fallacious interpretation of the Arrow-Lind theorem was provided by the development of the Consumption-based Capital Asset Pricing Model (CCAPM) by Rubinstein (1976), Lucas (1978) and Breeden (1979). In a Gaussian world, it justifies using a discounting system that combines three ingredients: A "risk-free" discount rate for projects whose net benefits are independent from aggregate consumption, a systematic risk premium, and a CCAPM cash-flow beta (later on referred to as the "beta"). (8) The beta is specific to the project, and, potentially, to the maturity of the benefit under scrutiny. It is defined as the elasticity of the net social benefit of the...