The welfare cost of ignoring the beta

Abstract

Because of risk aversion, any sensible investment valuation system should value less projects that contribute more to the aggregate risk, i.e., that have a larger income- elasticity of net benefits. In theory, this is done by adjusting discount rates to consumption betas. But in reality, for various reasons (Arrow-Lind and WACC fallacies, market failures), most public and private institutions and people use a discount rate that is rather insensitive to the risk profile of their investment projects. I show in this pa- per that the economic consequences of the implied misallocation of capital are dire. To do this, I calibrate a Lucas model in which the investment opportunity set contains a myriad of projects with different expected returns and risk profiles. The welfare loss of using a single discount rate is equivalent to a permanent reduction in consumption that lies somewhere between 15% and 45%, either at the level of the irrational agents, or at equilibrium if all agents make the same mistake. Economists should devote more energy to support a reform of public discounting systems in favor of what has been advocated by the normative interpretation of modern asset pricing theories over the last four decades.

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Reference

Christian Gollier, The welfare cost of ignoring the beta, January 2021, revised April 2022.