First-Order Prudence and Its Implications for Precautionary Savings and the Risk-Free Rate
Sebastian Ebert, Paul Karehnke
Operations Research · 2025 · Volume 73 · Issue 6
Abstract
Prudence is widely known for inducing saving in response to future risk—precautionary saving. In this paper, we revisit this important implication by providing definitions of first- and second-order prudence that parallel Segal and Spivak’s [Segal U, Spivak A (1990) First order versus second order risk aversion. J. Econom. Theory 51:111–125] definitions of first- and second-order risk aversion. Second-order prudence means that the decision-maker is almost prudent-neutral for small risks, whereas under first-order prudence small risks remain a major concern. In the expected utility (EU) framework and when utility is smooth, prudence is second order. In that case, a small, positive-mean risk to future wealth reduces savings because of the consumption smoothing motive, but it can increase savings under first-order prudence. The latter is the case for non-EU theories, such as rank-dependent or reference-dependent utility, but also in the EU framework with a novel utility function that we propose. In equilibrium, first-order prudent preferences predict realistically low risk-free rates, thereby resolving the so-called risk-free rate puzzle. Funding: This research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program [Grant agreement no. 803380]. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0739 .
Keywords
Decision Analysis, prudence, precautionary behavior, risk-free rate puzzle, expected utility, rank-dependent utility
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