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Risk-Free Rate Puzzle

The asset-pricing anomaly that a CRRA model calibrated to the observed equity premium predicts a real risk-free rate far above the ~1% seen — because the single parameter γ is overloaded as both risk aversion and the inverse elasticity of intertemporal substitution, so fitting one target misfits the other.

Core Idea

The risk-free rate puzzle is a quantitative anomaly in consumption-based asset pricing: standard representative-agent CRRA models calibrated to match the historical equity premium simultaneously predict a real risk-free rate far above the observed ~1%. It is the companion of the equity premium puzzle. Its structural source is a mechanical coupling in CRRA utility: the same parameter γ governs both risk aversion and the inverse elasticity of intertemporal substitution, so raising γ to fit the premium forces the risk-free rate to implausible levels.

Scope of Application

The puzzle operates wherever a consumption-based representative-agent model is calibrated against historical returns.

  • Asset-pricing theory — the home turf; the double target motivating Epstein-Zin-Weil, habit, disasters, long-run risk.
  • Calibration of representative-agent macro models — checking a plausible risk-free rate.
  • Behavioral finance — evidence the expected-utility framework needs supplementation.
  • Long-horizon discounting and climate policy — the Stern-Nordhaus discount-rate debate.
  • Sovereign-debt and pension economics — the adjacent social-discount-rate question.

Clarity

Naming the puzzle imposes a discipline the equity premium puzzle alone leaves invisible: a model must match not just the spread between equity and bond returns but the level of the risk-free rate. It converts a one-dimensional anomaly into an explicit double target — premium and level jointly. Beneath that, it localizes the culprit with unusual precision: the single γ is overloaded, and any single-parameter resolution reintroduces the puzzle, so the coupling itself, not γ's value, is the defect.

Manages Complexity

The bewildering post-1989 proliferation — recursive preferences, habit, disasters, long-run risk, heterogeneous agents — compresses by fixing the defect every model must address to one mechanical fact: γ is overloaded. The modeler asks one question of all of them: how does this stop one knob from turning two dials? Success collapses to a single low-dimensional double target — a ~6-point premium and a ~1% risk-free level held jointly — against which each candidate is read off without re-deriving its internals.

Abstract Reasoning

The reasoning turns on the parameter-overloading diagnosis and the double target. A diagnostic move traces a misfit to the overloaded γ, not a wrong value, reading a high implied rate as the coupling's fingerprint; an interventionist move asks how each model decouples or supplements and scores it on both targets; a boundary-drawing move insists a model hit premium and level jointly; and comparative reasoning ranks the resolution menu on common terms.

Knowledge Transfer

Within asset pricing and macrofinance the puzzle transfers as a diagnostic and double-target across theory, calibration, behavioral finance, and discounting debates. Beyond macrofinance it is discipline-bound — there is no physical "risk-free rate puzzle." The generalizable lesson is at two levels: loosely, one parameter cannot satisfy two independent targets (identifiability, parsimony); sharply, unintended coupling of distinct quantities in one formal device (a candidate parameter_overloading pattern). The contrapositive diagnostic — a stubborn two-target misfit signals overcoupling, so decouple the device — travels usefully.

Relationships to Other Abstractions

Local relationship map for Risk-Free Rate PuzzleParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Risk-Free Rate PuzzleDOMAINDomain-specific abstraction: Equity premium puzzle — presupposesEquitypremium puzzleDOMAIN

Current abstraction Risk-Free Rate Puzzle Domain-specific

Parents (1) — more general patterns this builds on

  • Risk-Free Rate Puzzle presupposes Equity premium puzzle Domain-specific

    The Risk-Free Rate Puzzle arises when raising CRRA risk aversion to repair the Equity Premium Puzzle drives the same model's risk-free-rate prediction implausibly high.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Risk-Free Rate Puzzle sits in a moderately populated region (45th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Macroeconomic Equilibria & Consumer Demand (19 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12