Finance

Physics

Arbitrage pricing theory

Nonlinear system

Capital asset pricing model

Equity (law)

Mathematics

Short rate

Equity premium puzzle

Statistics

Linearization

Risk premium

Interest rate

Political science

Econometrics

Order (exchange)

Predictability

Economics

Yield curve

Computer science

Monetary economics

Quantum mechanics

Computer security

Asset (computer security)

The Journal of Finance

ABSTRACT This paper shows that the latest generation of asset pricing models with long‐run risk exhibit economically significant nonlinearities, and thus the ubiquitous Campbell‐Shiller log‐linearization can generate large numerical errors. These errors translate in turn to considerable errors in the model predictions, for example, for the magnitude of the equity premium or return predictability. We demonstrate that these nonlinearities arise from the presence of multiple highly persistent processes, which cause the exogenous states to attain values far away from their long‐run means with nonnegligible probability. These extreme values have a significant impact on asset price dynamics.

Higher Order Effects in Asset Pricing Models with Long‐Run Risks