Risk premia: Exact solutions vs. log-linear approximations

Frederik Lundtofte*, Anders Wilhelmsson

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)


We derive exact expressions for the risk premia for general distributions in a Lucas economy and show that the errors when using log-linear approximations can be economically significant when the shocks are nonnormal. Assuming growth rates are Normal Inverse Gaussian (NIG) and fitting the distribution to the data used in Mehra and Prescott (1985), the coefficient of relative risk aversion required to match the equity premium is more than halved compared to the finding in their article. We also consider a standard long-run risk model and, by comparing our exact solutions to the log-linear approximations, we show that the approximation errors are substantial, especially for high levels of risk aversion.

Original languageEnglish
JournalJournal of Banking and Finance
Issue number11
Pages (from-to)4256-4264
Number of pages9
Publication statusPublished - 1 Nov 2013
Externally publishedYes


  • Cumulants
  • Equity premium puzzle
  • Log-linear approximations
  • Long-run risk
  • NIG distribution


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