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Risk premia: Exact solutions vs. log-linear approximations

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  • Lundtofte, Frederik
  • Wilhelmsson, Anders

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 37 (2013)
Issue (Month): 11 ()
Pages: 4256-4264

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Handle: RePEc:eee:jbfina:v:37:y:2013:i:11:p:4256-4264

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Web page: http://www.elsevier.com/locate/jbf

Related research

Keywords: Log-linear approximations; Equity premium puzzle; Cumulants; NIG distribution; Long-run risk;

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References

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  1. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  2. Robert J. Shiller & John Y. Campbell, 1986. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Cowles Foundation Discussion Papers 812, Cowles Foundation for Research in Economics, Yale University.
  3. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  4. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
  5. John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
  6. Kocherlakota, N., 1995. "The Equity Premium: It's Still a Puzzle," Working Papers 95-05, University of Iowa, Department of Economics.
  7. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
  8. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 14, pages 889-938 Elsevier.
  9. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  10. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  11. Lars Peter Hansen & John Heaton & Nan Li, 2005. "Consumption Strikes Back?: Measuring Long-Run Risk," NBER Working Papers 11476, National Bureau of Economic Research, Inc.
  12. Ravi Bansal & Dana Kiku & Amir Yaron, 2012. "Risks For the Long Run: Estimation with Time Aggregation," NBER Working Papers 18305, National Bureau of Economic Research, Inc.
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