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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.

Suggested Citation

  • Lundtofte, Frederik & Wilhelmsson, Anders, 2013. "Risk premia: Exact solutions vs. log-linear approximations," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4256-4264.
  • Handle: RePEc:eee:jbfina:v:37:y:2013:i:11:p:4256-4264 DOI: 10.1016/j.jbankfin.2013.07.035
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    References listed on IDEAS

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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    4. 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.
    5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    6. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 745-773.
    7. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    8. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    9. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, pages 487-512.
    10. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, pages 195-228.
    11. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
    12. 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.
    13. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March.
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    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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