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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. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2016. "Risks for the long run: Estimation with time aggregation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 52-69.
    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. 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.
    5. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
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    7. George M. Constantinides & Anisha Ghosh, 2011. "Asset Pricing Tests with Long-run Risks in Consumption Growth," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 1(1), pages 96-136.
    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. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    10. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
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    12. 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.
    13. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
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    3. Fischer, Thomas & Lundtofte, Frederik, 2020. "Unequal returns: Using the Atkinson index to measure financial risk," Journal of Banking & Finance, Elsevier, vol. 116(C).
    4. Abootaleb Shirvani & Stoyan V. Stoyanov & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Equity premium puzzle or faulty economic modelling?," Review of Quantitative Finance and Accounting, Springer, vol. 56(4), pages 1329-1342, May.

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    More about this item

    Keywords

    Log-linear approximations; Equity premium puzzle; Cumulants; NIG distribution; Long-run risk;
    All these keywords.

    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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