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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. 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.
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    Cited by:

    1. Yifan He & Abootaleb Shirvani & Barret Shao & Svetlozar Rachev & Frank Fabozzi, 2024. "Beyond the Bid-Ask: Strategic Insights into Spread Prediction and the Global Mid-Price Phenomenon," Papers 2404.11722, arXiv.org, revised Oct 2024.
    2. Abootaleb Shirvani & Stefan Mittnik & W. Brent Lindquist & Svetlozar T. Rachev, 2021. "Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes," Papers 2109.15051, arXiv.org, revised Aug 2023.
    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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    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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