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Idiosyncratic Risk and Higher-Order Cumulants

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Abstract

We show that, when allowing for general distributions of dividend growth in a Lucas economy with multiple "trees," idiosyncratic volatility will affect expected returns in ways that are not captured by the log linear approximation. We derive an exact expression for the risk premia for general distributions. 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.

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  • Lundtofte, Frederik & Wilhelmsson, Anders, 2011. "Idiosyncratic Risk and Higher-Order Cumulants," Working Papers 2011:33, Lund University, Department of Economics.
    • Handle: RePEc:hhs:lunewp:2011_033
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    1. Ian Martin, 2013. "The Lucas Orchard," Econometrica, Econometric Society, vol. 81(1), pages 55-111, January.
    2. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409, June.
    3. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 745-773.
    4. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    5. Fu, Fangjian, 2009. "Idiosyncratic risk and the cross-section of expected stock returns," Journal of Financial Economics, Elsevier, vol. 91(1), pages 24-37, January.
    6. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    7. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
    8. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    9. 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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    More about this item

    Keywords

    diosyncratic risk; idiosyncratic volatility; risk premia; cumulants; NIG distribution;
    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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