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The Sharpe Ratio And Preferences: A Parametric Approach

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  • Lettau, Martin
  • Uhlig, Harald

Abstract

We use a log-normal framework to examine the effect of preferences on the market price for risk, that is, the Sharpe ratio. In our framework, the Sharpe ratio can be calculated directly from the elasticity of the stochastic discount factor with respect to consumption innovations as well as the volatility of consumption innovations. This can be understood as an analytical shortcut to the calculation of the Hansen–Jagannathan volatility bounds, and therefore provides a convenient tool for theorists searching for models capable of explaining asset-pricing facts. To illustrate the usefulness of our approach, we examine several popular preference specifications, such as CRRA, various types of habit formation, and the recursive preferences of Epstein–Zin–Weil. Furthermore, we show how the models with idiosyncratic consumption shocks can be studied.

Suggested Citation

  • Lettau, Martin & Uhlig, Harald, 2002. "The Sharpe Ratio And Preferences: A Parametric Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 242-265, April.
    • Handle: RePEc:cup:macdyn:v:6:y:2002:i:02:p:242-265_03
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    Cited by:

    1. Borenstein, Eliezer & Elkayam, David, 2014. "The equity premium in a small open economy and an application to Israel," Economic Modelling, Elsevier, vol. 43(C), pages 81-99.
    2. Budria, Santiago & Díaz, Antonia, 2006. "Term premium and equity premium in economies with habit formation," UC3M Working papers. Economics we065522, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Felix KUBLER & Karl SCHMEDDERS, 2010. "Life-Cycle Portfolio Choice, the Wealth Distribution and Asset Prices," Swiss Finance Institute Research Paper Series 10-21, Swiss Finance Institute.
    4. Santiago Budría, 2008. "An Exploration of Asset Returns in a Production Economy with Relative Habits," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 36(3), pages 261-274, September.
    5. Kanamura, Takashi & Ohashi, Kazuhiko, 2009. "Pricing summer day options by good-deal bounds," Energy Economics, Elsevier, vol. 31(2), pages 289-297, March.
    6. Farah Said & Uzma Afzal & Ginger Turner, 2014. "Attitudes Towards Risk in the Wake of a Rare Event: Evidence from Pakistan," CREB Working papers 2-2014, Centre for Research in Economics and Business, The Lahore School of Economics, revised 2014.
    7. Said, Farah & Afzal, Uzma & Turner, Ginger, 2015. "Risk taking and risk learning after a rare event: Evidence from a field experiment in Pakistan," Journal of Economic Behavior & Organization, Elsevier, vol. 118(C), pages 167-183.
    8. Johannes Brumm & Michael Grill & Felix Kubler & Karl Schmedders, 2015. "Collateral Requirements And Asset Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(1), pages 1-25, February.
    9. Grishchenko, Olesya V., 2011. "Asset pricing in the production economy subject to monetary shocks," Journal of Economics and Business, Elsevier, vol. 63(3), pages 187-216, May.
    10. Harald Uhlig, 2007. "Explaining Asset Prices with External Habits and Wage Rigidities in a DSGE Model," American Economic Review, American Economic Association, vol. 97(2), pages 239-243, May.
    11. Bullard, James & Evans, George W. & Honkapohja, Seppo, 2010. "A Model Of Near-Rational Exuberance," Macroeconomic Dynamics, Cambridge University Press, vol. 14(2), pages 166-188, April.
    12. Elie Appelbaum & Parantap Basu, 2010. "A new methodology for studying the equity premium," Annals of Operations Research, Springer, vol. 176(1), pages 109-126, April.
    13. Kliem, Martin & Uhlig, Harald, 2013. "Bayesian estimation of a DSGE model with asset prices," Discussion Papers 37/2013, Deutsche Bundesbank.
    14. Henin, Pierre-Yves & Weitzenblum, Thomas, 2005. "Employment protection and the stock market: the common shock case," Economic Modelling, Elsevier, vol. 22(1), pages 127-146, January.
    15. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.
    16. Zhang, Wenlang & Semmler, Willi, 2009. "Prospect theory for stock markets: Empirical evidence with time-series data," Journal of Economic Behavior & Organization, Elsevier, vol. 72(3), pages 835-849, December.
    17. Santiago Budría & Antonia Díaz, 2006. "Term and Equity Premium in Economies with Habit Formation," Working Papers 2006-23, FEDEA.
    18. Stefano Athanasoulis & Oren Sussman, 2007. "Habit formation and the equity–premium puzzle: a skeptical view," Annals of Finance, Springer, vol. 3(2), pages 193-212, March.
    19. Harald Uhlig, 2010. "Easy EZ in DSGE," 2010 Meeting Papers 111, Society for Economic Dynamics.

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