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Jump Dynamics: The Equity Premium and the Risk-Free Rate Puzzles

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  • Aase, Knut K.

    () (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

The paper develops a consumption based equilibrium model, focusing on the risk premium and the risk-free interest rate. We derive testable expressions for these quantities, and confront these with sample estimates for the 20. century. Our framework is a dynamic model in continuous time, allowing for random jumps at random time points, in addition to diffusion uncertainty. Preferences are time separable and additive. The classical equity premium puzzle and the risk-free rate puzzle are re-examined. We present values for the parameters of the representative agent's utility function for different values of risk premia and interest rates, calibrated to two first moments of the US-data of the last century. Relatively low values for agents' risk aversion are consistent with the model, but positive values of the subjective interest rate seem harder to fit.

Suggested Citation

  • Aase, Knut K., 2004. "Jump Dynamics: The Equity Premium and the Risk-Free Rate Puzzles," Discussion Papers 2004/12, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2004_012
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    File URL: http://hdl.handle.net/11250/164036
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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. M. S. Feldstein, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 5-12.
    3. Ellen R. McGrattan & Edward C. Prescott, 2003. "Average Debt and Equity Returns: Puzzling?," American Economic Review, American Economic Association, pages 392-397.
    4. Knut K. Aase, 1993. "A Jump/Diffusion Consumption-Based Capital Asset Pricing Model and the Equity Premium Puzzle," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 65-84.
    5. Aase, Knut K., 1993. "Continuous trading in an exchange economy under discontinuous dynamics: A resolution of the equity premium puzzle," Scandinavian Journal of Management, Elsevier, pages 3-28.
    6. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    7. Xiaohong Chen & Sydney C. Ludvigson, 2009. "Land of addicts? an empirical investigation of habit-based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1057-1093.
    8. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    9. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    10. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    11. James Tobin, 1969. "Comment on Borch and Feldstein," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 13-14.
    12. Olivier Allais, 2004. "Local Substitution and Habit Persistence: Matching the Moments of the Equity Premium and the Risk-Free Rate," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 265-296, April.
    13. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    14. 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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    16. K. Borch, 1969. "A Note on Uncertainty and Indifference Curves," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 1-4.
    17. Knut K. Aase, 2002. "Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 173-198.
    18. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
    19. Aase, Knut K. & ├śksendal, Bernt, 1988. "Admissible investment strategies in continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 291-301, December.
    20. Haug, Jorgen, 2001. "Explicit characterizations of financial prices with history-dependent utility," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 337-356, December.
    21. Salyer, Kevin D., 1998. "Crash states and the equity premium: Solving one puzzle raises another," Journal of Economic Dynamics and Control, Elsevier, vol. 22(6), pages 955-965, June.
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    Citations

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    Cited by:

    1. Aase, Knut K, 2005. "Using Option Pricing Theory to Infer About Historical Equity Premiums," University of California at Los Angeles, Anderson Graduate School of Management qt3dd602j5, Anderson Graduate School of Management, UCLA.
    2. Aase, Knut K, 2005. "The perpetual American put option for jump-diffusions with applications," University of California at Los Angeles, Anderson Graduate School of Management qt31g898nz, Anderson Graduate School of Management, UCLA.
    3. Aase, Knut K., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Norwegian School of Economics, Department of Business and Management Science.

    More about this item

    Keywords

    Consumption based CAPM; Equilibrium interest rate; The equity premium puzzle; The risk-free rate puzzle; jump/diffusions;

    JEL classification:

    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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