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Equilibrium in securities markets with heterogeneous investors and unspanned income risk

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  • Christensen, Peter Ove
  • Larsen, Kasper
  • Munk, Claus

Abstract

In a finite time horizon, incomplete market, continuous-time setting with dividends and investor incomes governed by arithmetic Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and stock price for an economy with finitely many heterogeneous CARA investors and unspanned income risk. In equilibrium, the Sharpe ratio is the same as in an otherwise identical complete market economy, whereas the risk-free rate is lower and, consequently, the stock price is higher. The reduction in the risk-free rate is highest when the more risk-averse investors face the largest unspanned income risk.

Suggested Citation

  • Christensen, Peter Ove & Larsen, Kasper & Munk, Claus, 2012. "Equilibrium in securities markets with heterogeneous investors and unspanned income risk," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1035-1063.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1035-1063
    DOI: 10.1016/j.jet.2012.01.007
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    3. Kim Weston, 2017. "Existence of a Radner equilibrium in a model with transaction costs," Papers 1702.01706, arXiv.org, revised Feb 2018.
    4. Kim Weston & Gordan Zitkovic, 2018. "An incomplete equilibrium with a stochastic annuity," Papers 1809.05947, arXiv.org.
    5. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    6. Jiun-Hua Su, 2019. "Model Selection in Utility-Maximizing Binary Prediction," Papers 1903.00716, arXiv.org, revised Jul 2020.
    7. Akbas, Ferhat & Boehmer, Ekkehart & Jiang, Chao & Koch, Paul D., 2022. "Overnight returns, daytime reversals, and future stock returns," Journal of Financial Economics, Elsevier, vol. 145(3), pages 850-875.
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    9. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2023. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment (Forthcoming in "Insurance: Mathematics and Economics")," CARF F-Series CARF-F-576, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    11. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    12. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    13. Tyler Abbot, 2017. "General Equilibrium Under Convex Portfolio Constraints and Heterogeneous Risk Preferences," Papers 1706.05877, arXiv.org, revised Jun 2018.
    14. Su, Jiun-Hua, 2021. "Model selection in utility-maximizing binary prediction," Journal of Econometrics, Elsevier, vol. 223(1), pages 96-124.
    15. Liang, Xiaoqing & Young, Virginia R., 2018. "Annuitization and asset allocation under exponential utility," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 167-183.
    16. Jin Hyuk Choi & Kasper Larsen, 2013. "Taylor approximation of incomplete Radner equilibrium models," Papers 1310.2973, arXiv.org, revised Sep 2014.
    17. Xiaoyu Deng & Jing Tian & Rong Chen, 2019. "Effect of Social Security System on Consumption through Income and Uncertainty: Evidence from China," Sustainability, MDPI, vol. 11(7), pages 1-16, March.
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    More about this item

    Keywords

    Unspanned income; Heterogeneous preferences; Continuous-time equilibrium; Risk-free rate puzzle; Equity premium; Incomplete markets; Brownian motion;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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