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Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications

Author

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  • Jérome Detemple
  • Marcel Rindisbacher

Abstract

A new decomposition of the optimal portfolio, in dynamic models with von Neumann--Morgenstern preferences and Ito prices, is established. The formula rests on a change of numéraire that uses pure discount bonds as units of account. The dynamic hedging demand has two components. The first hedge insures against fluctuations in an optimally designed bond with a maturity date matching the investor's horizon. The second hedge immunizes against fluctuations in the market price of risk in the bond numéraire. Various applications are examined. New results concerning the behavior of extremely risk-averse individuals, the demand for bonds and its long-horizon limit, and the optimal portfolio in incomplete markets are derived. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

Suggested Citation

  • Jérome Detemple & Marcel Rindisbacher, 2010. "Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications," The Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 25-100, January.
    • Handle: RePEc:oup:rfinst:v:23:y:2010:i:1:p:25-100
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    File URL: http://hdl.handle.net/10.1093/rfs/hhp040
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    Cited by:

    1. Damir Filipovic & Martin Larsson & Anders B. Trolle, 2018. "On the Relation Between Linearity-Generating Processes and Linear-Rational Models," Papers 1806.03153, arXiv.org.
    2. Veniamin Mokhov & Sergei Aliukov & Anatoliy Alabugin & Konstantin Osintsev, 2023. "A Review of Mathematical Models of Macroeconomics, Microeconomics, and Government Regulation of the Economy," Mathematics, MDPI, vol. 11(14), pages 1-37, July.
    3. Paolo Guasoni & Constantinos Kardaras & Scott Robertson & Hao Xing, 2014. "Abstract, classic, and explicit turnpikes," Finance and Stochastics, Springer, vol. 18(1), pages 75-114, January.
    4. Yao, Haixiang & Li, Danping & Wu, Huiling, 2022. "Dynamic trading with uncertain exit time and transaction costs in a general Markov market," International Review of Financial Analysis, Elsevier, vol. 84(C).
    5. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    6. Beissner, Patrick & Rosazza Gianin, Emanuela, 2018. "The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time," Rationality and Competition Discussion Paper Series 72, CRC TRR 190 Rationality and Competition.
    7. Collin-Dufresne, Pierre & Daniel, Kent & Sağlam, Mehmet, 2020. "Liquidity regimes and optimal dynamic asset allocation," Journal of Financial Economics, Elsevier, vol. 136(2), pages 379-406.
    8. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    9. Hubar, Sylwia & Koulovatianos, Christos & Li, Jian, 2020. "The role of labor-income risk in household risk-taking," European Economic Review, Elsevier, vol. 129(C).
    10. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    11. Peter Christoffersen & Mathieu Fournier & Kris Jacobs, 2018. "The Factor Structure in Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 595-637.
    12. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    13. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    14. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    15. Anna Battauz & Alessandro Sbuelz, 2018. "Non†myopic portfolio choice with unpredictable returns: The jump†to†default case," European Financial Management, European Financial Management Association, vol. 24(2), pages 192-208, March.
    16. Chenxu Li & Olivier Scaillet & Yiwen Shen, 2020. "Wealth Effect on Portfolio Allocation in Incomplete Markets," Papers 2004.10096, arXiv.org, revised Aug 2021.
    17. Lioui, Abraham & Tarelli, Andrea, 2019. "Macroeconomic environment, money demand and portfolio choice," European Journal of Operational Research, Elsevier, vol. 274(1), pages 357-374.
    18. Mellios, Constantin & Six, Pierre & Lai, Anh Ngoc, 2016. "Dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield," European Journal of Operational Research, Elsevier, vol. 250(2), pages 493-504.
    19. Dai, Zhifeng & Zhu, Huan, 2021. "Indicator selection and stock return predictability," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    20. Scott Robertson & Hao Xing, 2014. "Long Term Optimal Investment in Matrix Valued Factor Models," Papers 1408.7010, arXiv.org.
    21. Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
    22. Sami Attaoui & Pierre Six, 2014. "Hedging demand and the certainty equivalent of wealth," Economics Bulletin, AccessEcon, vol. 34(3), pages 1742-1750.
    23. Sergey Nadtochiy & Michael Tehranchi, 2013. "Optimal investment for all time horizons and Martin boundary of space-time diffusions," Papers 1308.2254, arXiv.org, revised Jan 2014.
    24. Castaneda, Pablo & Rudolph, Heinz P., 2011. "Upgrading investment regulations in second pillar pension systems : a proposal for Colombia," Policy Research Working Paper Series 5775, The World Bank.

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