IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2021_001.html
   My bibliography  Save this paper

The optimal spending rate versus the expected real return of a sovereign wealth fund

Author

Listed:
  • Aase, Knut K.

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

  • Bjerksund, Petter

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

Abstract

We consider a sovereign wealth fund that invests broadly in the international financial markets. The influx to the fund has stopped. We adopt the life cycle model and demonstrate that the optimal spending rate from the fund is significantly less than the fund’s expected real rate of return. The optimal spending rate secures that the fund will last ”forever”. Spending the expected return will deplete the fund with probability one. Moreover, this strategy is inconsistent with optimal portfolio choice. Our results are contrary to the idea that it is sustainable to spend the expected return of a sovereign wealth fund.

Suggested Citation

  • Aase, Knut K. & Bjerksund, Petter, 2021. "The optimal spending rate versus the expected real return of a sovereign wealth fund," Discussion Papers 2021/1, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2021_001
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/11250/2726376
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Tobin, James, 1974. "What Is Permanent Endowment Income?," American Economic Review, American Economic Association, vol. 64(2), pages 427-432, May.
    3. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    4. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    5. Svensson, Lars E. O., 1989. "Portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 30(4), pages 313-317, October.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Fatih Guvenen, 2009. "A Parsimonious Macroeconomic Model for Asset Pricing," Econometrica, Econometric Society, vol. 77(6), pages 1711-1750, November.
    8. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    9. Campbell, John Y. & Sigalov, Roman, 2022. "Portfolio choice with sustainable spending: A model of reaching for yield," Journal of Financial Economics, Elsevier, vol. 143(1), pages 188-206.
    10. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    11. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    12. Mossin, Jan, 1969. "A Note on Uncertainty and Preferences in a Temporal Context," American Economic Review, American Economic Association, vol. 59(1), pages 172-174, March.
    13. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    14. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Aase, Knut K., 2016. "Life Insurance And Pension Contracts Ii: The Life Cycle Model With Recursive Utility," ASTIN Bulletin, Cambridge University Press, vol. 46(1), pages 71-102, January.
    17. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    19. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    20. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aase, Knut K., 2023. "Optimal spending of a wealth fund in the discrete time life cycle model," Discussion Papers 2023/7, Norwegian School of Economics, Department of Business and Management Science.
    2. Knut Anton Mork & Haakon Andreas Trønnes & Vegard Skonseng Bjerketvedt, 2022. "Capital Preservation and Current Spending with Sovereign Wealth Funds and Endowment Funds: A simulation Study," IJFS, MDPI, vol. 10(3), pages 1-24, August.
    3. Knut Anton Mork & Haakon Andreas Trønnes & Vegard Skonseng Bjerketvedt, "undated". "Capital preservation and current spending with Sovereign Wealth Funds and Endowment Funds: A simulation study," Working Paper Series 19222, Department of Economics, Norwegian University of Science and Technology.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shigeta, Yuki, 2020. "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    2. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    3. Kraft, Holger & Munk, Claus & Weiss, Farina, 2022. "Bequest motives in consumption-portfolio decisions with recursive utility," Journal of Banking & Finance, Elsevier, vol. 138(C).
    4. Roche, Hervé, 2011. "Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 80-96, January.
    5. Yu Chen & Thomas Cosimano & Alex Himonas & Peter Kelly, 2014. "An Analytic Approach for Stochastic Differential Utility for Endowment and Production Economies," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 397-443, December.
    6. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    7. Kabderian Dreyer, Johannes & Sharma, Vivek & Smith, William, 2023. "Warm-glow investment and the underperformance of green stocks," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 546-570.
    8. Max Gillman & Michal Kejak & Michal Pakoš, 2015. "Learning about Rare Disasters: Implications For Consumption and Asset Prices," Review of Finance, European Finance Association, vol. 19(3), pages 1053-1104.
    9. Thomas Douenne, 2020. "Disaster Risks, Disaster Strikes, and Economic Growth: the Role of Preferences," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 38, pages 251-272, October.
    10. Li, Minqiang, 2010. "Asset Pricing - A Brief Review," MPRA Paper 22379, University Library of Munich, Germany.
    11. Smith, William T., 1999. "Risk, the Spirit of Capitalism and Growth: The Implications of a Preference for Capital," Journal of Macroeconomics, Elsevier, vol. 21(2), pages 241-262, April.
    12. Aase, Knut K., 2014. "Recursive utility and jump-diffusions," Discussion Papers 2014/9, Norwegian School of Economics, Department of Business and Management Science.
    13. Aase, Knut K., 2014. "The Life Cycle Model with Recursive Utility: New insights on optimal consumption," Discussion Papers 2014/19, Norwegian School of Economics, Department of Business and Management Science, revised 16 Oct 2015.
    14. Campani, Carlos Heitor & Garcia, René, 2019. "Approximate analytical solutions for consumption/investment problems under recursive utility and finite horizon," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 364-384.
    15. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    16. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    17. Campbell, John Y. & Sigalov, Roman, 2022. "Portfolio choice with sustainable spending: A model of reaching for yield," Journal of Financial Economics, Elsevier, vol. 143(1), pages 188-206.
    18. Pakoš, Michal, 2013. "Long-run risk and hidden growth persistence," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1911-1928.
    19. Aase, Knut K. & Bjerksund, Petter, 2019. "The optimal extraction rate versus the expected real return of a sovereign wealth fund: Some simulations," Discussion Papers 2019/7, Norwegian School of Economics, Department of Business and Management Science, revised 03 Feb 2021.
    20. Smith, William T., 1996. "Taxes, uncertainty, and long-term growth," European Economic Review, Elsevier, vol. 40(8), pages 1647-1664, November.

    More about this item

    Keywords

    Optimal spending rate; endowment funds; expected utility; risk aversion; EIS; recursive utility;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:nhhfms:2021_001. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.