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The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund

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  • Knut K. Aase

    (Department of Business and Management Science, Norwegian School of Economics, 5045 Bergen, Norway)

  • Petter Bjerksund

    (Department of Business and Management Science, Norwegian School of Economics, 5045 Bergen, Norway)

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 ensures 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

  • Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
  • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:9:p:425-:d:629686
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    References listed on IDEAS

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    1. Tobin, James, 1974. "What Is Permanent Endowment Income?," American Economic Review, American Economic Association, vol. 64(2), pages 427-432, May.
    2. 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..
    3. Svensson, Lars E. O., 1989. "Portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 30(4), pages 313-317, October.
    4. 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.
    5. Fatih Guvenen, 2009. "A Parsimonious Macroeconomic Model for Asset Pricing," Econometrica, Econometric Society, vol. 77(6), pages 1711-1750, November.
    6. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    12. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    13. 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.
    14. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    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. 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.
    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," The 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.
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    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 Kristian Aase, 2024. "Optimal Spending Strategies for Sovereign Wealth Funds Using a Discrete-Time Life Cycle Model," JRFM, MDPI, vol. 17(8), pages 1-41, July.
    3. 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.
    4. 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.

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    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

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