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Optimal Spending Strategies for Sovereign Wealth Funds Using a Discrete-Time Life Cycle Model

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  • Knut Kristian Aase

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

Abstract

The paper analyses optimal spending of an endowment fund. The purpose is to find a spending rule which is optimal for the owners and which secures that the fund will last “forever”. This we do by finding closed form solutions of the optimal consumption to wealth ratio. We solve this problem using the life cycle model, where the agent can have preferences represented by expected utility or recursive utility. We apply our results to a sovereign wealth fund, and demonstrate that the optimal spending rate is significantly lower than the fund’s expected real rate of return, a rule which is in common use. Employing the latter as the spending rate, implies that the fund’s value deteriorates both in probability and in expectation, as time goes. For both kinds of long term convergence we find closed form threshold values. Spending below these values secures a sustainable fund.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:8:p:327-:d:1446285
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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. 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. 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.
    5. 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.
    6. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. 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.
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