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Optimal Asset Allocation and Consumption Rules for Oil-Based Sovereign Wealth Funds

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Khouzeima Moutanabbir - American University in Cairo
Diaa Noureldin - American University in Cairo
ERF Conference on “Arab Oil Exporters: Coping with a New Global Oil Order”

Kuwait, November 26-27, 2017
www.erf.org.eg

Published in: Government & Nonprofit
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Optimal Asset Allocation and Consumption Rules for Oil-Based Sovereign Wealth Funds

  1. 1. Optimal Asset Allocation and Consumption Rules for Oil-Based Sovereign Wealth Funds Khouzeima Moutanabbir* and Diaa Noureldin** *Dept. of Mathematics and Actuarial Science, American University in Cairo Dept. of Economics, American University in Cairo Policy Conference on Arab Oil Exporters: Coping with A New Global Oil Order Arab Fund for Economic and Social Development, Kuwait November 26-27, 2017
  2. 2. Outline I Introductory remarks. I Overview of sovereign wealth funds (SWFs). I Motivation for optimal rules. I Modelling framework and key assumptions. I Optimal asset allocation and consumption rules. I Concluding remarks.
  3. 3. Introductory remarks I Signi…cance of SWFs in international …nancial markets: I US$ 7.4 trillion in total assets, and rising! I 57% of the funds (by assets) are oil-based funds. I The majority of existing SWFs belong to states in the Middle East and Asia. I Signi…cance of SWFs for their respective economies: I Large assets relative to GDP and annual oil income. I Small ratio of assets to oil reserves (except Norway). I Current investment strategies for large oil-based SWFs: I Equity share roughly equal to 60%. I The rest is divided between bonds and alternative investments. I Transparency and governance issues: I Agency problems. I Investment strategy drivers. I Fiscal rules (or lackthereof).
  4. 4. Overview of SWFs: The world’s largest SWFs SWF Name Country Assets Origin (US$ Bn.) Government Pension Fund (Global) Norway 922 Oil Abu Dhabi Investment Authority UAE (Abu Dhabi) 828 Oil China Investment Corporation China 814 Non-comm. Kuwait Investment Authority Kuwait 524 Oil SAMA Foreign Holdings Saudi Arabia 514 Oil Hong Kong Monetary Authority China (Hong Kong) 457 Non-comm. SAFE Investment Company China 441 Non-comm. Singapore Investment Corporation Singapore 359 Non-comm. Qatar Investment Authority Qatar 320 Oil & gas National Social Security Fund China 295 Non-comm. Investment Corporation of Dubai UAE (Dubai) 210 Non-comm. Temasek Holdings Singapore 197 Non-comm. Public Investment Fund Saudi Arabia 183 Oil Mubadala Investment Company UAE – Abu Dhabi 125 Oil Abu Dhabi Investment Council UAE – Abu Dhabi 110 Non-comm. Korea Investment Corporation South Korea 108 Non-comm. Source: Sovereign Wealth Fund Institute database (July 2017 update). Notes: Estimates are at di¤erent time points, and the most recent are as of end of March, 2017.
  5. 5. Overview of SWFs: Accumulated assets relative to GDP, oil rents and proved oil reserves Country SWF Assets Assets GDP Oil rents GDP Assets Oil rents Assets Oil reserves UAE 1,098 3.15 0.11 28.10 0.25 Norway 922 2.49 0.03 81.79 4.09 Saudi Arabia 697 1.08 0.23 4.82 0.06 Kuwait 524 4.59 0.38 11.93 0.12 Qatar 320 2.10 0.06 35.86 0.29 Russia 88 0.07 0.06 1.26 0.03 Kazakhstan 67 0.38 0.06 6.83 0.05 Notes: I For total assets, all of the oil-based funds for each country are grouped together, and the source is the Sovereign Wealth Fund Institute database (July 2017 update). I GDP data is obtained from the International Monetary Fund IFS database and refer to 2016 …gures, except for Kazakhstan and Kuwait where the GDP …gure is for 2015. I Oil rents are from the World Bank WDI database, and all …gures are for 2015. I Proved oil reserves (as of end of 2016) are from the U.S. Energy Information Administration.
  6. 6. Overview of SWFs: Current asset allocation Norw ay UAE Kuwait Saudi Arabia Qatar 0 10 20 30 40 50 60 70 80 90 100 Equity Bonds Other Source: Sovereign Wealth Fund Institute database (July 2017 update). Notes: The asset class "other" includes real estate, alternative investments, hedge funds, and private equity (particularly in infrastructure projects)
  7. 7. Motivation for optimal rules Our objective is to determine: I The optimal asset allocation for a SWF based on income from oil: I Risk aversion attributes. I Nature of the available investment opportunity. I Correlation between oil income shocks and the risky asset returns. I Optimal path for consumption out of the fund: I The willingness to substitute future for present consumption: The elasticity of intertemporal substitution. I Mature vs. immature funds.
  8. 8. Related literature Our paper draws on the following strands of the literature: I Optimal asset allocation for a SWF: I Gintschel & Scherer (2008); Scherer (2009); Balding and Yao (2011); Scherer (2011); van den Bremer, van der Ploeg & Wills (2016). I Asset allocation given a stochastic stream of income: I Mayers (1972); Fama and Schwert (1977); Bodie, Merton & Samuelson (1992); Koo (1995, 1998): Veceira (2001). I Asset allocation in the presence of state variables: I Campbell and Veceira (1999); Campbell, Chan and Veceira (2003).
  9. 9. Modelling framework and key assumptions Main equations I Intertemporal budget constraint: Ft+1 = (Ft + Yt Ct ) RF ,t+1, where Ft is the value of the fund at time t. I Yt is the income from oil allocated to the fund at time t. It follows the dynamic: ln Yt+1 ln Yt = g + ξt+1. I Ct is the consumption out of the fund at time t. I The utility of consumption is given by the Epstein-Zin (1989) utility: Ut = (1 δ)C 1 γ θ t + δ h Et U 1 γ t+1 i1 θ θ 1 γ , where γ > 0 is the coe¢ cient of relative risk aversion, ψ > 0 is the elasticity of intertemporal substitution, 0 < δ < 1 is the time discount factor, and θ = 1 γ 1 ψ 1 .
  10. 10. Modelling framework and key assumptions Financial Market Assumptions I RF ,t+1 = π0,t R0,t+1 + π 0 t Rt+1 is the continuously compounded return on the fund. I Time-varying investment opportunities: zt+1 = Φ0 + Φ1zt + νt+1, where zt+1 = 0 @ r0,t+1 xt+1 st+1 1 A , xt+1 = 0 B B B @ r1,t+1 r0,t+1 r2,t+1 r0,t+1 ... rn,t+1 r0,t+1 1 C C C A . I The shocks νt+1 and ξt+1 are correlated through the vector β: ξt+1 = β 0 νt+1 + σ(o)ξ (o) t+1, and ξ (o) t+1 is the own oil shock.
  11. 11. Modelling framework and key assumptions The objective of the fund manager is to maximize the expected present value of future consumption at discount rate δ: max fCt ,πt g∞ t=0 E " ∞ ∑ t=0 δt U (Ct ) # , subject to the intertemporal budget constraint: Ft+1 = (Ft + Yt Ct ) RF ,t+1.
  12. 12. Optimal asset allocation and consumption rules The optimal portfolio allocation and consumption are given by: πt = A0 + A1zt , ct = a + bft + (1 b) yt + B 0 1zt + z 0 t B2zt . I The optimal portfolio allocation can be decomposed to track: (i) myopic demand, (ii) normal hedging demand, and (iii) oil hedging demand. I The solution enables us to …nd the optimal equity-to-bond ratio and how it changes with risk aversion, the elasticity of intertemporal substitution, and oil income volatility, among other variables.
  13. 13. Optimal asset allocation 1 2 3 4 5 6 7 8 9 10 11 12 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 γ Optimalequity-to-bondsratio ψ = 1.2 ψ = 1.3 ψ = 1.4
  14. 14. Optimal asset allocation 2 2 3 4 5 6 7 8 9 10 11 12 0.8 1 1.2 1.4 1.6 1.8 2 γ Optimalequity-to-bondsratio 0.8*σ (o) 2 1.0*σ (o) 2 1.2*σ (o) 2
  15. 15. Optimal asset allocation 3 ψ 1.2 1.3 1.4 γ = 2 Myopic demand (% of total demand) 0.843 0.820 0.799 Hedging demand (% of total demand) 0.157 0.180 0.201 γ = 5 Myopic demand (% of total demand) 0.794 0.739 0.702 Hedging demand (% of total demand) 0.206 0.261 0.298 γ = 10 Myopic demand (% of total demand) 0.869 0.793 0.736 Hedging demand (% of total demand) 0.131 0.207 0.264 γ = 15 Myopic demand (% of total demand) 0.926 0.855 0.793 Hedging demand (% of total demand) 0.074 0.145 0.207 γ = 20 Myopic demand (% of total demand) 0.961 0.903 0.844 Hedging demand (% of total demand) 0.039 0.097 0.156
  16. 16. Optimal consumption rule Recall that the optimal consumption rule is: ct = a + bft + (1 b) yt + B 0 1zt + z 0 t B2zt . Now let us focus on the behavior of a "mature fund". A mature fund means b = 1, and thus we have ct = a + ft + B (z)0 1 zt + z 0 t B2zt , ct ft | {z } Cons-wealth ratio = a|{z} constant + B (z)0 1 zt + z 0 t B2zt | {z } Inv. opportunity , For a mature fund, which is not very dependent on oil income, the consumption-out-of-wealth ratio becomes constant, unless there is a change in the available investment opportunities: I Better asset returns would increases consumption out of wealth, and vice versa.
  17. 17. Optimal consumption rule ψ 1.2 1.4 1.6 1.8 2.0 Panel A: γ = 2.8 Equity-to-bond ratio 1.293 1.480 1.674 1.620 1.534 b (fund maturity) 1.000 1.000 1.000 0.924 0.825 Ct /Ft (mean value) 0.135 0.086 0.054 0.049 0.051 Panel B: γ = 3.0 Equity-to-bond ratio 1.288 1.487 1.687 1.732 1.625 b (fund maturity) 1.000 1.000 1.000 0.955 0.861 Ct /Ft (mean value) 0.143 0.092 0.061 0.048 0.050 Panel C: γ = 3.2 Equity-to-bond ratio 1.278 1.489 1.692 1.857 1.724 b (fund maturity) 1.000 1.000 1.000 0.982 0.893 Ct /Ft (mean value) 0.150 0.098 0.068 0.047 0.048 Panel D: γ = 3.4 Equity-to-bond ratio 1.266 1.485 1.691 1.954 1.832 b (fund maturity) 1.000 1.000 1.000 1.000 0.923 Ct /Ft (mean value) 0.158 0.104 0.073 0.048 0.047
  18. 18. Historical allocation 1975 1980 1985 1990 1995 2000 2005 2010 2015 -50 0 50 100 150 200 250 Inpercentoftotalallocation Equity share Bonds share
  19. 19. Concluding remarks I The optimal asset allocation and consumption path naturally depends on "behavioral assumptions": risk aversion, elasticity of intertemporal substitution and the e¤ective investment horizon. I Optimal policies for a mature fund is a useful benchmark: I Lower dependence on oil in the future. I The evolution in the ratio of above-ground to under-ground wealth. I The model structure a¤ords us some ‡exibility (utility preferences, and asset-class universe), however parameter estimation is naturally subject to uncertainty. I The model is silent about the size of the fund’s contribution to general government revenue, which would link it explicitly to the business cycle and the SWF’s role as a macro stabilizer.

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