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1
The Elephant in the Ground:Managing Oil and Sovereign Wealth
CAMP Workshop 2014BI Business School, Oslo
Ton van den Bremer, Rick van der Ploeg and Samuel Wills*Oxford Centre for the Analysis of Resource Rich EconomiesDepartment of Economics, University of Oxford*Corresponding author: [email protected]
O XCARRE O x f o r d C en t r e f o r t h e A n a l y s i s
o f R e s o u r c e R i c h E c o n o m i e s
2
ChinaUAE
Norway
Saudi A
rabia
Singa
pore
Kuwait
Hong Kong
Russia
Qatar
Kazakh
stan
Australi
a
Algeria
South Kore
Libya Ira
nAlas
ka
Malaysi
aBrunei
Azerbaij
anFra
nceChile
0
200
400
600
800
1000
1200
1400
Sovereign Wealth Funds account for US$ 6.4 trillion in assets. Norway is a useful example as the largest single fund
Largest SWFs by country, total SWF assets (US$ billion, 2014)
Source: Sovereign Wealth Fund Institute (2014)
CommodityNon-commodity
27 countries have commodity funds
Largest single fund
3
Norway’s fund is worth US$ 840 billion and is allocated between equity and bonds (some real estate) according to Gov’t mandate
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110%
10%20%30%40%50%60%70%80%90%
100%EquityFixed IncomeThe overall
asset mix has been stable...
...and is set by mandate from the Ministry of Finance
Change in mandate
Equity: 60%
Bonds: 40%Government: 70%
Corporate: 30%
Asset Sub-asset BenchmarkMinistry of Finance Mandate:
• FTSE Global All Cap index
• Barclays Global indices
Norway Government Pension Fund Global, asset mix (%)
4
Norway’s equity allocation across sectors has been stable, and seems independent of correlation with oil prices
Oil & G
as
Basic M
aterials
Utilities
Industrials
Technology
Financia
ls
Telecom.
Cons. Se
rvice
s
Cons. Goods
Health Care
0%
5%
10%
15%
20%
25%
(0.20)
(0.10)
-
0.10
0.20
0.30
0.40
0.50 20092011corr_O,i (RHS)
Norway GPFG equity allocation by sector and correlation with oil price (%) Snapshot
Diversified:• Holds equity in 7427 companies (2012)
Well-performing:• Net returns: - 2012: 11.2% - Since 1998: 3.0%
Well-managed:• 10/10: Linaburg-Maduell Transparency Index (SWF Institute)• 2nd : Governance and transparency index (Truman, 2008)
Zero/negative correlation with oil
5
However, Norway has a large and volatile exposure to oil and gas prices in its subsoil reserves
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000GasOil
Source: NBIM and EIA (2013)
Value of Norway’s GPFG and Proven subsoil reserves at market prices(NOK billion)Government Pension
Fund Global Proven subsoil reserves
6
Questions
1. How should assets above the ground be allocated if there are also assets below the ground?a. What if the assets below the ground are... “illiquid”?b. What if some financial assets cannot be invested in?
2. When should assets below the ground be converted into assets above the ground?
3. How quickly should the proceeds be consumed?
7
This paper combines three strands of literature
Asset Allocation
•Markowitz (1952): Mean-variance portfolio theory•Tobin (1958): Separation theorem•Sharpe (1964): CAPM and market portfolio•Merton (1990): Continuous time finance•Elton and Gruber (1998): Many extensions
Oil Extraction
•Hotelling (1931): Marginal oil rent grows at rate of interest (det.)•Pindyck (1981): Volatility hastens extraction (stoch.)•Gaudet and Khadr (1991): Includes technology shocks•Note: Few SWFs established when this work was being done.
'''( ) / ''( )C CCR UP U C''( ) / '( )CRRA CU C U C
Consumption under volatility
•Kimball (1990) and Carroll (1992): Build up buffer stock of savings if income stream is volatile. Driven by third moment of utility, “prudence”:
This Paper
8
Punchlines
Asset allocation
Portfolio Equation: • Leverage Effect: Hold more of all risky assets – wealth outside fund.• Hedging Effect: Hold fewer assets positively correlated with oil (simplest case) – offset oil fluctuations.
ConsumptionEuler Equation: • Spend a constant share of total wealth• Precautionary savings: Save more to to manage residual volatility
ExtractionHotelling Equation:• Risk premium: Extract faster if oil price is pro-cyclical – increase rate of return on subsoil assets to compensate for extra risk
Norway’s sovereign wealth fund is well managed according to existing theory. However, it is not coordinated with subsoil oil. Incorporating oil would involve:
9
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
10
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
11
1. Portfolio allocation without oil: Model
Risky asset weights i ii
Nw
F
P
Model (following Merton, 1990)
The optimisation problem
11
1(
1)C
U C
,, Max ( )t
w Ct
J F t E U C e d
Maximise
utility
1 1
m m
i i i i ii i
dF w F r dt rF C dt w F dZ
s.t. budget constraint
where:1 i i
n
iN PF
Fund assets
i ii ii idP Pdt PdZ Asset prices
→ Proceed by setting up Hamilton-Jacobi Bellman equation, take first-order conditions (Ito’s lemma) and solve value function explicitly
12
1. The asset allocation problem can be separated into two steps, allowing us to solve it as a two asset problem
iiw w
ii. The mix of the optimal risky portfolioi. The size of the optimal risky portfolio
Size of portfolio depends on:• Risk aversion: 1/θ
• More risk averse → fewer risky assets• Risk/return of the market as a whole:
Weight in portfolio depends on:• Return:
• Covariance with other assets:
• Risk/return of market as a whole: ν
1
1( )
m
i ij jjv r
w v
1jij iv
1 1)(
m
j
m
i ji jv v r
( )i r
The optimal weight of each asset
→ The problem will simplify to a two asset problem: one risky and one risk-free
13
1. Consumption will be a fixed proportion of wealth in the fund
The optimal consumption level
( ) ( )C s tFt
• Consumption is a fixed proportion of wealth (CRRA preferences)
• Total Sovereign Wealth Fund assets will follow a geometric Brownian Motion
*dF Fdt w FdZ
14
1. Portfolio allocation without oil: This theory is consistent with current practice in Norway’s GPFG
Theory Norway’s GPFG
The mandates for Norway’s GPFG seem consistent with standard portfolio theory
Source: Merton (1990) Source: www.nbim.no
a. Asset allocation can be split into two steps
a. Assets are allocated in two stages, according to government mandate
i. Construct a diversified portfolio of all risky assets, independent of preferences (..ice cream and raincoats)
i. The FTSE All Cap index is the benchmark for asset shares in the Equity fund
ii. Find mix between the optimal risky portfolio and the risk free asset based on preferences
ii. The Equity/Bond mix is set by government, and can change with risk appetite (eg. 2009)
b. Consumption a linear function of wealth: b. Fixed drawdown rule:
( ) ( )C s tFt 0.04*( ) ( )C t F t
15
16
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
17
2. Portfolio allocation for a given path of extraction: Model
Model
The optimisation problem
11
1(
1)C
U C
,, Max ( )t
w Ct
J t E U C dW e
Maximise
utility
s.t. budget constraint
where:
1( ) i
n
i iPF t N
Fund assets:
1
1
( ) ( )m
i ii
m
i i i
O
i
d w F r dt rF C dt
w
W P O dV
F dZ
( ) ( ) ( )W t F t V t Total wealth:
Oil prices: ( ) ( ) ( )O O O O O OdP t P t dt P t dZ
New
Oil wealth: ( ) ( ) ( ) /OV t P t O t
Oil extraction: ( ) (0) tO t O e
risk-adjusted
Assume oil wealth is not just sold upfront – problem becomes trivial
18
2. Oil can be valued using an arbitrage relationship with the traded assets in the market
( ) ( )( ) OP t O tV t
1
( )m
O i ii
r r
The present value of oil wealth:
Risk-adjusted discount rate:
Valuing Oil Wealth
What you need to know: - Current oil price and production - Future path of production - Co-movement of oil with traded assets
What you don’t need to know: - Future oil prices
( ) ( )O tP O t
i
Assume can’t just sell all claims to oil wealth: problem becomes trivial
19
2. The effect of oil on the portfolio will depend on its covariance with other assets
,0 ,1 , 0
1,1 1,1 1
,1 ,
0
0
O O O mO
m
m m mm m
dZ du
dZ du
dZ du
• The (correlated) return on all assets is a linear combination of independent normal random variables
Spanning the market
Asset return residuals (correlated)
Underlying shocks (uncorrelated)
Dependence structure - eigen-decomposition
1/2 1/2( )( )dt dt
• The return on oil can be expressed in terms of traded assets and a residual 1
0,0O O Od dd ZZ u
20
2. Oil introduces additional (offsetting) leverage and hedging demands for each asset
• Oil should have a wealth and a substitution effect on portfolio weights.
Portfolio Weights
Asset weight in SWF
Asset weight in total wealth
Leverage Effect Oil/SWF value
)(i i i i
Vw w
Fw
Hedging Effect: depends on - The asset’s covariance with oil - The asset’s “uniqueness”
Use two indices as a benchmark:1. Market index2. Oil hedging index
21
2. The leverage and hedging effects can be seen using a simple three-asset example
Overview Asset 1: Uncorrelated with oil
Asset r:Risk-free
Asset 2:Correlated with oil
Asset Weights, no investment restrictions
22
2. Asset Allocation: The punchline
• Assets positively correlated with oil:• Oil and Gas stocks• Green Energy (in the short term)
Invest less in
Invest more in
• Assets negatively correlated with oil:• Businesses where oil is an input... eg:
- Plastic manufacturing - Transport - Consumer goods (see slide 4)
• Green Energy (in the long term)
Oxford 23
2. The consumption rule for resource-exporters should be a constant share of above and below ground wealth.
• The government should consume a fixed proportion of total wealth (W=F+V)• Consistent with the permanent income rule
(( ))C t s W t
Consumption
• Total wealth, appropriately hedged, will follow a geometric Brownian Motion
W W WdW Wdt w WdZ
24
2. Consuming a constant share of total wealth leads to smoother spending, like Friedman’s Permanent Income Hypothesis.
Oil Extraction
Oil Value (V)
Wealth ConsumptionW
F
V
25
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
26
2. Norway is currently considering divesting oil and gas stocks from its portfolio, which was also considered in 2008
Oxford 27
2. Consciously excluding certain asset classes requires a different hedging portfolio, and more precautionary savings
Asset Allocation
• Construct the closest hedging portfolio
Total Wealth
• The risk/return tradeoff will depend on the asset that is being removed, and how important it is for hedging oil shocks
Consumption
• More precautionary savings to manage the risk from less diversification• Lower spending rate.
28
2. Consciously excluding asset classes from their portfolio will limit the ability to hedge oil
Overview Asset 1: Uncorrelated with oil
Asset r:Risk-free
Asset 2:Correlated with oil
Asset Weights, excluding asset 2 from the portfolio
29
2. Removing an asset class from the portfolio reduces the ability to hedge oil, requiring more precautionary savings
2222 22
11(1 )2
t
O O
E dC r VdC W
wt
Euler Equation
Spending path
More precautionary savings…
Builds up a buffer stock of assets.
Additional precautionary savings
30
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
31
3. Portfolio allocation when oil extraction can be chosen
Model
The optimisation problem
11
1(
1)C
U C
, ,, , Max (, )o t
wt
OCJ F P t E US C e d
Maximise
utility
s.t. budget constraint 1
1
( ) ( ( , ))m
i ii
m
i i i
o
i
dF P Ow F r dt rF C dt
w F dZ
New
dS Odt
Oil prices: ( ) ( ) ( )O O O O O OdP t P t dt P t dZ
Oil reserves:
Oil rents: ( , ) ( )o oP O PO G O
• First we’ll consider extraction, then asset weights and consumption
32
3. Extraction should be faster when financial assets are taken into account, but the size of the fund shouldn’t matter
• We find an endogenous risk premium on the Hotelling hurdle rate, based on systematic oil risk
Optimal Extraction
Standard Hotelling rule Faster extraction due to SWF
Co-movement of SWF and oil
•Risk premium generated by extracting faster• O declines faster• Extraction costs decline faster
•Extraction is positively correlated with the oil price – extract more when price is high
1 1 12 2( ) ( )O O
k kk k OO OdO r r P r r O dt O dZ
33
3. Oil price volatility should hasten extraction when it is positively correlated with the market, generating a risk premium
Optimal Extraction Reserve Depletion
Stylised illustration, see previous calibration
• Supports and extends previous results (Pindyck, 1981; van der Ploeg, 2010)• Volatility only works through unlikely extraction costs (extractive prudence)• Ignore other assets
34
Outline
1. Portfolio allocation without oil (recap)
3. Portfolio allocation if oil extraction can be chosen
2. Portfolio allocation for given oil extraction
a. No investment restrictions
b. Investment restriction
4. Application to Norway
35
4. We can study the implications of this theory for Norway’s oil wealth in practice
Data
Norway’s benchmarks:• FTSE All Cap index: Monthly, 2009-2014
• Disaggregated by sector• Barclays Global Aggregate Index: Monthly, 2009-2014• Brent Crude Oil Price: Monthly, 2009-2014
Method
• With hedging:• Closed form for value function• Monte Carlo simulations
• Without hedging:• Monte Carlo simulation
Assumptions
• Exponentially declining oil production
36
0 50 100 150 200 2500
5
10
15
20
25
30
35
40
4. Hedging oil in the GPFG makes consumption smoother – in mean and variance – and increase welfare as if the dividend was 3-9% higher
USD billions, preliminary
0 50 100 150 200 2502
3
4
5
6
7
8
9
10
New
Existing
0 50 100 150 200 250500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
Consumption
Assets
Average Single realisation
Welfare
Equivalent to consumption from the GPFG: USD 4000 → USD ~4300for every man, woman and child in Norway (permanent)
37
4. Achieving this result involves taking large short positions in particular sectors, such as Oil and Gas
100 200 300 400 500 600
-3
-2
-1
0
1
2
3
OGASBMATINDSCGDSHEALCSRVTELEUTILFINLTECH
Weight of each sector in GPFG portfolio, per cent
Months
38
4. In 2014 the Norwegian Ministry of Finance reported to the Parliament on this work, highlighting some practical constraints faced by SWFs
Source: Norwegian Ministry of Finance report to Storting, “The Management of the Government Pension Fund in 2013”, Section 2.4
Short Positions
Transaction Costs
Time-varying Correlations
Other elements of National Wealth
• Politically difficult to understand and monitor
• Expensive to dynamically rebalance each month
• Between oil and each sector – source of the shock matters (Kilian, 2009)
• Between each sector• Particularly during the crisis
• Pension liabilities• Tax revenues
(Next steps)
39
4. But, we have other policy tools at our disposal, namely the equity/bond mix and the consumption rule
Asset allocation
Consumption
Extraction
i) Mix within equities
ii) Mix between equities and bonds
iii) Spending rule
iv) Extraction rate
Policy lever
X
?
?
X
Practicality Reason
Simplicity and Transaction Costs
Possibly
Possibly
Geological constraints
40
4. The relative weight of equities should rise as oil is extracted, because oil is positively correlated with the FTSE All Cap
)(i i i i
Vw w
Fw
Early years Today After exhaustion
-1
-0.5
0
0.5
1
1.5
Share of equities in the GPFG portfolio
Leverage demand
Hedging demand
0% ~50% 60%
V/F >4 ~1 0
41
4. The residual volatility in total wealth should be managed by more precautionary savings in the spending rule
0 50 100 150 200 2500
5
10
15
20
25
30
35
40
GPFG Spending Rule
2222 22
11(1 )2
t
O O
E dC r VdC W
wt
New
Existing
Somewhere here
Months
42
Conclusion
Asset allocation
Portfolio Equation: • Leverage Effect: Hold more of all risky assets – wealth outside fund.• Hedging Effect: Hold fewer assets positively correlated with oil (simplest case) – offset oil fluctuations.
ConsumptionEuler Equation: • Consume a constant share of total wealth•Precautionary savings: Save more to to manage residual volatility
ExtractionHotelling Equation:• Risk premium: Extract faster if oil price is pro-cyclical – increase rate of return on subsoil assets to compensate for extra risk
Norway’s sovereign wealth fund is well managed according to existing theory. However, it is not coordinated with subsoil oil. Incorporating oil would involve:
43
Appendix
44
The Ministry of Finance considered subsoil oil in 2008, when evaluating whether oil and gas stocks should be excluded from the SWF
• 2008: Norway’s Ministry of Finance considered divesting Oil and Gas stocks– Oil and gas stocks highly correlated with oil price– Rejected because: small benefit, lower returns/higher volatility, manage oil
price risk through contracts/GPFG– Ignored coordinating extraction and investment, and spreading risk over many
asset classes
• 2014: Reconsidering divesting Oil and Gas stocks– Environmental reasons
45
1b. Consumption adjusts to the risk in the portfolio through precautionary savings
The optimal consumption path (Euler equation)
• Builds up buffer stock to manage any non-diversifiable portfolio risk.
2 2[ ]( )
/ 1
2t rE dC d
CRPwt
C
Deterministic term: Inter-temp. subst.
Stochastic term: Prudence
C
t
• Prudence leads to precautionary savings by increasing the slope of consumption