The Elephant in the Ground: Managing Oil and Sovereign Wealth CAMP Workshop 2014 BI Business School,...

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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

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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

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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:

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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







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

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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

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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

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Outline







17

2. Portfolio allocation for a given path of extraction: Model

Model


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

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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

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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

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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

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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

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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

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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







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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.

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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

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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







31

3. Portfolio allocation when oil extraction can be chosen

Model


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

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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

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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

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Outline







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

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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)

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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)

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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

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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:

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Appendix

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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

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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

The Elephant in the Ground: Managing Oil and Sovereign Wealth CAMP Workshop 2014 BI Business School,...

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