The Elephant in the Ground: Managing Oil and Sovereign Wealth

The Elephant in the Ground:Managing Oil and Sovereign Wealth CAMP Workshop 2014 BI Business School, Oslo Ton van den Bremer, Rick van der Ploeg and Samuel Wills* Oxford Centre for the Analysis of Resource Rich Economies Department of Economics, University of Oxford *Corresponding author: samuel.wills@economics.ox.ac.uk

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) Commodity Non-commodity Largest single fund 27 countries have commodity funds Source: Sovereign Wealth Fund Institute (2014)

Norway’s fund is worth US$ 840 billion and is allocated between equity and bonds (some real estate) according to Gov’t mandate The overall asset mix has been stable... Norway Government Pension Fund Global, asset mix (%) Change in mandate ...and is set by mandate from the Ministry of Finance Ministry of Finance Mandate: Asset Sub-asset Benchmark Equity: 60% • FTSE Global All Cap index Bonds: 40% Government: 70% • Barclays Global indices Corporate: 30%

Norway’s equity allocation across sectors has been stable, and seems independent of correlation with oil prices 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

However, Norway has a large and volatile exposure to oil and gas prices in its subsoil reserves Value of Norway’s GPFG and Proven subsoil reserves at market prices(NOK billion) Government Pension Fund Global Proven subsoil reserves Source: NBIM and EIA (2013)

Questions • How should assets above the ground be allocated if there are also assets below the ground? • What if the assets below the ground are... “illiquid”? • What if some financial assets cannot be invested in? • When should assets below the ground be converted into assets above the ground? • How quickly should the proceeds be consumed?

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 This Paper 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”: 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.

Punchlines Norway’s sovereign wealth fund is well managed according to existing theory. However, it is not coordinated with subsoil oil. Incorporating oil would involve: 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. Consumption • Euler Equation: • Spend a constant share of total wealth • Precautionary savings: Save more to to manage residual volatility Extraction • Hotelling Equation: • Risk premium: Extract faster if oil price is pro-cyclical – increase rate of return on subsoil assets to compensate for extra risk

Outline 1. Portfolio allocation without oil (recap) 2. Portfolio allocation for given oil extraction a. No investment restrictions b. Investment restriction 3. Portfolio allocation if oil extraction can be chosen 4. Application to Norway

1. Portfolio allocation without oil: Model Model (following Merton, 1990) The optimisation problem Maximise utility s.t. budget constraint Fund assets where: Risky asset weights Asset prices → Proceed by setting up Hamilton-Jacobi Bellman equation, take first-order conditions (Ito’s lemma) and solve value function explicitly

1. The asset allocation problem can be separated into two steps, allowing us to solve it as a two asset problem The optimal weight of each asset i. The size of the optimal risky portfolio ii. The mix 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 → The problem will simplify to a two asset problem: one risky and one risk-free

1. Consumption will be a fixed proportion of wealth in the fund The optimal consumption level • Consumption is a fixed proportion of wealth (CRRA preferences) • Total Sovereign Wealth Fund assets will follow a geometric Brownian Motion

1. Portfolio allocation without oil: This theory is consistent with current practice in Norway’s GPFG Theory Norway’s GPFG 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: Source: Merton (1990) Source: www.nbim.no The mandates for Norway’s GPFG seem consistent with standard portfolio theory

2. Portfolio allocation for a given path of extraction: Model New Model The optimisation problem Maximise utility s.t. budget constraint where: Oil prices: Oil extraction: Oil wealth: risk-adjusted Fund assets: Total wealth: Assume oil wealth is not just sold upfront – problem becomes trivial

2. Oil can be valued using an arbitrage relationship with the traded assets in the market Valuing Oil Wealth The present value of oil wealth: Risk-adjusted discount rate: 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 Assume can’t just sell all claims to oil wealth: problem becomes trivial

2. The effect of oil on the portfolio will depend on its covariance with other assets Spanning the market • The (correlated) return on all assets is a linear combination of independent normal random variables Asset return residuals (correlated) Dependence structure - eigen-decomposition Underlying shocks (uncorrelated) • The return on oil can be expressed in terms of traded assets and a residual

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 Leverage Effect Oil/SWF value Asset weight in total wealth Hedging Effect: depends on - The asset’s covariance with oil - The asset’s “uniqueness” • Use two indices as a benchmark: • 1. Market index • 2. Oil hedging index

2. The leverage and hedging effects can be seen using a simple three-asset example Asset Weights, no investment restrictions Overview Asset 1: Uncorrelated with oil Asset 2: Correlated with oil Asset r: Risk-free

2. Asset Allocation: The punchline Invest less in • Assets positively correlated with oil: • Oil and Gas stocks • Green Energy (in the short term) 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)

2. The consumption rule for resource-exporters should be a constant share of above and below ground wealth. Consumption • The government should consume a fixed proportion of total wealth (W=F+V) • Consistent with the permanent income rule • Total wealth, appropriately hedged, will follow a geometric Brownian Motion Oxford

2. Consuming a constant share of total wealth leads to smoother spending, like Friedman’s Permanent Income Hypothesis. Oil Extraction Oil Value (V) W Wealth Consumption F V

2. Norway is currently considering divesting oil and gas stocks from its portfolio, which was also considered in 2008

2. Consciously excluding certain asset classes requires a different hedging portfolio, and more precautionary savings • Construct the closest hedging portfolio Asset Allocation Total Wealth Consumption • The risk/return tradeoff will depend on the asset that is being removed, and how important it is for hedging oil shocks • More precautionary savings to manage the risk from less diversification • Lower spending rate. Oxford

2. Consciously excluding asset classes from their portfolio will limit the ability to hedge oil Asset Weights, excluding asset 2 from the portfolio Overview Asset 1: Uncorrelated with oil Asset 2: Correlated with oil Asset r: Risk-free

2. Removing an asset class from the portfolio reduces the ability to hedge oil, requiring more precautionary savings Euler Equation Spending path Additional precautionary savings More precautionary savings… Builds up a buffer stock of assets.

3. Portfolio allocation when oil extraction can be chosen New Model The optimisation problem Maximise utility s.t. budget constraint Oil prices: Oil reserves: Oil rents: • First we’ll consider extraction, then asset weights and consumption

3. Extraction should be faster when financial assets are taken into account, but the size of the fund shouldn’t matter Optimal Extraction • We find an endogenous risk premium on the Hotelling hurdle rate, based on systematic oil risk Co-movement of SWF and oil Standard Hotelling rule Faster extraction due to SWF • 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

3. Oil price volatility should hasten extraction when it is positively correlated with the market, generating a risk premium Stylised illustration, see previous calibration Optimal Extraction Reserve Depletion • Supports and extends previous results (Pindyck, 1981; van der Ploeg, 2010) • Volatility only works through unlikely extraction costs (extractive prudence) • Ignore other assets

4. We can study the implications of this theory for Norway’s oil wealth in practice • 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 Data Method Assumptions • Exponentially declining oil production • With hedging: • Closed form for value function • Monte Carlo simulations • Without hedging: • Monte Carlo simulation

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 Average Single realisation Consumption Existing New Assets Welfare Equivalent to consumption from the GPFG: USD 4000 → USD ~4300 for every man, woman and child in Norway (permanent)

4. Achieving this result involves taking large short positions in particular sectors, such as Oil and Gas Weight of each sector in GPFG portfolio, per cent Months

4. In 2014 the Norwegian Ministry of Finance reported to the Parliament on this work, highlighting some practical constraints faced by SWFs Short Positions • Politically difficult to understand and monitor Transaction Costs • 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 Time-varying Correlations Other elements of National Wealth • Pension liabilities • Tax revenues • (Next steps) Source: Norwegian Ministry of Finance report to Storting, “The Management of the Government Pension Fund in 2013”, Section 2.4

4. But, we have other policy tools at our disposal, namely the equity/bond mix and the consumption rule Policy lever Practicality Reason Asset allocation i) Mix within equities ii) Mix between equities and bonds X ? Simplicity and Transaction Costs Possibly Consumption Possibly iii) Spending rule ? Extraction iv) Extraction rate X Geological constraints

4. The relative weight of equities should rise as oil is extracted, because oil is positively correlated with the FTSE All Cap Share of equities in the GPFG portfolio 0% ~50% 60% Leverage demand Hedging demand >4 ~1 0 V/F

4. The residual volatility in total wealth should be managed by more precautionary savings in the spending rule GPFG Spending Rule Existing New Somewhere here Months

Conclusion Norway’s sovereign wealth fund is well managed according to existing theory. However, it is not coordinated with subsoil oil. Incorporating oil would involve: 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. Consumption • Euler Equation: • Consume a constant share of total wealth • Precautionary savings: Save more to to manage residual volatility Extraction • Hotelling Equation: • Risk premium: Extract faster if oil price is pro-cyclical – increase rate of return on subsoil assets to compensate for extra risk

Appendix

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

1b. Consumption adjusts to the risk in the portfolio through precautionary savings The optimal consumption path (Euler equation) Deterministic term: Inter-temp. subst. Stochastic term: Prudence • Prudence leads to precautionary savings by increasing the slope of consumption C t • Builds up buffer stock to manage any non-diversifiable portfolio risk.

The Elephant in the Ground: Managing Oil and Sovereign Wealth