Asset Allocation For Sovereign Wealth Funds

Introduction and FactsTheoretical Framework

ImplementationConclusion

Asset Allocation for Commodity-BasedSovereign Wealth Funds

Implications for Emerging Economies

Rolando Avendaño - Javier Santiso

OECD Development Centre, 2008

OECD Development Centre Asset Allocation for Commodity-Based Sovereign Wealth Funds



Outline

1 Introduction and Facts

2 Theoretical Framework

3 Implementation

4 Conclusion




SWFs and Foreign InvestmentConceptual IssuesLiterature on Asset Allocation for Sovereign Funds

INTRODUCTIONMotivation and some Basic Facts

SWF concept: investment vehiclewith high foreign asset exposure,nonstandard liabilities and long(intergenerational) time horizon.

Assets: Long-term, active,diversified investments. Main assetclasses: bonds, equity, alternatives.

Size: Low commodity-price/exportsscenario has affected some, but stillresilient (11.6 tr to 9.5 tr estimateNov. 08)

Incentives and purpose

Stabilisation vs. SavingsPreventive/oriented strategy

Challenges for current SWFs

National strategy vs.commercial returnPassive vs. active policyStabilizing financial marketsvs. market jeopardy

Source: COFER database and International Financial Statistics





INTRODUCTIONContext, related research at the Centre

Today: Financing needs for the shortrun are important. Dry global liquidityscenario and contraction ofcross-border capital flows

Home bias / Regional bias →

Challenge to stimulate domesticeconomies. Affects allocation?

Standard portfolio approach (CAPM,VaR, etc.) insufficient for activemanagement.

Some related work at the Centre:

H. Reisen. "Commodity andnon-commodity SWFs" DeutscheBank WP, "Fonds souverains etéconomie du développement"Revue d’Economie Politique.J. Santiso "SovereignDevelopment Funds", Revued’Economie Financière.Avendano, Reisen, Santiso."Macro Management ofCommodity Booms".

External

financing

needs 2009

FX Reserves

(Dec 08)

Gap between reserves and

financing needs

Argentina 6.4 12.7 6.3

Brazil 6.7 12.5 5.8

Chile 18.6 12.1 -6.5

Colombia 8 9.7 1.7

Ecuador 6.8 11.3 4.5

Mexico 6.1 7.7 1.6

Hungary 23.3 13.8 -9.5

Kazakhstan 18.4 16.3 -2.1

Nigeria 2.7 24.3 21.6

Poland 19.7 11.9 -7.8

Russia 9.4 26.2 16.8

South Africa 16.8 10.9 -5.9

Turkey 15.8 9.4 -6.4

Ukraine 25.9 18.9 -7

China 0.3 43 42.7

India 8.8 71.9 63.1

Indonesia 10.3 10.8 0.5

Korea 21.1 24.3 3.2

Malaysia 4.5 46.6 42.1

Thailand 19.2 38.5 19.3

Source: Credit Suisse, "Are EM funding needs driving financial market\nprices?", Dec.08.

Financing Needs and International Reserves -2009





How are commodity-SWF assets allocated?Considerations for Asset Allocation

1 Traditional reserves approach

Multiple, conflicting investmentobjectives: liquidity, peg, foreigndebt, trade.Tranching facilitates management.Difficult to optimise "as a whole"

2 Country-specific criteria:

Size of reservesTransparency or accountabilityPurpose of holding reservesObjectives in managing reservesConstraints and risk-return profile

3 Market related criteria

Structural changesCyclical changes

Criteria for public sector (Reisen2008, van der Ploeg 2007):

Depleting: Hotelling,steady-stateSaving: Hartwick,commodity priceDomestic investment:Excess return, constructionprice smoothingRetiring debt: Excess costof public debt over globalreturn





Variables/constraints for SWF 6= reservesObjectives and Constraints

Constraints

Non-financial risk:reputation, operationCurrency/Asset classexposureDerivative usageInstitutional: Frequencydisclosure, benchmark

Risk-return preferences

Time HorizonUnit of accountNominal vs real returnFinding distribution by returnor risk

Risk-return expectations

Forward-looking of risk,return, asset classesSome approaches

Markowitz mean-varianceMonte Carlo simulationAsset-LiabilityOECD Development Centre Asset Allocation for Commodity-Based Sovereign Wealth Funds




Approaches to SWF Asset AllocationStudies on Reserves, Asset Management and SSA

1 Management of Reserves

International currencies → Linder (1969), Hartmann (1998),Eichengreen (2005).Jeanne and Rancière (2008) → Optimal level of reserves foremerging countries.Portes et al. (2006) → Optimal Currency Shares inInternational Reserves

2 Portfolio Choice

Dynamic stochastic optimisation (Claessens and Kreuser2004).Monte Carlo Simulation → (Weiberger and Golub 2007)Portfolio choice → Campbell 2003, Scherer 2008.

3 Contingent Claims Approach

Alfaro and Kanczuk (2003), Caballero and Panageas (2004) →Contingent reserves management.Asset-Liability approach: Rudolf and Ziemba (2004),Rozanov (2006), Binsbergen and Brandt (2006)Real Capital preservation → (Bonza et al. 2006)





Outline

1 Introduction and Facts

2 Theoretical Framework

3 Implementation

4 Conclusion




Tackling the ProblemBasic Model of Asset AllocationOptimal Allocation between Growth Assets and Hedge Assets

Portfolio Choice and the sovereign investor

Scherer (2008): Risk from non-financial assets can be hedged, at least partially,through financial assets. Different to classical CAPM, where only financial assetsare considered.

Key factor: exploit the correlation between financial and non-financial assets toreduce overall SWF risk.

Advantages:

Timely for resource-rich economiesAddressing the lack of data for SWF asset allocation studies.Similar to asset-liability management approach (both sides of the balancesheet).Defined objective: reduce total wealth volatility.Non-normal returns in short run "controlled" by SWF long-term investmentapproach (utility function)

Extensions:

Application for other commodity fundsApply to a multi-asset context: alternatives, other commodities, infrastructure,real estateLook at exposure to emerging markets





The Sovereign investor problemCase 1: Investing in one risky asset

The decision making problem The SWF can invest its financial wealth into a singleasset or cash.

r̃a ∼ N(µa, σ2a)

µa: Expected risk premium (over cash)

σa: Volatility.

The government budget moves with changes on its claim on economic net wealth.

Commodity price changes are also normally distributed:

r̃o ∼ N(µo, σ2o)

and correlate positively with asset returns, i.e.

Cov(ra, r̃o) = ρa,o > 0

.

Hotelling-Solow rule (indifferent to depletion or keeping commodity) → µo = 0.

Let θ be the fraction of importance of the SWF plays in the economies governmentbudget. Therefore:

r̃ = θwr̃a + (1 − θ)r̃o

with 1 − w representing cash holding that carries a zero risk premium and no riskin one period.





The Sovereign investor problemDecomposing demand

The SWF manager is charged to maximize the utility of total governmentwealth rather than narrowly maximizing the utility for its direct assetsunder management. Utility defined as a (quadratic) function of uncertainwealth. The goverment seeks to maximize the function:

Maxw(θwµa −

λ

2

[θ2w2σ2

a + (1 − θ)2σ2o + 2wθ(1 − θ)ρσaσo

])

Taking first order conditions and solving for w , the optimal assetallocation for a resource based SWF:

w∗ = w∗

s + w∗

h =1θ

µa

λσ2a−

1 − θ

θ

ρσo

σa

Total demand = w∗ = w∗

s︸︷︷︸

Speculative demand

+ w∗

h︸︷︷︸

Hedging demand

In the case of uncorrelated assets and commodity resources the optimalsolution is a leveraged position (with factor 1/θ) in the asset withmaximum Sharpe-ratio (reward/variance).

Observation 1:

Demand for risky assets can be descomposed between speculative andhedging. Risk-return (Sharpe) criteria is not the only one. The optimal weightof risky assets is independent from his wealth level.





Two types of DemandHegding vs Speculative demand

Hedging demand: the desirability of the asset does not only depend on Sharpe-ratio butalso on its ability to hedge out unanticipated shocks to commodity wealth. Hedgingdemand is given as the product of leverage and commodity asset beta,

βo,a =ρσo

σa

.

This is equivalent to the slope coefficient of a regression of (demeaned) asset returnsagainst (demeaned) commodity returns of the form:

(ro − ro) = βo,a(ra − ra) + ε

Positive correlation between asset and commodity price risk increases the volatility oftotal wealth. A 100% short position in the risky asset helps to manage total risk.However, in case the correlation was negative it would be necessary to increase theallocation to the risky asset.

Observation 2:

Corelation patterns between commodity prices and other assets may depict the bestinvestment profile for the SWF. The best investment profile for SWFs balances returns withhedging against commodity prices. Specific sectors provide hedging against commodityprices.





Growth and Hedge AssetsCase 2: Optimal portfolio with several assets

Extended case with two assets: one asset hedging asset (i.e. it show negativecorrelation) and another asset provides growth orthogonal to commodity wealthchanges. The setup if summarized with the following distribution:

r̃g ∼ N(µg , σ2g), r̃h ∼ N(µh, σ

2h)

where rg and rh stand for the return of growth and hedge assets with µg > µh.

The correlation assumptions are:

Cov(rh, rg) = ρh,gσhσg > 0, Cov(rh, ro) = ρh,oσhσo < 0, Cov(rg, ro) = 0

The government budget evolves to:

r̃ = θ[wg r̃g + wh r̃h] + (1 − θ)r̃o

where utility is given by

u = E(r̃ ) −λ

2

[E(r̃2) − E2(r̃)

]

And solve for wg and wh:

w∗

g =µg − βg,h · µh

λθ(1 − ρ2g,h)σ

2g−

1 − θ

θ

βg,hρh,oσoσh

(1 − ρ2g,h)

w∗

h =µh − βh,g · µg

λθ(1 − ρ2g,h)σ

2h

−1 − θ

θ

βo,h

(1 − ρ2g,h)





Demand for the growth asset can be split again into speculative demandand hedging demand:

Speculative demand will depend on its "alpha", µg − βg,h · µh,versus the hedge asset, i.e. Beta, βg,h, adjusted excess returndivided by the risk not explained by the hedge asset returns.The term ρ2

g,h can interpreted as the R2 of a regression of hedgeversus growth asset returns. If the indirect correlation is set to zero,i.e. ρr ,g = 0 then:

w∗

g =µg

λθσ2g

w∗

h =µh

λθσ2h

− ρh,oσo

σh

(1 − θ)

θ

Observation 3:

The growth asset is entirely driven by the Sharpe-ratio while the hedge assetcombines both speculative and hedge demand.

How does hedge demand change with θ?

dw∗

h

dθ=

−µh + λρh,oσhσo

λσ2hθ2

< 0

Observation 4:

Economies with falling levels of commodity resources should be moreconservative in their investments.




Implementation: "Commodity-Asset Betas"Bond Benchmark and Commodity Price Changes

US Benchmark

DS 2 Years

US Benchmark

DS 3 Years

US Benchmark

DS 5 Years

US Benchmark

DS 7 Years

US Benchmark

DS 10 Years

US Benchmark

DS 30 Years

0.007 0.003 -0.001 -0.003 -0.005 -0.021

0.108 0.050 -0.017 -0.051 -0.080 -0.314

0.013 0.007 -0.002 -0.001 -0.008 -0.027

0.201 0.105 -0.026 -0.013 -0.114 -0.409

0.110 0.096 0.071 0.065 0.048 0.020

1.666 1.455 1.074 0.976 0.729 0.293

0.006 0.005 0.001 -0.002 -0.009 -0.031

0.096 0.074 0.013 -0.024 -0.142 -0.473

0.008 0.004 -0.008 -0.004 -0.019 -0.038

0.118 0.057 -0.117 -0.063 -0.293 -0.574

-0.044 -0.048 -0.078 -0.077 -0.116 -0.133

-0.668 -0.716 -1.172 -1.157 -1.748 -2.018

-0.033 -0.037 -0.040 -0.036 -0.036 -0.054

-0.494 -0.559 -0.595 -0.547 -0.549 -0.817

-0.044 -0.052 -0.056 -0.039 -0.042 -0.070-0.659 -0.782 -0.847 -0.593 -0.626 -1.053

-0.117 -0.128 -0.182 -0.180 -0.213 -0.252

-1.774 -1.944 -2.787 -2.745 -3.285 -3.908

Note: Benchmarks for bonds from Thomson Datastream (DS Bemchmark) from January 1990 to

January 2009. The first line is the correlation coefficient, and the second provides itst-value,

Monthly

Quarterly

Yearly

Monthly

Quarterly

Yearly

Monthly

Asset Returns vs Oil Price Changes

Asset Returns vs Copper Price Changes

Asset Returns vs Commodity Index Change

Correlation U.S Benchmark Bonds with Commodity Price Changes

Quarterly

Yearly

Monthly data → No pattern oncorrelations. Reducing datafrequency shows negativecorrelations.

Correlation and significance risewhen decreasing the frequency.Global equities provide no hedgeagainst oil price changes.

Sector equity indexes →

Significant negative correlationfor two sectors (defensiveconsumer and health care) thattend to do well when theeconomy does badly.




Global Equities and CommoditiesGlobal Equities and Commodity Price Changes

World

Global

Equity

World Oil

and Gas

World Basic

Materials

World

Industrials

World

Consumer

Goods

World Health

Care

World

Consumer

Services

World

Telecoms

World

Utilities

World

Financials

0.074 0.046 0.063 0.077 0.059 0.038 0.090 0.082 0.024 0.068

1.116 0.686 0.954 1.167 0.895 0.576 1.361 1.238 0.358 1.0250.152 0.102 0.150 0.161 0.127 0.084 0.177 0.156 0.073 0.155

2.313 1.547 2.274 2.452 1.918 1.272 2.705 2.371 1.100 2.361

0.308 0.175 0.215 0.312 0.238 0.158 0.332 0.464 0.115 0.237

4.873 2.680 3.302 4.943 3.691 2.407 5.299 7.882 1.745 3.673

0.065 0.052 0.062 0.073 0.044 0.040 0.086 0.002 0.013 0.100

0.981 0.786 0.934 1.102 0.662 0.605 1.305 0.034 0.193 1.511

0.161 0.140 0.157 0.180 0.123 0.096 0.191 0.033 0.067 0.228

2.449 2.129 2.391 2.748 1.858 1.447 2.921 0.499 1.014 3.522

0.213 0.171 0.218 0.249 0.178 0.059 0.234 0.060 0.057 0.309

3.270 2.611 3.355 3.866 2.726 0.893 3.626 0.901 0.863 4.878

0.144 0.110 0.142 0.156 0.104 0.115 0.178 0.012 0.071 0.210

2.190 1.666 2.159 2.368 1.566 1.733 2.721 0.179 1.068 3.2360.265 0.218 0.261 0.279 0.190 0.207 0.306 0.057 0.147 0.358

4.124 3.357 4.061 4.367 2.907 3.184 4.830 0.858 2.229 5.766

0.449 0.326 0.397 0.447 0.380 0.320 0.458 0.168 0.222 0.605

7.557 5.184 6.512 7.506 6.182 5.075 7.742 2.566 3.422 11.430

Note: Benchmarks for bonds from Thomson Datastream (DS Bemchmark) from January 1990 to January 2009. The first line is the correlation coefficient, and the second proveds its t-value,

Monthly

Quarterly

Yearly

Global Equities and Commodities

Monthly

Quarterly

Yearly

Monthly

Quarterly

Yearly

Global Equity Indexes (per sector) vs Copper Price Changes

Global Equity Indexes (per sector) vs Commodity Price Index Change

Global Equity Indexes (per sector) vs Oil Price Changes




Emerging Bonds and CommoditiesEMBI and Commodity Price Changes

Brazil Chile China Indonesia Kazakhstan Mexico Malaysia Morocco Poland Russia South Turkey Thailand Venezuela

-0.014 -0.004 -0.013 0.180 0.695 0.024 0.030 -0.004 0.004 0.077 0.074 0.054 0.027 0.103

-0.138 -0.034 -0.126 1.777 9.366 0.237 0.287 -0.038 0.042 0.746 0.721 0.523 0.264 1.0070.009 0.054 -0.021 0.400 0.953 0.084 0.077 0.008 0.022 0.162 0.144 0.129 0.060 0.235

0.048 0.296 -0.112 2.392 17.184 0.459 0.423 0.046 0.119 0.899 0.795 0.714 0.327 1.324

-0.103 0.095 -0.093 0.207 1.000 0.051 0.069 -0.015 0.048 0.198 0.088 0.024 0.159 0.341-0.252 0.234 -0.228 0.518 N.A. 0.126 0.170 -0.037 0.119 0.495 0.218 0.059 0.394 0.888

-0.003 -0.007 -0.012 0.133 0.582 0.025 0.031 0.007 -0.007 0.099 0.090 0.075 0.073 0.151

-0.025 -0.064 -0.117 1.300 6.940 0.245 0.302 0.072 -0.064 0.963 0.878 0.730 0.710 1.480

0.024 0.038 -0.038 0.301 0.845 0.076 0.057 0.036 -0.012 0.175 0.144 0.139 0.134 0.281

0.130 0.206 -0.210 1.730 8.655 0.416 0.315 0.195 -0.067 0.974 0.800 0.766 0.741 1.602-0.101 0.010 -0.275 0.205 1.000 -0.024 -0.051 0.010 -0.151 0.171 0.003 0.005 0.222 0.490

-0.249 0.024 -0.700 0.514 N.A. -0.059 -0.126 0.024 -0.373 0.426 0.007 0.012 0.557 1.376

0.024 0.038 -0.038 0.301 0.845 0.076 0.057 0.036 -0.012 0.175 0.144 0.139 0.134 0.281

0.130 0.206 -0.210 1.730 8.655 0.416 0.315 0.195 -0.067 0.974 0.800 0.766 0.741 1.6020.062 0.076 0.050 0.646 0.884 0.134 0.126 0.043 0.061 0.222 0.210 0.185 0.101 0.286

0.342 0.415 0.272 4.631 10.384 0.740 0.693 0.235 0.336 1.247 1.179 1.034 0.555 1.638

-0.080 0.033 -0.217 0.719 1.000 0.020 -0.021 0.059 -0.083 0.200 0.019 0.011 0.173 0.479

-0.197 0.081 -0.543 2.537 N.A. 0.049 -0.050 0.146 -0.204 0.500 0.046 0.026 0.430 1.336

Note: Benchmarks for Emerging Market bonds from JP Morgan EMBI index (Thomson) from January 2001 to

January 2009. The first line is the correlation coefficient, and the second proveds its t-value,

Emerging Market Bonds with Commodity Price Changes

Bond Returns vs Oil Price Changes

Bond Returns vs Copper Price Changes

Bond Returns vs Commodity Index Change

Yearly

Monthly

Quarterly

Yearly

Monthly

Quarterly

Monthly

Quarterly

Yearly




Emerging Equity and CommoditiesEmerging Equity Index and Commodity Price Changes

Emerging

Equity

Emerging

Oil and

Gas

Emerging

Basic

Materials

Emerging

Industrials

Emerging

Consumer

Goods

Emerging

Health

Care

Emerging

Consumer

Services

Emerging

Telecoms

Emerging

Utilities

Emerging

Financials

Emerging

Technology

0.085 0.074 0.098 0.100 0.068 -0.050 -0.091 0.051 0.051 0.076 0.196

0.828 0.717 0.955 0.977 0.661 0.487 0.881 0.495 0.498 0.739 1.939

0.204 0.184 0.217 0.217 0.166 -0.140 -0.221 0.147 0.140 0.199 0.380

1.140 1.027 1.219 1.219 0.922 0.776 1.243 0.814 0.776 1.114 2.251

0.247 0.266 0.282 0.265 0.269 -0.147 -0.220 0.154 0.135 0.242 0.163

0.625 0.675 0.720 0.673 0.685 0.364 0.552 0.381 0.333 0.611 0.404

0.030 0.042 0.015 0.033 0.024 0.069 0.045 -0.009 0.009 0.019 0.145

0.295 0.410 0.143 0.318 0.237 0.675 0.436 -0.090 0.083 0.189 1.425

0.117 0.148 0.082 0.108 0.078 -0.164 -0.145 0.045 0.054 0.106 0.360

0.647 0.817 0.452 0.596 0.429 0.912 0.801 0.248 0.296 0.584 2.112

0.178 0.217 0.106 0.166 0.134 -0.200 -0.251 0.049 0.050 0.177 0.462

0.443 0.544 0.260 0.414 0.332 0.501 0.635 0.119 0.123 0.441 1.278

0.125 0.124 0.110 0.138 0.112 0.114 0.136 0.080 0.097 0.120 0.260

1.221 1.214 1.071 1.352 1.092 1.108 1.331 0.775 0.941 1.170 2.606

0.232 0.246 0.210 0.235 0.194 0.193 0.243 0.159 0.170 0.224 0.460

1.304 1.388 1.178 1.325 1.084 1.080 1.374 0.885 0.942 1.262 2.840

0.352 0.387 0.293 0.353 0.295 0.233 0.398 0.210 0.246 0.363 0.545

0.923 1.028 0.751 0.925 0.757 0.587 1.061 0.525 0.621 0.953 1.592

Note: Benchmarks for Emerging Market Equity Indexes from Thomson from January 2001 to

January 2009. The first line is the correlation coefficient, and the second proveds its t-value,

Quarterly

Yearly

Emerging Equities vs Commodities

Emerging Equity Indexes (per sector) vs Oil Price Changes

Emerging Equity Indexes (per sector) vs Copper Price Changes

Emerging Equity Indexes (per sector) vs Commodity Price Index Change

Monthly

Quarterly

Yearly

Monthly

Monthly

Quarterly

Yearly




Summary: Oil




Summary: Copper




Remarks

U.S. bonds provide hedgingagainst oil/copper for highmaturities.

Emerging bonds show lowcorrelation and positive withoil/copper, with exceptions.

Global equities and Emergingequities show a positive beta withcommodities.




Conclusion

Principles of portfolio theory apply for SWF, but non-financial assets should be considered.

The SWF decision making problem can be modeled as optimal asset allocation with endowed,non-tradable wealth.

Allocations can be separated: an optimal growth portfolio and an oil price risk hedgingportfolio. Countries need to look at the commodity fluctuations in the long run

What drives the optimal asset allocation for a SWF over time? The fraction of risky assets isdriven by financial wealth relative to resource wealth.

For young SWF where financial wealth is low relative to resource wealth a more risky assetallocation is optimal. Young SWFs need to invest more aggresively in the beginning, beforeshifting to non-risky assets. Comparable with real data. Mature SWFs with large assetsrelative to natural resources should dial back their risks.

Investment in uncorrelated sectors with commodity are beneficial for reducing volatility.Domestic spending may be beneficial under these circumstances. Implication for SWFs anddomestic investment.

New asset classes (e.g. infrastructure) can provide risk reduction.




Next step: Asset Allocation Chile

Implement standard dynamicprogramming for optimalextraction using Bellmanequation where

Vt = Max(

ftξt−φξ2t

)

+1

1 + rVt+1(ot−ξt)

ft : Projected oil price for period t.

ξt : is the level of extraction.

ftξt : Copper revenues.

ot : State variable (copper rvs)

Calibrate for Chile:

Copper reserves= 77 millions tmfin reserves (2008)

Copper price= 6500 U$/MT -A.M. OFFICIAL ME-Copper

Current extraction= 1,665 milliontmf per year.

Copper price growth=3.56%

Risk free rate=4%




Thank you


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