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97

* Corresponding author. King Abdullah Petroleum Studies and Research Center (KAPSARC), P.O. Box 88550, Riyadh

11672, Saudi Arabia. Phone: 966-536002497, E-mail: axel.pierru@kapsarc.org.

** King Abdullah Petroleum Studies and Research Center (KAPSARC), P.O. Box 88550, Riyadh 11672, Saudi Arabia.

Phone: 966-536004253, E-mail: walid.matar@kapsarc.org.

The Energy Journal, Vol. 35, No. 2. Copyright 䉷2014 by the IAEE. All rights reserved.

The Impact of Oil Price Volatility on Welfare in the Kingdom of

Saudi Arabia: Implications for Public Investment

Decision-making

Axel Pierru* and Walid Matar**

ABSTRACT

Since real oil price is positively correlated with real consumption and domestic

income in Saudi Arabia, a risk premium needs to be considered when assessing

the net present value of oil-related public investment projects. For projects gen-

erating additional oil exports, this risk premium quantiﬁes the cost of increased

dependence on oil revenues. For projects transforming oil into products whose

prices are less correlated with the Saudi economy, it quantiﬁes the beneﬁt from

reducing the aggregate risk. The value of this risk premium depends on expec-

tations about future consumption and oil price. By considering alternative as-

sumptions, we show that over a one-year horizon this risk premium could range

between 1.3% and 5% of the expected oil-related cash ﬂow, with higher premia

for longer planning horizons. We discuss the implications of these calculations

for energy-related public projects in Saudi Arabia and, more generally, for public

decision-making in resource-rich countries.

Keywords: Risk premium, Oil, Public investment, NPV, Domestic income,

Saudi Arabia.

http://dx.doi.org/10.5547/01956574.35.2.5

1. INTRODUCTION

Maximizing economic welfare is a primary objective of policymakers worldwide. How-

ever, under the reasonable premise that agents are risk averse, the uncertainty surrounding the

economic growth rate has a social cost, usually determined as the loss of welfare that a representative

agent is willing to incur to get rid of ﬂuctuations in his consumption or income. Though this cost

may be negligible in certain economies, this may not be the case for countries that rely on com-

modity exports revenue. Since the Kingdom of Saudi Arabia is the world’s largest oil exporter, a

considerable portion of its gross domestic income and government revenues depends on the crude

oil price. As a consequence, Saudi domestic income and aggregate consumption are likely to be

variable throughout time and signiﬁcantly correlated with the crude oil price. In recent years, oil-

related exports have on average represented around half of the Saudi nominal Gross Domestic

Product (GDP). Over the last two decades, the standard deviation of changes in the annual average

price of Arabian Light crude oil is 25%. A one-standard-deviation shock to the oil price therefore

98 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

1. The proposals for solar and nuclear energy were announced by the King Abdullah City for Atomic and Renewable

Energy at the Fourth Saudi Solar Energy Forum (2012).

represents an income shock equivalent to 12.5% of Saudi GDP, which is high relative to the GDP

volatility in most countries.

For public investment decision-making in Saudi Arabia, this raises the question of the risk

premium associated with the crude oil price. In other words, when assessing a public project’s net

present value, by which amount should its expected oil-related cash ﬂows be adjusted? This ad-

justment quantiﬁes the social cost—or beneﬁt—generated by the correlation of these cash ﬂows

with economic growth. Considering this risk premium may affect the decision making pertaining

to energy-related public projects in Saudi Arabia.

The sustainability of the current path of Saudi domestic oil consumption has recently been

questioned (e.g., Gately et al. (2012)). To curb the growth in domestic oil demand and thus free

additional oil for export, various options are currently being considered by Saudi authorities, es-

pecially the diversiﬁcation of the Saudi energy mix and investments in energy efﬁciency. In partic-

ular, the Saudi power sector relies almost exclusively on oil and natural gas. Developing new energy

sources for power generation would therefore help preserve oil exports, as in some regions of the

Kingdom the marginal power generation technology is based on the combustion of oil products.

Saudi Arabia thus announced

1

a solar power generation capacity target of 41 GW by 2032 in an

attempt to decrease oil consumption in the electricity sector. The Kingdom is also exploring the

possibility of introducing nuclear power capacity in its energy mix over the coming decades. Co-

operation and research agreements have thus been signed with France, South Korea and China to

advance this effort. In addition, the national oil company Saudi Aramco is developing oil and gas

ﬁelds in the eastern and northern provinces to secure additional future production. All these projects,

whose proﬁtability is ultimately driven by increased oil exports, may potentially be negatively

impacted by this risk premium.

Alternatively, any project turning oil into a product whose price is less correlated with the

Saudi economy should beneﬁt from an adjustment quantifying the gain from increased risk diver-

siﬁcation (i.e., a negative risk premium). The ongoing move towards downstream chemicals re-

quiring crude-oil-based feedstock may provide examples of such diversifying projects. More gen-

erally, the Kingdom is committed to use its oil resources to diversify its economy and reduce its

dependence on oil revenues through physical and social investments.

Quantifying the risk premium will provide a more accurate valuation of all public energy-

related projects in the Kingdom. The literature dealing with macroeconomic ﬂuctuations in Saudi

Arabia (e.g., Rosser and Sheehan (1995), Dibooglu and Aleisa (2004), Mehrara and Oskoui (2006))

has not addressed this issue. The international literature in general offers very few empirical as-

sessments of risk premia to consider when valuing public investment projects. For instance, Van

Ewjik and Tang (2003) discuss the value of risk premia for public projects in the Netherlands;

Gollier et al. (2011) discuss this issue in the French context. For the European Union, Durand-

Lasserve et al. (2010) compute a risk premium associated with the CO

2

price that is consistent with

the optimum of their global general equilibrium model. However, to the best of our knowledge,

there is no empirical assessment of the risk premium that would be associated with a commodity

exported by a resource-rich country. This paper proposes an empirical assessment of the risk pre-

mium that could be attributed to crude oil price by Saudi authorities. A signiﬁcant part of the

considerations and methodology presented here could however be transposed to other resource-rich

countries, like other OPEC members.

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia /99

Copyright 䉷2014 by the IAEE. All rights reserved.

Figure 1: Real Oil Price and Saudi GDP, Command-basis GDP and Consumptions

(1987–2010)

The next section establishes a simple framework for public investment decision making.

Subsection 2.1 examines how past Saudi aggregate consumption and domestic income have been

volatile and correlated with crude oil price. In this respect, to become a measure of domestic income,

the real GDP has to be adjusted for improvements (or deteriorations) in the Kingdom’s terms of

trade. We suggest using a command-basis GDP. Subsection 2.2 resumes Gollier’s (2007) derivation

of the risk premium formula and discusses practical issues for the assessment of this risk premium,

as well as related questions on public investment decision-making in the Kingdom. Subsection 2.3

makes some assumptions that will serve to compute the risk premium. Through a simple assessment

of the social cost of macroeconomic risks, Section three proposes a ﬁrst calibration of the short-

term (i.e., over a one-year horizon) risk premium associated with oil price. Section four uses two

alternative approaches to provide estimates of this risk premium in the long run (i.e., over longer

planning horizons): an approach based on a restrictive joint log-normal assumption and another

based on cointegration analysis. The last section discusses the implications of these calculations for

energy-related public projects in Saudi Arabia and, more generally, for public decision-making in

resource-rich countries.

2. A SIMPLE FRAMEWORK FOR PUBLIC INVESTMENT DECISION-MAKING

2.1 Real Oil Price, Saudi Consumption and Domestic Income: A First View

Figure 1 shows the Kingdom’s per-capita Gross Domestic Product (GDP), command-basis

GDP, private and gross consumptions, as well as the oil price, all series being expressed in real

terms with 1999 as the base year. The data used are provided by Table A6.

A country’s real gross domestic income measures the purchasing power of the total in-

comes generated by its domestic production. The Saudi real GDP, which is computed by the Saudi

authorities at constant 1999 prices, ignores the changes in the relative prices of exports and imports

and, therefore, likely underestimates the actual ﬂuctuations in the Kingdom’s domestic income. As

100 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

2. To benchmark our calculation, we have also used a real income per capita measure adjusted for terms oftrade provided

by Penn World Tables (RGDPTT in PWT 7.0, deﬁned as per-capita PPP Converted Gross Domestic Income at 2005 constant

prices). Over the period considered, the annual relative change in this measure and that in our command-basis GDP exhibit

a high correlation coefﬁcient of 87% (signiﬁcant at a 1% level). Both real domestic income series also display similar

volatilities of 10% and 11% (whereas the per-capita real GDP exhibits a volatility of 2.6%). They seem therefore consistent.

3. It has to be noted that the exchange rate has remained constant at 3.75 Saudi riyals per U.S. dollar since mid-1986.

the world’s largest oil exporter, the Kingdom has the nominal value of its exports driven by the

volatile crude oil price, while a large portion of its imports consists of manufactured products,

which have stickier prices. Over short horizons, the changes in the relative prices of exported oil

and imported goods may have a strong impact on the Saudi domestic income; an impact not nec-

essarily reﬂected in the real GDP. For instance, between 1998 and 1999 a decrease in the volume

of Saudi oil exports, along with a simultaneous increase in the nominal price of oil relative to that

of imported goods, has led to a decrease in the Saudi real GDP but an increase in the Saudi real

domestic income.

To be interpreted as real domestic income, real GDP has to therefore be adjusted for

improvements (or deteriorations) in the Kingdom’s terms of trade. We suggest using the Kingdom’s

command-basis GDP per capita as a measure of the Saudi real domestic income. As discussed by

Kohli (2004), instead of deﬂating nominal imports by the price of imports and nominal exports by

the price of exports as in the case of real GDP, the net exports are deﬂated by the import price

deﬂator. The rationale for this approach is that to quantify real income, what matters is not the

quantity of goods and services that are exported, but rather the quantity of imports that is made

possible through these exports. The command-basis GDP values used here result from our own

2

calculations. For the sake of simplicity, we adjusted the real GDP by considering that all exports

were oil-related, since non-oil exports represent only a small fraction of Saudi exports (12.7% on

average between 2007 and 2010); half of them being made of petrochemical products whose prices

are reasonably well-correlated with oil price. Since the geographical origin of the Saudi imports is

relatively well-diversiﬁed, with a large share of consumer goods, the World Bank’s world consumer

price index (world CPI) is used as a proxy for the import price deﬂator. The adjustment for year t

is therefore the difference between the nominal exports deﬂated by the world CPI and the product

of the nominal exports by the ratio of the oil price in 1999 over the nominal oil price in year t.

In this paper, the real price of crude oil, given

3

in 1999 USD per barrel, is deﬁned as the

nominal price of the Arabian Light deﬂated by the World Bank’s world CPI. The gross consumption

is the sum of private and government consumptions. The government consumption, whose share

in the Kingdom’s economy is relatively important, includes non-durable public goods. In this paper,

the gross consumption is therefore considered as a relevant indicator for consumption. Data in real

terms are only available from 1998 to 2010. Since during this period the deﬂator used is almost

indistinguishable from the Saudi Arabian cost of living index, we have used this index to deﬂate

the pre-1998 data.

The ﬁve series appear to be non-stationary. Table A1 shows that all series are integrated

of order one since the null hypothesis of a unit root cannot be rejected whereas for the differenced

series, this hypothesis can be rejected at 5% signiﬁcance; Table A2 shows that the series of annual

relative percentage changes are stationary.

Table 1 gives the coefﬁcients of correlation between the relative percentage changes in

real gross/private consumption and real GDP, command-basis GDP or real crude oil price. The

positive coefﬁcient of correlation between gross consumption and command-basis GDP is signiﬁ-

cant at a 1% level, and the coefﬁcient of correlation between private consumption and command-

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 101

Copyright 䉷2014 by the IAEE. All rights reserved.

Table 1: Coefﬁcients

a

of Correlation between Relative

Percentage Changes (1988–2010)

Real GDP per

capita

Command-

basis GDP per

capita

Real crude oil

price

Real gross consumption per

capita

33.4% 56.9%*** 55.1%***

Real private consumption per

capita

1.59% 34.8% 39.0%*

a

The conﬁdence intervals are calculated by ﬁrst applying a Fisher transformation.

Here and in the remainder of the paper, ***, **, and * denote statistical signiﬁcance

at 1%, 5%, and 10% levels, respectively.

Figure 2: Relative Changes in Real Oil Price (dotted line) and in—real per-capita—Gross

Consumption (solid line), Private Consumption (long dashes), and Command-

basis GDP (short dashes)

basis GDP is signiﬁcant at an 11% level. By suggesting that changes in terms of trade translate into

changes in consumption, this substantiates the idea that the command-basis GDP is more closely

associated with the Saudi society’s utility curve and more in line with the Kingdom’s real private

and government consumptions than the real GDP. By regressing real private and government con-

sumptions on real GDP and trading gains over the period 2003–2007, MacDonald (2010) obtains

similar results for OECD resource-rich nations, like Norway or Australia. She ﬁnds that real con-

sumption advanced more than real production in these countries which have experienced large

terms-of-trade improvements.

Figure 2 illustrates the coefﬁcients of correlation between the relative percentage changes

for the period of 1988 to 2010 for the crude oil price, the per capita gross and private consumptions,

and the per capita command-basis GDP.

For public investment decision-making, since Saudi consumption and income measures

appear to be positively correlated with crude oil price, risk premiums have to be considered when

102 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

4. This formula, derived under certain assumptions, yields a constant discount rate r

t

deﬁned as the sum of q, a wealth

effect and a precautionary effect. The wealth effect is equal to the relative risk aversion times the expected consumption

growth rate (i.e., the more future generations will consume, the higher the discount rate). The precautionary effect is equal

to minus half the product of the variance of this growth rate, the relative risk aversion, and one plus the relative risk aversion

(i.e., the more uncertain the future consumption, the lower the discount rate).

calculating an oil-related project’s net present value (NPV). In the next subsection, the standard

formula of the risk premium to consider is derived as in Gollier (2007) and discussed in the context

of our paper.

2.2 Standard Formula of the Risk Premium

Following a classical approach, we consider that the expected total utility, which is deﬁned

as the sum of expected utilities of per-capita consumption for current and future populations, is the

welfare measure maximized by the Saudi authorities. Let C

t

denote the optimal consumption per

capita in year t, with tranging from zero to inﬁnity. Only C

0

is deterministic, whereas (C

1

,C

2

,...)

are exogenous random variables whose distributions, conditional on the information available at

t= 0, are assumed to be known. The expected total utility is written as follows:

–

q

t

eE(lu(C))

∑

tt

t=0

Where u( ) is the utility function, l

t

is the size of the Saudi population in year t, and qis

the rate of time preference (used to discount utility).

Let us now consider a public oil-related investment project that in year t(t=0,1,...∞)

would generate the (uncertain) cash ﬂow F

t

+b

t

P

t

, where P

t

is the oil price, b

t

is a coefﬁcient

representing the number of barrels freed for export (or consumed if b

t

⬍0), and F

t

may be a capital

expenditure, an operating expense or even a revenue. With the exception of F

0

+b

0

P

0

, all these

future cash ﬂows are uncertain. This investment project is proﬁtable if it increases the welfare of

the Saudi society:

F+bP

ttt

–

q

t

–

q

t

eEluC+

≥

eE(lu(C)) (1)

∑∑

tt tt

冢冢 冣冣

l

t=0 t=0

t

With a ﬁrst-order Taylor expansion in C

t

and simple manipulation (that is valid as long as

the project size does not exceed a small fraction of the Saudi gross domestic income), (1) becomes:

E(u⬘(C)) u⬘(C)

tt

–

q

t

eE(F+bP)+cov F +bP,

≥

0 (2)

∑

ttt ttt

冢冢 冣冣

u⬘(C)E(u⬘(C))

t=0 0t

By setting r

t

=q

–

, we introduce the public discount rate r

t

which is in-

1E(u⬘(C))

t

ln 冢冣

tu⬘(C)

0

dependent from the project under study. This discount rate represents a trade-off betweenimmediate

marginal utility and future expected marginal utility. Estimating the value of the discount rate that

could be used by Saudi public authorities is not in the scope of this paper. This value primarily

depends on their expectations about future economic growth. However, for the sake of illustration,

we can apply Gollier’s (2007) generalized form

4

of the Ramsey rule. For instance, by setting q=0

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 103

Copyright 䉷2014 by the IAEE. All rights reserved.

for intergenerational equity and considering a relative risk aversion coefﬁcient ranging between one

and three (this issue is discussed in Subsection 2.3), using historical gross consumption we obtain

very low values for the real social discount rate, ranging from 0.5% to 0.8%.

We can rewrite (2) as follows:

u⬘(C)

t

–

rt

t

eE(F+bP)+cov F +bP,

≥

0 (3)

∑

ttt ttt

冢冢 冣冣

E(u⬘(C))

t=0 t

As emphasized by Gollier (2007), to implement this approach, the following ﬁrst-order

approximation is usually made:

E(u⬘(C)) 艑E(u⬘(E(C)) + (C

–

E(C))u⬙(E(C))) = u⬘(E(C))

tttttt

We can therefore make the following approximation:

u⬘(C)C

tt

cov F +bP,艑

–

αcov F+bP, (4)

ttt ttt

冢冣冢冣

E(u⬘(C)) E(C)

tt

Where αdenotes the coefﬁcient of relative risk aversion at the expected consumption,

with α=

–

E(C

t

)u⬙(E(C))

t

.

u⬘(E(C))

t

By combining (3) and (4), we obtain the standard condition in public economics that to

be proﬁtable the project must have a non-negative NPV:

CC

tt

–

rt

t

F+bP +eE(F)

–

αcov F,+E(bP)

–

αcov bP,

≥

0 (5)

∑

000 t t tt tt

冢冢冣 冢冣冣

E(C)E(C)

t=1 tt

Every cash ﬂow therefore impacts the project’s NPV through its expected value and a risk

premium proportional to its covariance with . This risk premium is positive if the cash ﬂow

C

t

E(C)

t

is positively correlated with the Saudi economic activity, since receiving this cash ﬂow then in-

creases the global risk borne by the Saudi society.

So far we made no speciﬁc assumption about b

t

. However, the operating costs of projects

like the development of solar or nuclear power generation capacities are relatively low (compared

to oil or gas-based power generation), which implies that the capacity envisioned by Saudi author-

ities should be used. The same reasoning can be held for investments in energy efﬁciency. We may

therefore consider that b

t

is deterministic, or, at least, not correlated with the economic activity or

the crude oil price. For projects for which this assumption cannot be made, additional elements,

like the correlation between the demand addressed to the project and the economic activity, would

have to be considered.

The formula of the consumption risk premium associated with one barrel of oil in year t

is consequently: αcov .

C

t

P,

t

冢冣

E(C)

t

As previously shown, the oil price is positively correlated with all measures of Saudi

consumption or income. Therefore, all projects whose proﬁtability is ultimately driven by additional

Saudi oil exports are likely to increase the macroeconomic risk borne by the Saudi society. On the

104 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

contrary, any project transforming oil (i.e., b

t

⬍0) into a product whose price is less correlated with

the Saudi economy will have a negative risk premium, i.e. a positive cash ﬂow, quantifying the

beneﬁt from risk diversiﬁcation. This negative risk premium can be viewed as an insurance value,

since undertaking the project reduces the aggregate risk in the economy.

2.3 Scenarios for Future Consumption and Relative Risk Aversion

When assessing the proﬁtability of an oil-related project, public authorities may conse-

quently take into account a risk premium proportional to αcov . This term, which does

C

t

P,

t

冢冣

E(C)

t

not depend on the project under study, needs to be determined at the level of the Saudi economy.

All equations in Section 2.2 are derived from marginal changes around a future optimal

stream of consumption C

t

that is currently unknown. It might be argued that the income of the

representative agent is uncertain (as it is subject to external shocks, like those on the oil price) and

that, to a certain extent, this uncertainty spills over to consumption (and results in consumption

ﬂuctuations) through the arbitrage between consumption and saving. The ﬂuctuations in future

consumption will therefore depend on government’s saving policy. In Saudi Arabia, on a historical

basis, the path followed by consumption (with historical volatilities of 4% and 4.9% for private

and gross consumptions respectively) is much smoother than that followed by domestic income

(with a volatility of 11% for command-basis GDP), as saving has been used as a buffer against oil-

price shocks. Calibrating the risk premium on historical real consumption thus corresponds to a

‘moderate-volatility scenario’ for future consumption.

However, in the future, government and private consumption might adjust to changes in

income in a different way. In this respect, making the theoretical assumption that saving would

represent a constant proportion of real domestic income generates a ‘high-volatility scenario’ for

future consumption. We do not pretend to provide any foundation or credibility for this scenario,

we just consider that it can serve to deﬁne an upper bound for the risk premium. The risk premium

can then be assessed by computing the covariance between the real oil price and command-basis

GDP. This risk premium will be higher than that determined using historical consumption. In this

paper, we consequently calibrate the risk premium on both historical real domestic income (toobtain

an upper bound) and historical real consumption (to obtain a lower bound).

Furthermore, it should be noted that the risk premium is proportional to the coefﬁcient of

relative risk aversion. As mentioned by Lucas (2003), estimates of the parameter αin use in

macroeconomics and public ﬁnance applications range from 1 to 4. As far as we know, there is not

any speciﬁc study addressing the value of αfor the Kingdom of Saudi Arabia. However, when the

risk relates to ﬂows of costs or beneﬁts, a relative risk aversion coefﬁcient of two has often been

used in the literature (e.g. Chetty (2006), Gollier (2007), Hall and Jones (2007), Dasgupta (2008),

Weitzman (2009)). In a report commissioned by the French government, Gollier et al. (2010) also

recommend using a coefﬁcient of two for public decision purposes. This value will consequently

play a central role in the numerical illustrations performed in this paper. However, sensitivity

analyses around this value will also be provided.

3. CALIBRATION OF THE SHORT-TERM RISK PREMIUM ASSOCIATED WITH OIL

PRICE

In a very simple way suggested by Gollier (2001), we ﬁrst assess the social cost of the

volatility of the Saudi domestic income over one year. We consider that all inhabitants of the

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 105

Copyright 䉷2014 by the IAEE. All rights reserved.

5. For each income growth rate series, a normal distribution is not rejected by the Jarque-Bera test. This supports the

validity of a second-order approximation in the left-hand side of (6), since E((I

1

–

E(I

1

))

3

) is proportional to the third moment

of the growth rate variable G(introduced below).

6. Consistent with formula (5), the cost kE(I

1

) can be considered as a cumulative risk premium resulting from increased

exposure to the systematic risk: .

sI αvar (I)

111

αcov sI ,ds ==kE(I)

11

∫

0

冢冣

E(sI )2E(I)

11

7. For each income measure, we have also determined the cost kby assuming that all growth rates realized in the past

may occur with equal probability next year (which deﬁnes a probability distribution for G). For α= 2, this amounts to

numerically solving E((1 + G)

–

1

) = ((1

–

k)(1 + E(G)))

–

1

. The cost kthus obtained is very close, which conﬁrms the robust-

ness of the approximations made in this section.

Kingdom can be represented by a single representative agent. The risk faced by this representative

agent is then measured by the uncertainty surrounding the domestic income per capita. The social

cost of the macroeconomic risk can be measured by the reduction in the expected income that the

risk-averse representative agent would be ready to pay to eliminate the income volatility. To compute

the cost, we therefore need to determine the certain income that generates the same level of utility

as the volatile income I

1

. Expressed as a fraction of the expected income, the cost of macroeconomic

risk, denoted as k, is consequently deﬁned by the following equation:

E(u(I)) = u((1

–

k)E(I)) (6)

11

By Taylor expansion

5

in E(I

1

), we have:

2

(I

–

E(I))

11

u(I)艑u(E(I)) + (I

–

E(I))u⬘(E(I)) + u⬙(E(I))

11111 1

2

u((1

–

k)E(I)) 艑uE(I))

–

kE(I)u⬘(E(I))

1111

By replacing the left-hand and right-hand sides of (6) with the expanded forms, we have:

6

αvar (I)

1

k艑(7)

2

2E(I)

1

Where αdenotes the coefﬁcient of relative risk aversion at the expected income.

For the measure of the Saudi per-capita domestic income under consideration, let usassume

that next year the growth rate of this income will be an outcome of the random variable G, with

E(G) (the expected value of G) and var(G) (the variance of G) respectively given by the historical

mean and variance of the corresponding stationary time series. Let I

0

be the known income in the

current year, with consequently: I

1

=(1+G)I

0

. From (7), we have:

αvar (G)

k艑(8)

2

2(1 + E(G))

Table 2 gives the historical mean and variance of the relative percentage change for the

per-capita real GDP and command-basis GDP. Not surprisingly, the growth rate of the command-

basis GDP appears to be much more volatile than that of the real GDP.

For the sake of illustration, by considering α= 2 and using ﬁgures in Table 2, Formula (8)

yields

7

an estimate of short-term (one-year-ahead horizon) cost of macroeconomic risks equal to

106 / The Energy Journal

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Table 2: Mean and Variance of Annual Growth Rates (1988–

2010)

Growth rate of real GDP per

capita

Growth rate of command-

basis GDP per capita

Mean (E(G)) 0.12% 1.16%

Variance (var (G)) 0.07% 1.17%

1.14% when the command-basis GDP is the selected income measure and only 0.07% when the

real GDP is the selected measure. For a coefﬁcient of relative risk aversion equal to unity, the cost

is only 0.035% when the real GDP is the income measure considered, which is in line with results

obtained for other countries. Using annual U.S. data for the period of 1947–2001, for example,

Lucas (2003) shows that the welfare annually gained by eliminating all consumption ﬂuctuations

around an exponential consumption path would be about one-twentieth of one percent of con-

sumption. For the Kingdom, this cost is greater by more than an order of magnitude when the

income measure Iused is the command-basis GDP.

The oil price risk premium αcov over one year (i.e., the “short-term” risk

I

1

P,

1

冢冣

E(I)

1

premium) can now be calibrated, based on the value of kdetermined with the command-basis GDP.

In Appendix B, under simplifying assumptions, we calibrate the risk premium that should be con-

sidered in 2010 from a 2009 perspective and the risk premium that should be considered in 2009

from a 2008 perspective, for a relative risk aversion coefﬁcient of 2. Making these two calibrations

serves to test the sensitivity of the risk premium to the oil price. As a result, from a 2009 perspective,

the risk premium in 2010 would have amounted to 3.72 dollars per barrel (i.e., 6.1 percentagepoints

of the oil price realized in 2009). With similar calculations, from the 2008 perspective, in 2008

dollars the risk premium in 2009 would have been ﬁve dollars per barrel (i.e., 5.3 percentage points

of the oil price realized in 2008).

These calibrations suggest that for the Saudi economy, the short-term oil price risk pre-

mium may exceed 5% of the oil price when a relative risk aversion coefﬁcient of two is considered.

It represents almost 3% of the oil price when the relative risk aversion considered is only unity,

and may exceed 8% of the price for a relative risk aversion of 3. This risk premium, however,

depends on the covariance of two non-stationary variables and is therefore likely to increase with

respect to the time horizon considered. The next section proposes two alternative econometric

assessments of the ‘long-term’ risk premium.

4. ASSESSMENT OF THE LONG-RUN OIL PRICE RISK PREMIUM

As shown by Table A1, all series are integrated of order 1, which suggests that the co-

variance between oil price and Saudi income or consumption increases throughout time. As a result,

the farther in the future the expected oil-related cash ﬂow is located, the greater should be the risk

premium to consider. A ﬁrst and straightforward evaluation procedure of the risk premium in the

long run derives from the restrictive assumption that both times series are jointly lognormal. A

second procedure consists in testing for the existence of cointegration relationships between oil

price and variables speciﬁc to Saudi Arabia. These two procedures are successively applied in the

following subsections.

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 107

Copyright 䉷2014 by the IAEE. All rights reserved.

Table 3: Normality Test Results for Changes in Log of Saudi

Income and Consumptions

Command-basis

GDP per capita

Real gross

consumption per

capita

Real private

consumption per

capita

Jarque-Bera test

value

1.39 1.27 10.77***

Critical values: 4.61 (10%); 5.99 (5%); 9.21 (1%)

4.1 The Joint Lognormal Assumption

We assume here that the real oil price, the gross consumption per capita and the command-

basis GDP per capita follow a geometric Brownian motion. This assumption is supported by the

fact that the logarithms of these three series are ﬁrst-order integrated (as shown by Table A1) and

that the Jarque-Bera test does not reject a normal distribution for the corresponding seriesof changes

in log (as shown by Table 3). We cannot assume that the private consumption follows a geometric

Brownian motion since Table 3 shows rejection of the normal distribution for log change in this

series at 1% signiﬁcance level.

In addition to this geometric Brownian assumption, let us hypothesize here that the utility

function exhibits a constant relative risk aversion coefﬁcient . Under these speciﬁc assumptions,

the exact formula of the risk-premium can be derived from (3), as shown by Gollier (2012).

Let us ﬁrst consider the command-basis GDP, in order to derive an upper bound for the

risk premium. The risk premium in year tthen amounts to the fraction 1

–

e

–

α

⳯

2.4%

⳯

t

of the expected

oil price, where 2.4% is the estimated covariance between the changes in log of real oil price and

the changes in log of command-basis GDP. For a relative risk aversion of 2, the short-term risk

premium is therefore equal to 4.8% of the expected oil price, which is consistent with the calibration

achieved in Section 3. This risk premium represents half the expected oil price in a 15-year horizon,

and three quarters of the expected price over 30 years. Over an inﬁnite horizon, the risk premium

tends towards the expected oil price. It is noteworthy that subtracting this risk premium from the

expected oil price is equivalent to discounting the expected oil price at a rate that includes a 4.8%

risk premium. If the risk-free discount rate used were for instance 1% (see Section 2.2), the real

oil-price-related cash ﬂows would have to be discounted at a rate of almost 6%. Note that this

amounts to assuming an oil-price consumption beta of 2, computed as the estimated covariance

(2.4%) divided by the variance of the change in the log of command-basis GDP per capita (1.2%).

If we now consider the real gross consumption per capita, the calculated risk premium in

year tis much lower and equal to the fraction 1

–

e

–

α

⳯

0.64%

⳯

t

of the expected oil price (with a

corresponding consumption beta of 2.66). For a relative risk aversion of 2, over one year this risk

premium amounts to 1.27% of the expected oil price. It amounts to 12% of the expected oil price

in a 10-year horizon.

4.2 Estimation of Cointegration Relationships

To apply a more general approach, we test for cointegration between oil price and each

Saudi macroeconomic variable. The results of the Johansen cointegration tests are shown in Table

4, and the corresponding estimated bivariate vector error correction (VEC) models are given by

Tables A3 to A5.

108 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

Table 4: Johansen Cointegration Tests between Each Saudi consumption and Income

Variable and Real Crude Oil Price (1987–2010)

Trace Maximum eigenvalue

Null

hypothesis Test statistic

Signiﬁcance

level Test statistic

Signiﬁcance

level

Real gross consumption per

capita (one lag)

r = 0 20.31 ** 17.52 **

r

≤

1 2.79 — 2.79 —

Real private consumption per

capita (two lags)

r = 0 32.07 *** 19.03 **

r

≤

1 13.02 *** 13.02 ***

Real command-basis GDP

per capita (two lags, linear

trend)

r = 0 17.39 ** 16.65 **

r

≤

1 0.74 — 0.74 —

8. Since initially none of the two adjustment coefﬁcients was signiﬁcant, we restricted the adjustment coefﬁcient in the

oil price vector to zero.

9. A one-lag model yields a slightly lower Akaike information criterion, but with a signiﬁcant adjustment coefﬁcient in

the oil price vector, whereas weak exogeneity of oil price seems more plausible.

In all cases, the null hypothesis of absence of cointegration can be rejected. For private

consumption, the absence of a second cointegrating relationship can also be rejected. This would

however imply that neither oil price nor private consumption have a unit root, which seems unlikely.

This might result from the shortness of the period considered, since for a model with one lag the

tests indicate only one cointegrating relationship at 5% signiﬁcance level.

All models have been selected under the condition that the residuals behave well, with, at

5% signiﬁcance level, no rejection of the following null hypotheses: normal distribution, absence

of serial correlation, and homoscedasticity. For gross consumption and oil price, the one-lag model

minimizes both Schwarz and Akaike information criteria. For command-basis GDP and oil price,

the selected

8

two-lag model minimizes the Schwarz information criterion. For private consumption,

we selected

9

the two-lag model by considering that the oil price should be weakly exogenous. As

a result, in each model, the adjustment coefﬁcient estimated for the Saudi-variable equation is

signiﬁcant and of the expected sign.

Let us consider any of the three Saudi macroeconomic variables, for instance the real gross

consumption per capita, C

t

, and write the identiﬁed long-run equilibrium between this variable and

the real crude oil price:

C

–

k

–

kP=e

t01tt

Where k

0

and k

1

are the coefﬁcients estimated in the cointegration relationship, and e

t

is

the stationary disequilibrium term. Table 5 gives the values of k

0

and k

1

estimated in each vector

error correction model.

Hence, we have:

cov (P,C)=cov (P,k+kP+e)=kvar(P)+cov (P,e)

tt t01tt 1ttt

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 109

Copyright 䉷2014 by the IAEE. All rights reserved.

Table 5: Coefﬁcients Estimated for Each Long-run Equilibrium

k

0

k

1

Real gross consumption per capita 16,697 222.86

Real private consumption per capita 8,177 206.34

Command-basis GDP per capita 20,089 587.46

Table 6: Risk Premium over a One-year Horizon, in Percentage

of the Expected Oil Price

Relative risk

aversion (α)

Real private

consumption per

capita

Real gross

consumption per

capita

Command-basis

GDP per capita

1 1.15% 0.85% 1.21%

2 2.29% 1.69% 2.42%

3 3.44% 2.54% 3.63%

10. These short-term ﬁgures do not incorporate the disequilibrium-related term. Incorporating this term, estimated as

the historical covariance between the stationary variable e

t

and the non-stationary variable P

t

, gives a short-run risk premium

of 1.88% for command-basis GDP and 1.20% for gross consumption.

With:

cov (P,C)

tt

lim = k

1

冢冣

var (P)

t

r

∞

t

Consequently, to implement the approach, we may consider that in the long-run:

Cαkvar(P)

t1t

αcov P , = (9)

t

冢冣

E(C)k+kE(P)

t01 t

According to (9), a growth in the oil price variance throughout time induces a proportionate

growth in the risk premium. Therefore, the risk premium that the Saudi authorities should consider

in the long-run depends on their view of the future of the oil price.

For the sake of illustration, let us assume that the real oil price follows an arithmetic

random walk with a variance of annual price increments (estimated on the historical time series)

equal to 68.6. In addition, the expected value of the real oil price is assumed to remain constant

and equal to 100 in 2011 dollars. Using (9), Table 6 provides

10

the corresponding risk-premium

over a one-year horizon for different values of the relative risk aversion coefﬁcient. Under the

arithmetic random-walk assumption made here the variance of oil price, and therefore the risk

premium, is proportional to the time-horizon considered.

For a relative risk aversion coefﬁcient of 2, the risk premium over one year is thus equal

to 1.69% of the expected crude-oil price when gross consumption is used, 2.29% when private

consumption is used, and 2.42% when command-basis GDP is used. Over a 10-year horizon, this

risk premium consequently lies between 16.9% and 24.2% of the expected oil price.

To compare the alternative risk premium calibrations achieved in Sections 4.1 and 4.2,

from a 2011 perspective let us again adopt the view that, in 2011 dollars, the expected value of the

110 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

Figure 3: Risk Premium with Respect to Time (LN: joint lognormal assumption, RW:

random walk assumption) for a Relative Risk Aversion of 2

0

10

20

30

40

50

60

70

80

90

100

110

0 5 10 15 20

25

2011 USD per barrel

Time horizon (years)

Expected oil price

real oil price for the subsequent years remains constant at 100 dollars per barrel. Figure 3 illustrates

the upper and lower risk premium curves, based on historical data, for both joint lognormal and

random walk assumptions, under the assumption that the relative risk aversion coefﬁcient is 2.

5. CONCLUSIONS AND IMPLICATIONS FOR PUBLIC ENERGY-RELATED

DECISIONS

A considerable portion of the Saudi domestic income depends on volatile oil revenues. In

presence of risk aversion, this dependence has a social cost, which requires considering a risk

premium when valuing an energy-related public investment project. This risk premium has to be

subtracted from expected oil-price-related cash ﬂows when assessing the project’s net present value.

The literature in general does not provide any thorough estimate of the risk premium associated

with the price of an exported commodity for public decision-making in resource-rich countries.

In this paper, we attempt to quantify the risk premium associated with the crude oil price

for public investment decision-making in Saudi Arabia. As the magnitude of the risk premium

depends on future consumption patterns, possible upper and lower bounds have been determined

for this risk premium, by considering the historical per-capita gross domestic income (deﬁned as

the command-basis GDP) and real gross consumption.

When a relative risk aversion coefﬁcient of two is considered, over a one-year horizon this

risk premium may lie between 1.3% and 4.8% of the expected oil price. It is likely to increase for

longer planning horizons. In other words, the further in the future the expected oil-related cash

ﬂow, the higher is the risk premium to consider.

For a practical illustration, let us consider a 20-year stream of cash ﬂows derived from the

sale of an oil barrel at market price every year. Let us also assume that the expected real oil price

remains constant at 100 dollars per barrel for the next 20 year. Ignoring the risk premium would

imply determining the present value of this stream of cash ﬂows as the expected oil price multiplied

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 111

Copyright 䉷2014 by the IAEE. All rights reserved.

by the sum of discount factors. Taking into account the risk premium implies subtracting the sum

of discounted risk premia from this present value. By using the risk-premium estimates derived

from the historical Saudi real gross consumption per capita (and the corresponding discount rate

value in Subsection 2.2) for a relative risk aversion of 2, taking into account the risk premium is

here equivalent to reducing the expected oil price by 12 dollars (under the lognormal assumption)

or 17 dollars (under the random walk assumption). This reduction in the expected oil price lies

between 6.3 to 8.4 dollars for a relative risk aversion equal to unity, and between 17.6 and 25.3

dollars for a relative risk aversion of 3.

This risk premium is far from being negligible. Even if proﬁtable at current oil price levels,

public investment opportunities in alternative energies or energy efﬁciency may therefore yield

lower NPVs than one might expect at ﬁrst sight. Considering the risk premium may particularly

impact the decision made for projects whose breakeven price is relatively close to the expected

market price. Taking into account the risk premium may therefore inﬂuence the total amount of

public funds that could be invested in projects aiming to curb the growth in domestic oil demand.

Additionally, standard economics would generally recommend aligning domestic administered

prices of power or transportation fuels with corresponding marginal costs of production or market

prices. It might be noted that, as a second-order effect, the resulting decrease in domestic demand

would augment the Saudi economy’s exposure to oil-price volatility.

Furthermore, projects transforming oil into products less correlated with the Saudi econ-

omy generate a beneﬁt from reducing the aggregate risk in the economy. This beneﬁt can be priced

as the present value of the corresponding negative risk premia (which represent positive cash ﬂows).

Given the above discussion about the magnitude of the risk premium, the resulting increase in

project’s proﬁtability may be signiﬁcant.

This paper provides estimates that could serve to formalize a rigorous economic framework

for public investment decision-making in Saudi Arabia, an issue especially relevant at this time as

many energy-related investment opportunities are being considered by Saudi authorities. Further-

more, the great magnitude of the risk premium derived here suggests that similar computations

should be performed for other resource-rich nations whose domestic income signiﬁcantly depends

on the market price of an exported commodity. As far as we know, there was so far no empirical

literature on this subject. The methodological approach developed in this paper, especially the

estimation of the derived risk-premium formula with cointegration techniques, is a straightforward

process that could be transposed to other resource-rich countries.

ACKNOWLEDGMENTS

The authors are indebted to James Smith, Christian Gollier, Bashir Dabbousi, Dermot

Gately, Mustafa Babiker and three anonymous referees for helpful comments on this paper.

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APPENDIX A

Note: ***, **, and * denote statistical signiﬁcance at 1%, 5%, and 10% levels, respectively;

t-statistics are given in brackets.

Table A1: Unit Root Tests with Intercept (1987–2010)

Level First Difference

Test Test statistic

Signiﬁcance

level Test statistic

Signiﬁcance

level

Real GDP per capita ADF

–

2.18 —

–

4.94 ***

PP

–

2.18 —

–

5.01 ***

Command-basis GDP per

capita

ADF

–

1.42 —

–

5.27 ***

PP

–

1.37 —

–

5.27 ***

Log of command-basis GDP

per capita

ADF

–

1.35 —

–

4.84 ***

PP

–

1.35 —

–

4.84 ***

Real gross consumption per

capita

ADF

–

0.64 —

–

3.59 **

PP

–

0.42 —

–

3.59 **

Log of real gross

consumption per capita

ADF

–

0.71 —

–

3.66 **

PP

–

0.56 —

–

3.70 **

Real private consumption per

capita

ADF

–

2.53 —

–

3.25 **

PP

–

0.36 —

–

3.20 **

Real crude oil price ADF

–

1.38 —

–

5.98 ***

PP

–

1.28 —

–

5.98 ***

Log of real crude oil price ADF

–

1.35 —

–

5.08 ***

PP

–

1.37 —

–

5.16 ***

Critical values in level:

–

2.64 (10%);

–

3.00 (5%);

–

3.75 (1%); in ﬁrst difference:

–

2.64 (10%);

–

3.00 (5%);

–

3.77 (1%)

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 113

Copyright 䉷2014 by the IAEE. All rights reserved.

Table A2: Unit Root Tests with Intercept for Percentage Change Variables (1988–2010)

Test

Real GDP per

capita

Command-basis

GDP per capita

Real gross

consumption per

capita

Real private

consumption per

capita Real oil price

ADF

–

4.94***

–

4.72***

–

3.64**

–

3.17**

–

5.11***

PP

–

5.01***

–

4.73***

–

3.68**

–

3.13**

–

5.24***

Critical values:

–

2.64 (10% level);

–

3.00 (5% level);

–

3.77 (1% level)

Table A3: VEC Model of Real Gross Consumption Per Capita

and Real Crude Oil Price (1987–2010)

DC

t

DP

t

Constant

–

16,697*** [

–

48.91]

P

t

–

1

–

222.86*** [

–

20.31]

Adjustment coefﬁcient

–

0.963** [

–

2.86] 0.00146 [0.49]

DC

t

–

1

0.437** [2.17] 0.00226 [1.27]

DP

t

–

1

–

86.94 [

–

1.67]

–

0.23 [

–

0.50]

R

2

0.409 0.179

Akaike information criterion 23.002

Schwarz information criterion 23.449

Table A4: VEC Model of Real Private Consumption Per Capita

and Real Crude Oil Price (1987–2010)

DH

t

DP

t

P

t

–

1

–

8,177*** [

–

10.57]

Constant

–

206.34*** [

–

7.65]

Adjustment coefﬁcient

–

0.533*** [

–

4.26]

–

0.0015 [

–

0.70]

DH

t

–

1

–

0.243 [

–

1.15] 0.0069* [1.99]

DH

t

–

2

–

0.691** [

–

2.64]

–

0.0089* [

–

2.05]

DP

t

–

1

–

34.23 [

–

1.74]

–

0.454 [

–

1.40]

DP

t

–

2

–

1.20 [

–

0.05]

–

0.111 [

–

0.30]

R

2

0.619 0.463

Akaike information criterion 21.741

Schwarz information criterion 22.388

Table A5: VEC Model of Command-basis GDP Per Capita and

Real Crude Oil Price (1987–2010)

DI

t

DP

t

Cointegration constant

–

20,089 [NA]

P

t

–

1

–

587.46 [NA]

Adjustment coefﬁcient

–

0.636*** [4.26] 0

DI

t

–

1

1.01 [0.87] 0.00032 [0.16]

DI

t

–

2

0.66 [0.76] 0.0012 [0.76]

DP

t

–

1

–

709.1 [

–

1.08]

–

0.46 [

–

0.40]

DP

t

–

2

–

484.11 [

–

1.00]

–

0.641 [

–

0.75]

Error-correction constant 770.40 [0.68] 1.02 [0.51]

R

2

0.138 0.127

Akaike information criterion 23.890

Schwarz information criterion 24.587

114 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

Table A6: Saudi Arabian Income, Consumption, and Oil Price Data in the Period of

1987–2010

Year

World CPI

(1999 base

year)

Real price

of a barrel

of Arabian

Light (1999

USD)

Real GDP

per capita,

at 1999

prices

(SAR)

Command-

basis GDP

per capita

(1999 SAR)

PPP

converted

GDI per

Capita

(2005 USD)

Real gross

ﬁnal

consumption

per capita

(1999 SAR)

Real private

ﬁnal

consumption

per capita

(1999 SAR)

1987 42.6 40.42 31,138 39,962 11,292 24,742 14,901

1988 47.5 28.23 31,710 37,035 11,982 22,832 14,443

1989 54.4 29.79 30,334 35,922 11,504 23,467 14,179

1990 56.4 36.91 31,314 41,536 12,063 23,986 14,750

1991 57.3 30.42 32,617 40,940 13,334 25,431 14,309

1992 61.1 29.36 32,386 39,845 13,805 23,886 14,275

1993 63.2 24.81 31,425 35,741 13,137 22,324 14,394

1994 73.8 20.86 30,947 32,948 12,122 21,297 14,107

1995 79.9 20.93 30,324 32,474 11,646 20,518 13,650

1996 86.3 23.06 30,543 33,992 11,557 21,329 13,691

1997 91.3 20.48 30,593 32,529 11,544 21,880 13,516

1998 97.2 12.55 30,665 27,674 10,330 20,578 12,696

1999 100.0 17.45 29,720 29,720 11,282 20,331 12,620

2000 104.1 25.76 30,437 34,833 13,982 21,987 12,896

2001 107.9 21.38 29,995 32,064 13,086 21,592 12,685

2002 110.8 21.95 29,300 31,641 13,581 21,372 12,605

2003 115.4 23.99 30,796 34,545 14,891 21,503 12,469

2004 118.9 29.04 31,640 38,669 16,527 22,639 12,819

2005 123.8 40.50 32,300 45,640 19,659 24,208 13,486

2006 129.4 47.18 32,223 48,202 21,151 25,997 14,379

2007 135.9 50.60 31,788 48,695 21,984 27,871 16,365

2008 148.1 64.25 32,050 54,467 26,703 28,185 16,387

2009 152.1 40.35 31,023 41,117 22,254 28,428 16,906

2010 159.5 48.75 31,743 45,712 — 28,568 17,137

Sources: World Bank (world CPI), Saudi Arabian Monetary Agency (population until 2009, nominal price of Arabian Light,

real GDP, nominal exports, Saudi Arabian cost of living index), Saudi Central Department for Statistics & Information

(2010 population, nominal and post-1997 real private ﬁnal consumption and gross ﬁnal consumption), Penn World Tables

(PPP converted GDI)

APPENDIX B

The number of oil barrels that will be exported next year, denoted as q, is assumed to be

known; this assumption considerably simpliﬁes the developed expression of var (I

1

). By approxi-

mating that exports are all oil-related, we have:

I=real GDP +(P

–

P)q

111

Where P

1

is the real oil price (i.e., deﬂated with the World CPI) in the subsequent year

and is the oil price in 1999 (i.e., the price used to compute the real GDP). By deﬁning here nonoil

P

GDP as real GDP minus oil exports at 1999 price, we have:

I=nonoil GDP +Pq

111

Hence, (7) can be rewritten:

The Impact of Oil Price Volatility on Welfare in the Kingdom of Saudi Arabia / 115

Copyright 䉷2014 by the IAEE. All rights reserved.

2

αvar (I)α(var (nonoil GDP )+2qcov(P,nonoil GDP )+qvar(P))

11111

k==

22

2E(I)2E(I)

11

As cov (P

1

,I

1

)=cov (P

1

,nonoil GDP

1

)+q var (P

1

), we have:

αvar (nonoil GDP )αq I nonoil GDP

11 1

k=+cov P ,+cov P ,

11

冢冢 冣 冢 冣冣

2

2E(I)2E(I)E(I)E(I)

111 1

Which gives:

IE(I)2kvar (nonoil GDP )nonoil GDP

11 1 1

cov P ,=

––

cov P , (B1)

11

冢冣冢 冣冢 冣

2

E(I)qαE(I)E(I)

111

We use (B1) to calibrate the risk premium that should be considered in 2010 from a 2009

perspective and the risk premium that should be considered in 2009 from a 2008 perspective.

Let us ﬁrst note that, whatever the year considered, (8) gives:

2kvar (G)

艑艑1.14%.

2

α(1 + E(G))

In addition, it can be noticed that:

nonoil GDP E(nonoil GDP )nonoil GDP

11 1

cov P ,= cov P ,

11

冢冣 冢 冣

E(I)E(I)E(nonoil GDP )

11 1

The term can be interpreted as the oil price risk premium with

nonoil GDP

1

cov P ,

1

冢冣

E(nonoil GDP )

1

respect to nonoil GDP. This term, here multiplied by a factor smaller than unity, is certainly neg-

ligible since the cost of macroeconomic risks assessed with real GDP is smaller by more than one

order of magnitude than that determined with the command-basis GDP.

Let us now calibrate the risk premium in 2010 from a 2009 perspective. The expected

value of the command basis in 2010 is the value realized in 2009, i.e. 41,117 SAR per capita, times

one plus the expected growth rate 1.16%:

E(I) = 41,117 ⳯1.0116 = 41,594

1

var (nonoil GDP

1

) can be approximated as the squared value of the nonoil GDP realized

in 2009 (that amounts to 25,110 SAR per capita) times the variance of real GDP growth rate. We

consequently have:

2

var (nonoil GDP ) 0.07 25,110

1

= = 0.026%

冢冣

2

E(I) 100 41,594

1

According to SAMA 47th annual report, Saudi Arabia exported 2,772.15 million barrels of crude

oil and reﬁned products in 2010, which represents q= 101 barrels of oil per capita. Therefore, (B1)

gives:

116 / The Energy Journal

Copyright 䉷2014 by the IAEE. All rights reserved.

I41594

1

cov P , = (1.14%

–

0.026%) = 4.58

1

冢冣

E(I) 101

1

This ﬁgure, expressed in SAR, is computed with respect to an oil price expressed in 1999

dollars. The value of the covariance in 2009 U.S. dollars is consequently:

1.521

4.58 ⳯= 1.86

3.75

As a result, with a relative risk aversion coefﬁcient of two and from a 2009 perspective,

the risk premium in 2010 would have amounted to 3.72 dollars per barrel. From the 2008 perspective

and applying similar calculations, the risk premium in 2009 would have been ﬁve dollars per barrel

in 2008 dollars.