Empirical Evidence of News about Future Prospects in the Pricing of Oil Assets

Johnson Kakeu1 and Mohammed Bouaddi2 This draft: October 23, 2010

1 School

of Economics, Georgia Tech, Email: [email protected] of Applied Economics, HEC Montr´eal, Email:[email protected]

2 Institute

Abstract This paper provides strong empirical evidence for the role of news about future prospects in determining the pricing of exhaustible natural resource stock. It builds on the theoretical resource model of Kakeu (2009b) which shows how uncertainty about future prospects affects the optimal rule of management of a nonrenewable natural resource stock in a context of risk diversification. The econometric approach used combines the Latent Variable method and the Dynamic Conditional Correlation method (DCC). The results show that the parameter capturing news about future prospects is statistically significant and the term related to the revisions in expectation about future prospects account for roughly 50% in the total risk premium of oil reserves. Revisions in expectations about future prospects due to some important historical events such as the six day war of 1967, the oil crisis of the seventies, the economic crisis of the mid-eighties, the stock market crash of 1987, the first gulf war in 1990, the economics crisis of 1998 and 2000, and the second persian gulf war in 2003 are captured through the growth rate of the estimated value function. Another empirical finding is that the indicators related to both the labor market and the price indices shape heavily the expectations about future prospects. In addition to the empirical findings, another contribution of this paper follows from the econometric methodology used that provides a new way of estimating continuous time asset pricing models with stochastic differential utility.

Key words: Oil Reserves, Pricing, Future Prospects, News JEL Classification: C13, C22, G12

1

Introduction

The concept of news about future prospects is related to both the arrival of new information about the state of the economy and the revisions in expectations about future prospects in response to the realization of this new information. Empirical investigation of the role of news about future prospects in natural resource markets have been mentioned by many studies including Krautkraemer (1998), Graham-Tomasi et al. (1986), Livernois (2009) as to be a major issue in future research in natural resource economics. The importance of uncertainty about future prospects has also been mentioned by the U.S. Energy Secretary Steven Chu while arguing about the oil market behavior when he pointed out that ”There’s one thing for sure. It is not supply and demand currently. It is future. It’s all based on future prospects ... of what might happen”.1 This paper provides a strong empirical evidence for the role of news about future prospects in the pricing of nonrenewable resource stocks. The role of future prospects has long been unexplored since the traditional literature addressing uncertainty in natural resource economics relies almost on the standard additive utility. The standard additive utility framework does not allow the consumer to care about future prospects.2 As a consequence, no empirical work has been done to understand the role of uncertainty about future prospects in resource economics. A continuous time framework allowing consumer preferences to account for future prospects is the stochastic differential utility of Duffie and Epstein (1992). The stochastic differential utility framework captures the notion that one’s present sense of well-being can depend on one’s expected future utility levels in a not necessarily risk-neutral manner. With a stochastic differential utility, the current utility depends on both the consumption and the future utility index which is made a function of the distribution of the future consumption stream {cs : s > t}. Given the 1

speaking on june 9th 2009 at the Reuters Global Energy Summit in Washington. See the Reuters website

http://www.reuters.com/article/idUSTRE55068S20090601 2 Other well-known weaknesses of the standard additive utility, such as its inability to disentangle risk aversion and intertemporal substitution, and some related consequences in natural resource management have received attention, including in Shaw and Woodward (2008), Howitt et al. (2005), Knapp and Olson (1996), Peltola and Knapp (2001) and Epaulard and Pommeret (2003).

1

current information on the state of the economy, news about future prospects are introduced in the form of future utility growth forecasts. This definition implicitly involves the notion of reference points determined by the previous expectations as in the paper of Koszegi and Rabin (2009). A larger future utility index represents brighter future prospects of the economy while a decrease in future utility represents worsening future prospects of the economy. Future prospects are taken into account in the natural resource framework of Kakeu (2009b) which provides a pricing equation of nonrenewable resource stocks showing that the equilibrium rate of return required by investors in order to hold a resource stock includes a risk-adjusted discount factor, a risk premium which depends on how the return on holding the resource is correlated with current consumption growth, and a risk premium which can be thought of as related to news about future prospects. The latter depends on how the return on holding the resource stock is correlated with the growth rate of the value function, which captures revisions in expectations about future prospects. An intuitive connection can be made between this third term and what has been labeled ”long-run risk” in a previous empirical literature, including Bansal and Yaron (2004). To provide an empirical support for the role of news and uncertainty about future prospects in determining the pricing of oil assets, this empirical paper builds on the theoretical framework of Kakeu (2009b). The econometric approach used to estimate the pricing equation of the resource stock has three steps that includes computing the value function endogenously. This is done by representing the state of the economy by a small set of variables called the latent factors. They capture the available information on the state of the economy by extracting the relevant information from a great number of both financial and macroeconomic data. Going back from the seminal paper of Bai and Ng (2002), the use of latent factors has been the subject of an extensive literature including Bouaddi and Douch (2010) who address the equity premium puzzle in the consumption capital asset pricing model. Another step in our econometric approach includes the use of the Dynamic Condi-

2

tional Correlation model (DCC) to compute the dynamic correlations while estimating the pricing equation.3 The data we use are from February 1959 to December 2006. Data on market capitalization of oil companies from the Center for Research in Security Prices University of Chicago , data on world proven oil reserves are from the web site of BP Statistics, data on consumption are from the St. Louis Federal Reserve Bank. The results suggest future prospects account for roughly 50% in the cumulative pricing of oil stock. Furthermore some important historical events such as the six day war of 1965, the oil crisis of the seventies, the economic crisis of the mid-eighties, the stock market crash of 1987, the first gulf war in 1990, the economics crisis of 1998 and 2000, and the second persian gulf war in 2003 are captured by the time varying growth rate of the estimated value function. To the best of our knowledge, this is the first empirical study, built on a natural resource model, that measures the effects of news about future prospects in the valuation of a nonrenewable resource stock. The paper is organized as follows. Section 2 presents the pricing equation of the resource stock derived by Kakeu (2009b) which takes into account the uncertainty about future prospects of the economy. Section 3 describes the econometric approach. Section 4 presents the data, while Section 5 presents empirical results for oil. The last section offers concluding comments. 2

The pricing of a nonrenewable resource stock taking into account the news about the future prospects of the economy

A resource economic model that formalizes the effects of news about future prospects in the pricing of nonrenewable resource is that of Kakeu (2009b) which merges the stochastic differential utility framework of Duffie and Epstein (1992) and the resource economic framework of Gaudet and Khadr (1991). In this framework, the continuation utility of the 3

Another paper which uses the DCC model is Bali and Engle (2010)

3

representative consumer (value function) is defined recursively by the following stochastic integral equation J(t) = Et

hZ

∞

  i f c(s), J(s) ds

(1)

t

where the current utility is f (c(t), J(t)) depends on both the current consumption c(t) and the continuation utility J(t) which is attributable to the entire stream of future consumption {cs : s > t}. In a certain sense, the continuation utility expresses how the expectations about the future prospects or about the entire future consumption growth enter the current utility. In the equilibrium, the continuation utility is moved by the uncertainty about the future prospects as driven by the information on the current state of the economy. Two goods are produced in this economy, one of which is a nonrenewable natural resource, and is irreversibly reduced by extraction. The other is a reproducible composite good, that can be either consumed or accumulated. If it is accumulated, it can be either in the form of a physical capital or of a “bond”. The accumulated stock of bonds is assumed to reproduce itself at an exogenously given risk free rate. The productivity indices of both the production sector and the extraction sector are assumed to be stochastic. Kakeu (2009b) shows that the equilibrium expected instantaneous rate of return on the resource stock being held in the ground µS (t) =

1 1 E (dλ(t)) λ(t) dt t

can be expressed in the form

of a risk-adjusted discount rate plus a two risk factors as follows h i c(t)f (t) J(t)fcJ (t) cc σSc (t) − σSJ (t) µS (t) − r(t) = β + fJ (c(t), J(t)) − fc (t) fc (t)

(2)

where σSc (t) = covt ( dλ(t) , dc(t) ), σSJ (t) = covt ( dλ(t) , dJ(t) ), and fJ , fcc , fcJ are the partial λ(t) c(t) λ(t) J(t) derivatives of the current utility f (c, J). The pricing equation of the resource stock (2) has three components: an endogenous discount rate, the covariance between the return on the resource stock and consumption growth, and the covariance between natural asset returns and the instantaneous change of the utility index.4 The first component β + fJ (c(t), J(t)) shows how the discount rate is adjusted over time in the resource stock valuation. It may also be thought of as the effect of the time valuation 4

Notice that under certainty, if f (c, J) = U (c) − ρJ and if the resource investor is assumed to be risk

4

in the resource stock valuation. This effect depends on both the information on the state of the economy received by the resource investor and the level of uncertainty given this information. The second component is related to the shocks to current consumption growth (risk). It tells us that a non renewable resource stock is relatively undesirable when its return covaries positively with consumption. If a nonrenewable resource stock is such that its return tends to be high (low) when consumption tomorrow is high (low), (σSc > 0), holding such resource stock in one’s portfolio makes it difficult to smooth consumption over states of nature. Therefore, risk averse investors require a premium over the riskless return to hold this resource stock, reflecting the investor’s aversion to substitution over states of nature. The third component is related to news about the future prospects. It contains the covariance between the return on the resource stock and the rate of change of utility index which captures news about future prospects. If a resource stock is such that its return between today and tomorrow tends to be high (low) when there are good (bad) news about utility or consumption the day after tomorrow, then σSJ > 0. Such resource stock is not attractive for investors who are more risk averse (−fcJ > 0 ) than under the time-separable utility and they have a negative hedging demand for this resource stock because it tends to do worse when there is bad news (an increase in risk) about future consumption. It is an undesirable feature of holding this resource stock which therefore needs to generate a compensation through a relatively higher risk premium. The higher is the covariance the higher is the risk premium. On the other hand, investors who are less risk averse (−fcJ < 0 ), i.e. more aggressive than under the time separable utility, have a positive demand for this resource stock since they are willing to trade off worse performance when news are bad for extra performance when news are good. Holding such an asset smoothes the intertemporal neutral (U 00 = 0), equation (2) becomes λ˙ = r(t) (3) λ which is the pricing rule derived in the seminal paper of Hotelling (1931). It states that the price net of marginal cost (denoted by λ) must rise at the rate of interest in nonrenewable resource markets

5

consumption profile. So the more this investor is averse to intertemporal substitution, the more he is willing to hold this resource stock. If a resource stock is such that the covariance between its return and the change in the utility index capturing news on future prospects is negative (σSJ < 0) , it means that the future creates more hedging opportunities for investors who are more risk averse than the time separable utility (−fcJ > 0)) and thus makes agents particularly like the resource stock and this effect contributes to lower its risk premium. 3

The econometric methodology for estimating the pricing equation of the resource stock

The objective of this section is to present the econometric methodology used to estimate the pricing equation (2). In what follows we consider the parametric specification of the stochastic differential utility by Schroder and Skiadas (1999) whose normalized aggregator function f is given by

f (c, J) =

h γ α i  c 1+α − βJ  (1 + α) J   hγ

if γ 6= 0

(1 + αJ) log(c) − αβ log(1 + αJ)

i

(4)

if γ = 0

   with parameters α, β, γ such that β≥0  −1    α > −1 and γ < min (1, (1 + α) ) if γ 6= 0 α≤β

if γ = 0

   The coefficient β denotes time preference for the future, the coefficient

1 1−γ

denotes the

elasticity of intertemporal substitution. The coefficient α captures the dependency of the current utility to the future utility also called prospective utility by Koopmans (1960, p.292). If α 6= 0, it means that the uncertainty about future prospects affects the current decision making. A larger future utility index represents an increase in future prospects and affects the intertemporal choice. If α = 0, the decision maker cares only about the current consumption 6

and its intertemporal choices are not affected by the uncertainty about future prospects. Substituting this parametric stochastic differential utility and its derivatives into (2) makes the pricing equation of the resource stock to depend on the preferences parameters. The estimation of the parameters α, β, and γ requires to obtain the proxies of variables in both the right hand side and the left hand side of the pricing equation (2). The left hand side correspond to the expected rate of return of the resource stock and will be estimated using the method of estimating continuous time diffusion process of Nowman (1997). On the other hand, the variables that appear on the right hand side of the pricing rule of the resource stock (2) are the rate of return of the resource stock, the consumption and its growth rate, the value function and its growth rate. The value function is not observable but since in the equilibrium, the value function J(t) depends on the state of the economy, it can be estimated by using a small numbers of factors F = (F1 , ..., FL ) called latent variables that capture the relevant information in the economy. For the estimation purposes, we will assume that the value is a function of latent factors and takes the following functional form. PL

J(t) = e(δt+

)

i=1 θi Fi (t)

(5)

The estimation of the latent factors is done in the first step of the econometric procedure. e = J(F f1t , ..., F fLt ) is a function of those estimated latent The approximated value function J(t) e is a consistent estimate of the value function J(t) factors. The estimated value function J(t) that is not observable. When the value function is replaced by its approximate in the pricing equation, the estimation of the parameters δ, and (θi )i=1,..L in the expression (5) are done simultaneously with the preference parameters α, β, and γ described in the expression (4). That is, this specification allows the value function to be endogenously and jointly estimated

7

with the preference parameters in the structural model. The pricing equation (2) becomes   PL µS (t) − r(t) = β + fv c(t), e(δt+ i=1 θi Fi (t))   PL h c(t)fcc c(t), e(δt+ i=1 θi Fi (t))   σSc (t) − P δt+ L θi Fi (t)) ( i=1 fc c(t), e   PL PL L i e(δt+ i=1 θi Fi (t)) fcJ c(t), e(δt+ i=1 θi Fi (t)) X   + θi σ (t) (6) P SFi δt+ L ( i=1 θi Fi (t)) f c(t), e i=1 c where fJ , fcc , fcJ are the partial derivatives of current utility of Schroder and Skiadas (1999) given by equation (4) Our econometric approach consists of four steps: The first step estimates µS (t). The second step estimates the latent factors that capture the state of the economy (Fi )i=1,..,L . The third step estimates the covariances σSc and (σSFi )i=1,..,L . Finally, the fourth step estimates the structural parameters α, β, γ and (θi )i=1,..,L . 3.1

Estimation of µS (t)

One approach to estimate the drift µS (t) comes from the following continuous time model representing the equilibrium dynamic of the return on resource stock dRS (t) = (α1 + α2 RS (t))dt + σRS (t)α3 dζ(t).

(7)

We use the discrete approximation of 7 and given by S + RtS = eα2 Rt−1

α 1 α2 (e − 1) + ηt α2

where the error term ηt satisfies:  0 E(ηs η t ) =  σ2 (eα2 − 1)(RS )2α3 t−1 2α2

if s 6= t if s = t

The logarithm of the Gaussian likelihood function is: L(α1 , α2 , α3 , σ) =

T S X (RtS − eα2 Rt−1 − αα21 (eα2 − 1))2 [log E(ηt2 ) + ] 2 E(η ) t t=1

8

(8)

where E(ηt2 ) =

σ2 (eα2 2α2

S − 1)(Rt−1 )2α3

Maximum Likelihood Estimation consists of solving (b α1 , α b2 , α b3 , σ b) = arg max L(α1 , α2 , α3 , σ). α1 ,α2 ,α3 ,σ

It follows that the estimate of µS (t) is given by µ bS (t) = α b1 + α b2 RS (t). 3.2

(9)

Estimation of the latent factors (Fi )i=1,...,L that capture the state of the economy

We assume that the state of the economy is captured by a set of matrices Zi = (Zi,1 , ..., Zi,Ni ) of T × Ni observable economic variables that are related to the same aspect of the economy denoted by i. Each column vector of the matrix Zi represents a single observed variable consisting of T observations. This large number of economic variables Zi which represents the dynamic of the economy is used to construct a small number of factors F = (F1 , ..., Fr ) that capture the state of the economy as follows. The factors are estimated by the principal component analysis. See Appendix 1 for more details. It can be shown that each estimated factor Fei of the latent √ factor Fi is the eigenvector (multiplied by T ) associated with the largest eigenvalue of the matrix 1 0 Zi Zi T Ni

(10)

A convergence result by Bai and Ng (2002) says that, as T and N both tend to infinity, the estimated latent variables (Fei )i=1,..,L converge to their true scaled counterpart (Fi )i=1,..,L . The main advantage of factor models is that they allow to capture all relevant information related to the state of the economy in a small number of estimated indicators (Fei )i=1,..,L . A second advantage of factor models is that idiosyncratic movements which possibly include measurement error and local shocks can be eliminated. A third important advantage is that researchers can remain agnostic about the structure of the economy and do not need to rely on overly tight assumptions about the relevant indicators to use. 9

3.3

Estimation of the conditional second moments σSFi (t) and σSc (t)

To estimate the time varying covariances σSFi (t) and σSc (t), we apply the Dynamic Conditional Correlation (DCC) model introduced by Engle (2002) to model the conditional   dFeL,t dFe1,t covariance matrix of the innovations (t) of the vector dRtS , dc(t) , , ..., . The innoc(t) Fe Fe 1,t

L,t

vation vector (t) is obtained by using an ARMA(1,1) model for each variable as in (Engle 1

and Sheppard, 2001). We assume that (t) = Ht2 ξt where Ht is a conditional variance covariance matrix to be estimated and ξt is an iid vector error term such that ξt ∼ N (0, I). Such a variance covariance matrix Ht can always be decomposed into a diagonal matrix Dt which contains the conditional standard deviation and a correlation matrix Ωt which has ones on the diagonal and the pairwise conditional correlations as the off diagonal elements, i.e. Ht = Dt Ωt Dt ,

(11)

In other words, (t) ∼ N (0, Dt Ωt Dt ) where Dt and Ωt have to be estimated. The estimation of Dt and Ωt is done in a two-step procedure. In the first step, we estimate the diagonal elements of the matrix Dt which are the conditional standard deviations obtained by estimating   dFeL,t dFe1,t . , , ..., an ARMA(1,1)-GARCH(1,1) model for each variable of the vector dRtS , dc(t) c Fe Fe 1,t

L,t

The second step consists in estimating the conditional covariance matrix Q(t) of the standardized residuals obtained from the ARMA(1,1)-GARCH(1,1) model. This matrix Q(t) is then used to compute the conditional correlation matrix Ωt .5 Since the standardized errors Dt−1 (t) follow the distribution N (0, Qt ), it becomes easy to estimate Qt by assuming that they follow the dynamic conditional correlation below Qt = (1 − ρ1 − ρ2 )Q + ρ1 ξt ξt0 + ρ2 Qt−1 ,

Q0 given.

(12)

where the parameters ρ1 and ρ2 are non-negative scalars such that ρ1 + ρ2 < 1. We set Q to the sample unconditional correlation matrix of the standardized residuals obtained from P the estimation of Dt in the first step, that is Q = T1 Tt=1 ξt ξt0 .6 This estimation technique 5 6

The matrices Qt are positive definite but may not have ones on the diagonal Under this dynamic, the equation (12) has only two parameters to be estimated.

10

is known as the variance targeting approach. The estimate of the correlation matrix Ωt is computed by using the following equation 1

1

Ωt = diag(Qt )− 2 )Qt diag(Qt )− 2 ), where diag(Qt ) is a diagonal matrix consisting of diagonal elements of Qt .

3.4

Estimating the preference parameters α, β, γ along with δ, (θi )i=1,..L

To estimate the structural parameters α, β and γ as well as θi . We replace µS (t), Fi (t), σSc (t) and σSFi (t) by their estimates in (6) to get  P δt+ L θei Fei (t)) ( i=1 µ bS (t) − r(t) = β + fv c(t), e   PL e e h c(t)fcc c(t), e(δ1 t+ i=1 θi Fi (t))   σ − bSc (t) PL e e fc c(t), e(δt+ i=1 θi Fi (t))   P P δt+ L δt+ L θei Fei (t)) θei Fei (t)) ( ( i=1 i=1 L i fcJ c(t), e X e e   θi + σ bSFi (t) + εt PL e e fc c(t), e(δt+ i=1 θi Fi (t)) i=1 

(13)

where εt is a random error normally distributed. The estimated values of the parameters are obtained by maximazing the log-likelihood function. The standard errors of the parameters are estimated using a consistent covariance matrix for the presence heteroskedasticity and autocorrelation in εt . 4 4.1

Data description Proxy of the cumulative return of the resource in the ground

The return on resource stock in the ground is not observable. Based on the fact that the only way to invest in resource stocks in the ground is to buy mining firms stocks, Kakeu (2009a) showed that the difference between the growth rate of the market capitalization of mining firms and the growth rate of the proved reserves to proxy the return on resource stock. dλ(t) dX(t) dS(t) ≈ − . λ(t) X(t) S(t) 11

In this paper we use the same proxy for the return on resource stock in the ground (See Appendix 3 for the sample of oil companies used). We use the same data as in Kakeu (2009a). Briefly the sample consists of 56 oil & gas companies owning oil & gaz proved reserves and which are listed on the US stock exchange. Thirty nine are ranked in the Top 100 World’s oil companies established by Energy Intelligence in 2006. Data on world proved reserves are from the BP website.7

Figure 1: Cumulative return on oil RS The estimation of the drift in the structural equation (13) obtained from the cumulative return of oil is given by µ bS (t) = 13.4372 − 13.3638RS (t).

(14)

with others details including the student-t statistics are shown in the table below α1

α2

α3

σ

13.4372

-13.3638

-0.6719

0.2636

(474.3351)

(-478.7692)

(-2.3126)

(43.5670)

All the coefficients are statically significative which suggests that the right hand side of the pricing equation (2) is well estimated. 7

www.bp.com

12

4.2

Description of the proxy for the risk free rate asset returns and consumption per capita

To proxy the risk-free rate, the monthly yield on one-month U.S. The data range are from January 1959 to December 2006.

Figure 2: one-month U.S Treasury bill, proxy of risk free rate Consumption data come from the St. Louis Federal Reserve Bank and cover the period from February 1959 to December 2006. We use the monthly growth rate on real personal consumption expenditures of services and non durable goods and use the total civilian population to get the consumption per capita.

13

Figure 3: Consumption per capita growth rate 4.3

Data on the state of economy used to estimated the value function

The data containing the information about the state of the economy come from the DRIMcGraw–Hill Basic Economics database. The financial series are from the Fama-French data library.8 . They can be classified in four groups. The first group includes 180 series of the money market agregates and financial series (money stocks, interest rates, reserves, bond yields and stock prices). The second group contains 225 series of labor market agregates (number of employees, average hours worked, salaries, labor force, unemployment rates, unemployment durations, wages and compensations, personal incomes and compensations). The third group includes 125 series goods & services market agregates (industrial capacity, industrial production, personal consumption expenditures, personal saving, new orders and capacity utilization). The last group includes 155 series of price indices (commodity prices and CPIs). 8

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html

14

4.3.1

Estimation of the latent factors that capture the state of the economy

Each of the four groups described previously is used to estimate the latent factor which capture the most the information in the corresponding group. The estimations of the latent factors are obtained from the optimization program (20) − (20) presented in Appendix 1. Following the notations used previously, the factors are denoted by F1 , F2 , F3 , F4 . The factor F1 explains 76.15% of the total variation of the money and financial market group. The factor F2 explains 37.11% of the total variation of the labour market group . The factor F3 explains 43% of the total variation of the growth rate of the price indexes. The factor F4 explains 30% of the total variation of goods and services market’s aggregates. Recall that the value function is assumed to be a function of latent variables as follows PL

J(t) = e(δt+

)

i=1 θi Fi (t)

(15)

. 5

Empirical Results

The two following tables report the estimation results of the pricing equation (13). The first table presents the estimations obtained using the latent factors method. The second table presents the estimations using the aggregate wealth computed by Lettau and Sydney (2010) to proxy the value function.9 Table 1: Estimations using an endogenous specification of the value function. 9

The aggregate wealth can be easily computed from data on consumption wealth and consumption avail-

able on Lettau website

15

Coeff-value α

−0.304000

β

Std Error

T-Stat

Signif

0.001678 −181.133420

0.000000

0.156000

0.000275

568.113650

0.000000

γ

0.755600

0.000158

4785.879780

0.000000

δ

0.001791

0.000005

381.714250

0.000000

θ1

0.002210

0.001235

1.788880

0.073634

θ2

0.006346

0.001071

5.927900

0.000000

θ3

−0.002314

0.001077

−2.148590

0.031667

θ4

−0.000024

0.001251

−0.018940

0.984891

σε2

0.000005

0.000000

120.179950

0.000000

In the resource owner decision making, it appears that the factors that shapes heavily the expectations about future prospects are the current information on the labor market, the current information on the price indices and the current information on the financial markets. Table 2: Estimations using the aggregate wealth of Lettau and Sydney (2010) to proxy the value function10 Coeff

Std Error

T-Stat

Signif

α

0.035600

0.007918

4.493450

0.000007

β

0.049300

0.011200

4.393440

0.000011

γ

−0.455400

0.049700

−9.158480

0.000000

0.000004

0.000000

371.280310

0.000000

σε2

Each panel gives the point estimates of the parameters of the stochastic differential utility α, β, and γ and their Student-t statistics. The first column of the table 1 gives the point estimates. The second column gives the standard error of the estimates. The third column gives the Student-t Statistics. And the last column gives the significance level. All the Student-t Statistics coefficients suggest statistical significance at 5% level. Of great interest is the statistical significance of the parameter α which suggest oil resource investors care about fluctuations in future utilities. This channel is similar to the so- called long-run risk 10

The value function is replaced by the aggregate wealth computed by lettau. These data are are publicly

available on Martin Lettau’s webpage http://pages.stern.nyu.edu/ mlettau/

16

of Bansal and Yaron (2004). This suggest that the oil resource owners review his extraction plan each period based not only on their current consumption but also also their expectations about the long term prospects of the economy. The figure 4 plots the growth rate of the value function obtained by using the latent factor approach which allows us to estimate endogenously the value function jointly and consistently within the structural equation (13).

Figure 4: Growth rate of the value function The current state of the economy shapes the uncertainty about the future prospects of the economy. As it appears on the graph, the estimates of the growth rate of the value function capture some important historical events such as the oil crisis of the seventies, the economic crisis of the mid-eighties, the stock market crash of 1987 and the economics crisis of 1998, and 2000. These periods were marked by negative expectations about the future prospects of the economy.11 . This gives some empirical support to Cochrane (2005, page 50) who noted that the growth rate of the value function captures news about the investor’s future prospects or the updates in expectations about the future consumption growth, with zero being the statu quo. A negative change of future utility index may be viewed as resulting 11

For the news elasticity computed with the Lettau approach is used, see Appendix 2

17

from bad news about future prospects. Another interpretation of bad news about future prospects is that it is an increase in the probability of low levels of consumption in the future which results in a negative change of the future utility index. The fluctuations of the growth rate of the value function as shown by the graph above show that oil resource investors change expectations about the future prospects of the economy as new information becomes available. For example, an economic crisis is a bad news that means that the future prospects of the economy are not favorable. Since the non renewable resources are inputs in the production process of the economy, the resource investor should modify his extraction strategies given that information. h i cc (t) cJ (t) Let µD (t) = β + fJ (c(t), J(t)) , µU (t) = − c(t)f σSc (t), and µN E (t) = − J(t)f σSJ (t), fc (t) fc (t) then from the pricing equation of the resource stock (2), the risk premium of the nonrenewable resource stock can be decomposed in three parts. µS (t) − r(t) = µD (t) + µU (t) + µN E (t)

(16)

where the first part is related to the discount rate, the second part is related to the current consumption growth risk, and the latter part is related to the future prospects risk. To capture the effect of the news about future prospects on the variation of the total risk premium of the resource stock, we compute the news elasticity using the following formula N ewst Elasticity =

∆(µS −r(t)) µS −r(t) ∆µnews µnews

t = 1, ..., T.

The evolution of news elasticity of resource stock premium over time are shown below.

18

(17)

Figure 5: News elasticity of resource stock risk premium (using latent factors)

As we can see on figure 5, the pics of the news elasticity capture some stylized facts well known in the economic literature such as the oil crisis happened in 1973 and the financial market crash of 1987. These periods were marked by dramatic bad news about future prospects of the economy.

12

In order to measure the relative weight of the news component in the resource stock risk premium, we compute the ratio of the news premium in terms of other components that are consumption risk component and discount rate as follows N ewst P remium W eight =

1 + µN E (t) t = 1, ..., T. 1 + µU (t) + µD (t)

As shown in the figure below, this ratio equals mostly one. 12

For the news elasticity computed with the Lettau approach is used, see Appendix 2

19

(18)

Figure 6: weight of news in relation to others components of the resource premium It follows that, over time, risk factor related to news about future prospects account for roughly 50% of the premium on oil reserves. This suggests that there is a channel that is based on the economic agents’ expectations of the future prospects of the economy and which affects the resource stock. According to this ”expectations channel”, part of the oil value of the resource stock value is also determined in a forward-looking manner by the expectations about future growth prospects, given the current information on the state of the economy. This result provides an empirical validation to Krautkraemer (1998, p. 2077) who pointed out that the arrival of new information can cause a revision in future expectations about future prospects that completely alters the extraction and price paths. It is interesting to note that the parameters α and γ have opposite signs. This suggests that the resource owner is more risk averse than under the standard utility. If the return of resource stock tend to increase when there are bad news about future prospects, this resource stock is attractive and the investor requires a lower premium to hold oil stock. This result gives an empirical support to Graham-Tomasi et al. (1986, p. 244) who pointed out that resource stocks could be held as an hedging strategy against bad news about future prospects. 20

6

Conclusion

This paper has provided an empirical support for the role of news about future prospects in the resource stock valuation in the long run. First, We have found that news significantly affects the pricing of nonrenewable resource stocks. Oil resource investors care about the future prospects of the economy and this effect is very strong during the recessions in the economy. The arrival of new information causes a revision in the future expectations about the future prospects that affects the valuation path of the resource stock held in the ground. Recently, the U.S. Energy Secretary Steven Chu while arguing about the oil market behavior said that ”There’s one thing for sure. It is not supply and demand currently. It is future. It’s all based on future prospects ... of what might happen”.13 Second, Oil stocks could be held as an hedging strategy against bad news about the future prospects. The results of this paper comforts the role played by the uncertainty about future prospects in oil market. The same methodology can be used to investigate other exhaustible resource markets such as coal, natural gas, etc. References Bai, J., and S. Ng (2002) ‘Determining the number of factors in approximate factor models.’ Econometrica Bali, T., and R. Engle (2010) ‘The intertemporal capital asset pricing model with dynamic conditional correlations.’ Journal of Monetary Economics 57, 377–390 Bansal, R., and A. Yaron (2004) ‘Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.’ The Journal of Finance 59, 1481–1509 Bouaddi, M., and M. Douch (2010) ‘A model of factors-reference preferences.’ Mimeo, HEC Montreal 13

speaking on june 9th 2009 at the Reuters Global Energy Summit in Washington. See the Reuters website

http://www.reuters.com/article/idUSTRE55068S20090601

21

Cochrane, J. (2005) ‘Financial markets and the real economy.’ NBER Working Papers 11193, National Bureau of Economic Research, Inc, March Duffie, J., and L. Epstein (1992) ‘Stochastic differential utility.’ Econometrica 60, 353–394 Engle, R. (2002) ‘Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models.’ Journal of Business and Economic Statistics 20(3), 339–350 Epaulard, A., and A. Pommeret (2003) ‘Optimally eating a stochastic cake: a recursive utility approach.’ Resource and Energy Economics 25, 129–139 Gaudet, G., and A. Khadr (1991) ‘The evolution of natural-resource prices under stochastic investment opportunities: An intertemporal asset-pricing approach.’ International Economic Review 32, 441–455 Graham-Tomasi, Theodore, C. Ford Runge, and William F. Hyde (1986) ‘Foresight and expectations in models of natural resource markets.’ Land Economics 62(3), 234–249 Hotelling, H. (1931) ‘The economics of exhaustible resources.’ Journal of Political Economy 39 (2), 137–175 Howitt, R., S. MSangi, A. Reynaud, and K. Knapp (2005) ‘Estimating intertemporal preferences for natural resource allocation.’ American Journal of Agricultural Economics 5, 969– 983 Kakeu, J. (2009a) ‘Estimation of the hotelling rule under stochastic investment opportunities.’ Mimeo, Universit´e de montreal (2009b) ‘Future prospects and the management of natural ressource assets.’ Mimeo, Universit´e de montreal Knapp, Keith C., and L. Olson (1996) ‘Dynamic resource management: Intertemporal substitution and risk aversion.’ Journal of Agricultural Economics 78, 1004–1014 22

Koopmans, T. (1960) ‘Stationary ordinal utility and impatience.’ Econometrica 28(2), 287– 309 Koszegi, B., and M. Rabin (2009) ‘Reference-dependent consumption plans.’ American Economic Review 99(3), 909–936 Krautkraemer, J. (1998) ‘Nonrenewable resource scarcity.’ Journal of Economic Literature 36, 2065–2107 Lettau, M., and L. Sydney (2010) ‘Consumption, Aggregate Wealth, and Expected Stock Returns.’ Journal of Finance 56, 815–49 Livernois, J. (2009) ‘On the Empirical Significance of the Hotelling Rule.’ Review of Environmental Economics and Policy 3, 22–41 Nowman, K. (1997) ‘Gaussian estimation of single-factor continuous time models of the term structure of interest rates.’ The journal of Finance 52, 1695–1706 Peltola, J., and K. Knapp (2001) ‘Recursive preferences in forest management.’ Forest Science 47, 455–465 Schroder, M., and C. Skiadas (1999) ‘Optimal consumption and portfolio selection with stochastic differential utility.’ Journal of Economic Theory 89, 68–126 Shaw, W., and R. Woodward (2008) ‘On why environmental and resource economists should care about non-expected utility models.’ Resource and Energy Economics 30, 66–89

23

A

Appendix 1

This relation is expressed in a matrix form as Zi = Fi Λ0i + Ei , where Fi is a T × ri matrix of ri unobservable common factors (r =

(19) PL

i=1 ri ),

Λi are a

Ni × ri matrices of factor loadings and Ei are a T × Ni matrices of idiosyncratic errors that are uncorrelated with the components of Fi . The latent factors or latent variables Fi that capture the state of the economy. Their estimates are obtained by solving the following minimization program minT race F,Λ

(Zi − Fi Λ0i )(Zi − Fi Λ0i )0 Ni T

(20)

subject to 0

Fi Fi = Iri , T

(21)

where Iri is ri a dimentional identity matrix. Because Fi Λ0i = Fi AA−1 Λ0i = Fi∗ Λ∗0 i for any invertible ri ×ri matrix A, the factors and the factor loadings are not jointly identified. Thus, the normalization (??) is an identification constraint. It can be shown that each estimated √ factor Fei is the eigenvector (multiplied by T ) associated with the largest eigenvalue of the 0

matrix

Z(i) Z(i) TN

. A convergence result by Bai and Ng (2002) says that as T and N both tend

to infinity, the estimated latent variables (Fei )i=1,..,L converge to their true scaled counterpart (Fi )i=1,..,L .

B

Appendix 2

The economic variables used to construct the latent factors briefly are exposed in Section X. The data are presented as follows: series code, series mnemonic, series description and transformation code. The transformation codes are 1=no transformation, 2=First difference, 3=logarithm, 4=First difference of logarithms and 5=Second difference of logarithms. The series were taken directly from the DRI-McGraw–Hill Basic Economics database. The 24

portfolio returns are collected from the Fama-French data library, which is available from French’s web page14 . The mnemonics of data from DRI-McGraw–Hill are the original ones. The abbreviations appearing in the data definitions are: SAD for data seasonally adjusted, NSAD for data not seasonally adjusted, SAARD for data seasonally adjusted at an annual rate and FRBD for Federal Reserve Board. C

Appendix 3

Figure 7: News elasticity of resource stock risk premium (using Letau) D

Appendix 4 Table 1: Sample of oil & gas Companies Beginning15

End

UNITED STATES STEEL CORP

1959(02)

2006(12)

STANDARD OIL CO CALIFORNIA

1959(02)

2006(12)

PHILLIPS PETROLEUM CO

1959(02)

2006(12)

Companies

14 15

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html In the CRSP, the data on market capitalizations of some companies such as UNITED STATES STEEL

CORP begin in 1925, but due to the unavailability of data on monthly consumption at this period, we were constrained to begin in 1959

25

STANDARD OIL CO N J / EXXON MOBIL CORP

1959(02)

2006(12)

UNOCAL CORP

1959(02)

2005(12)

BRITISH PETROLEUM LTD

1962(07)

2006(12)

KERR MCGEE CORP

1956(03)

2006(12)

CANADA SOUTHERN PETROLEUM LTD

1962(08)

2006(12)

JEFFERSON LAKE PETROCHEMICALS

1962(08)

2006(12)

IMPERIAL OIL LTD

1962(08)

2006(12)

OCCIDENTAL PETROLEUM CORP

1962(08)

2006(12)

BRITALTA PETROLEUMS LTD / WILSHIRE OIL CO TX

1962(08)

2006(12)

MURPHY CORP

1962(02)

2006(12)

APACHE CORP

1963(08)

2006(12)

BARNWELL INDUSTRIES INC

1965(08)

2006(12)

BROWN TOM INC

1972(12)

2004(04)

FOREST OIL CORP

1972(12)

2006(12)

PATRICK PETROLEUM CO

1972(12)

2006(12)

NOBLE AFFILIATES INC

1972(12)

2006(12)

TIPPERARY LAND & EXPLORATION

1972(12)

2005(09)

WISER OIL CO DE

1972(12)

2004(06)

K R M PETROLEUM CORP

1974(07)

2006(12)

MAYNARD OIL CO

1975(08)

2002(06)

GEORESOURCES INC

1976(04)

2006(12)

PYRAMID OIL CO

1976(08)

2006(12)

CREDO PETROLEUM CORP

1979(03)

2006(12)

HARKEN OIL & GAS INC

1979(12)

2006(12)

DOUBLE EAGLE PETE & MNG CO

1980(01)

2006(12)

BELLWETHER EXPLORATION CO

1980(12)

2005(06)

CENTRAL PACIFIC MINERALS N L

1981(03)

2002(02)

PARALLEL PETROLEUM CORP DE

1981(01)

2006(12)

SANTOS LIMITED

1981(03)

2006(12)

MAGELLAN PETROLEUM CORP

1982(11)

2006(12)

SASOL LTD

1982(05)

2006(12)

ENSERCH EXPLORATION PARTNERS LTD

1985(04)

2002(12)

WALKER ENERGY PARTNERS

1985 (11)

2006(12)

ANADARKO PETROLEUM CORP

1986(10)

2006(12)

26

NORSK HYDRO A S

1986(07)

2006(12)

PARKER & PARSLEY DEVELOPMENT PAR

1987(12)

2006(12)

REPSOL S A

1989(05)

2006(12)

ENRON OIL & GAS CO

1989(10)

2006(12)

VINTAGE PETROLEUM INC

1990(09)

2005(12)

TOTAL S A

1991(11)

2006(12)

NEWFIELD EXPLORATION CO

1993(12)

2006(12)

SUNCOR INC

1994(01)

2006(12)

CROSS TIMBERS OIL CO

1993(06)

2006(12)

PETRO CANADA

1995(11)

2006(12)

LEVIATHAN GAS PIPELINE PTNERS LP

1998(09)

2004(09)

DEVON ENERGY CORP NEW

1988(10)

2006(12)

PETROLEO BRASILEIRO SA PETROBRAS

2000(09)

2006(12)

PANCANADIAN ENERGY CORP

2001(11)

2006(12)

STATOIL A S A

2001(07)

2006(12)

INTEROIL CORP

2004(10)

2006(12)

BILL BARRETT CORP

2005(01)

2006(12)

ROYAL DUTCH SHELL PLC

2005(07)

2006(12)

27