Estimating the Currency Risk Exposure of
Commodity Firms
Jan Sybren Zagema
Master Thesis Econometrics
Supervisors: Prof. Dr. Paul Bekker, University of Groningen Dr. Rob van den Goorbergh, APG
Acknowledgements
This master thesis is the result of many hours of research. During the research process which starts by selecting a subject and finishes with the presentation of the outcomes I have been fortunate to receive many answers to my numerous questions. Many individuals have been of great help, whom I would all like to thank for their suggestions and explanations. From the University of Groningen, my supervisor Prof. Dr. Paul Bekker has been of great help by providing useful feedback on my research.
About APG
APG carries out collective pension schemes for participants in the education, gov-ernment, and construction sectors, cleaning and window-cleaning companies, hous-ing corporations and energy and utility companies as well as social or sheltered employment. APG manages pension assets of in total approximately 337 billion euros as of September 2013 for these sectors. APG works for over 30,000 employers and provides for the income of around 4.5 million participants. APG administrates over 30% of all collective pension schemes in the Netherlands.
The Building Block Commodities of APG aims to add value by providing pension funds the opportunity to realize commodity exposure. This is done by means of investing in commodity futures and through the Natural Resources Fund by in-vestments in funds that invest in non-listed commodity producing companies. By investing in commodities the Building Block offers pension funds a way of hedging against inflation.
Estimating the Currency Risk Exposure of
Commodity Firms
Jan Sybren Zagema
February 25, 2014
Abstract
1
Introduction
Changes in exchange rates can substantially affect the cash flows of a firm, re-sulting in exposure to currency risk. To manage currency risk, the sensitivity of cash flows to changes in exchange rates needs to be estimated. Adler and Dumas (1984) first suggested that currency risk exposure can be estimated by means of regressions of stock returns on exchange rate movements. Many studies have fol-lowed this approach of using stock returns. Up to so far, most studies had limited success in detecting significant currency risk exposure.
Another approach of assessing currency risk exposure is to examine the sensitivity of cash flows to exchange rate movements. Garner and Shapiro (1984) are the first to apply this approach of estimating currency risk for a single company. This approach has the advantage of more directly measuring transaction and economic exposures. However, noise problems with cash flow data, especially near-zero and negative observations, often make direct estimation of currency risk difficult or im-possible. The only studies of samples of direct estimates are Bartram (2007), for U.S. nonfinancial firms, Martin and Mauer (2003, 2005), for U.S. financial firms, and Krapl and O’Brien (2012), for general U.S. firms.
The Natural Resources Fund (NRF) of APG invests in non-listed commodity pro-ducing companies. The prices of the commodities that firms produce are deter-mined by the international U.S. dollar denominated market. However, the firms have production costs in both U.S. dollars and local currency. As a result, the firms and therefore the NRF face currency risk. The NRF wants to assess this currency risk and decide upon whether or not this risk should be hedged. The research is conducted for the mining and oil & gas sectors only, due to the lack of availability of data on listed companies for the farmland and timberland sectors. As the NRF holds a U.S. dollar mandate, all currency risk exposures will be estimated versus the U.S. dollar.
fluctua-tions. Translation risk is the extent to which a firm’s financial reporting is affected by exchange rate movements. The process of consolidating financial statements for multinationals entails translating foreign assets and liabilities from foreign to domestic currencies. Transaction risk occurs whenever a firm has contractual cash flows whose values are subject to unanticipated changes in exchange rates due to a contract being denominated in a foreign currency. In this research, no distinction will be made between the various types of currency risk.
This paper contributes to the literature by presenting an analysis of the currency risk exposure of a sample of commodity firms. As pointed out by Bodnar and Wong (2003), the unavailability of suitable cash flow data makes the analysis of currency risk exposures using cash flow data generally impossible. The currency risk exposure of the firms in the NRF are however more suitable estimated using a cash flow based approach, given the illiquid nature of the firms. This paper presents the first large sample investigation of the currency risk of commodity firms using cash flow data.
The literature has shown that for many firms the currency risk exposure is in-significant. As this paper shows, currency risk exposure is found to be small and insignificant for most commodity firms as well. By focusing on the currency risk of hypothetical average firms, a different approach of estimating currency risk is taken. Using this method, a selection is made between firms of the exploration and development type and commodity producing firms. Exploration and development firms are found to have more instances of currency risk exposure. Commodity producing firms show less currency risk exposure.
Throughout this paper, the sensitivity of cash flows to changes in exchange rates is referred to as currency risk exposure. In practice and in the literature currency risk is also referred to as foreign exchange (FX) risk or exchange rate risk. Whenever these terms are encountered, they all refer to sensitivity of cash flows to changes in exchange rates in order to avoid any ambiguity about nomenclature.
research on currency risk exposure. Section 3 describes the problem and the setup which is used to estimate currency risk. In Section 4 the applied methodology used to estimate currency risk exposure is explained. Section 5 contains the sample data and a report of the research results. Section 6 concludes the research.
2
Literature Review
Exposure to currency risk is a key concern for investors, analysts, and managers, as cash flows and stock prices of firms can be affected by this type of risk. Cash flows are an important component of assessing the value of a firm. As a result, there have been many attempts over the past decades to quantify the impact of fluctuating exchange rates.
Estimating currency risk using popular regression approaches requires a cash flow measure. To estimate the currency risk of cash flows, two general types of ap-proaches are available. The first method, called the direct approach, or cash flow approach, uses cash flow data of accounting-based cash flow proxies. The second method is called the indirect approach, or capital markets approach, which uses stock returns. Company managers prefer a direct estimate of currency risk, if available, to an indirect one.
In research, the indirect approach is most often used, since direct estimates of currency risk are difficult to obtain. The advantage of using equity returns is the absence of the noise problem inherent in cash flow data and accounting-based cash flow proxies. The indirect method of estimating a firm’s currency risk exposure as a regression coefficient has been introduced by Adler and Dumas (1984). The co-efficient in a simple regression of a firm’s equity returns on currency rate changes, with no control variable, is usually referred to as an estimate of a stock’s total currency risk exposure.
affect stock returns. Following Jorion (1990), many have used an equity market index control variable. Examples are Bodnar and Gentry (1993), Choi and Prasad (1995), Chow et al. (1997a, b), He and Ng (1998), Allayanis and Ofek (2001), and Griffin and Stulz (2001).
The earliest studies had limited success in detecting significant currency risk ex-posure. The results of Jorion (1990) show that only few firms, namely 15 of 287 firms (representing 5.2% of the sample), face statistically significant currency risk at the 5% significance level. In portfolio tests, only 20% (Jorion, 1990) and 35% (Jorion, 1991) of all portfolios are significantly exposed to currency risk, respec-tively. Similarly, other early studies including Walsh (1994) and Simkins and Laux (1997) document that 14.2% of individual U.S. firms and 28.0% of industry portfo-lios show significant currency risk exposure, while Choi and Prasad (1995) report 14.9% for individual U.S. firms and 10.0% for industry portfolios.
The use of an equity index control variable has an important drawback, as noted by Bodnar and Wong (2003). Since an equity index is an aggregate of individual firm equities, the equity index itself reflects the aggregate of the net currency risk exposures of the firms in the index. Therefore an equity index also controls for the aggregate net currency risk exposure, which is undesirable. The currency risk co-efficient is an indirect estimate of the difference between a firm’s currency risk and the aggregate net currency risk of the firms in the equity index only. This finding could explain why empirical estimates of firms’ currency risk exposure have tended to be surprisingly low and statistically insignificant, as reviewed by Bartram and Bodnar (2007).
contain any aggregate net currency risk exposure, resulting in a valid estimate of a firm’s currency risk. However, this method ignores that a domestic-firm equity index actually might have some unobserved currency risk exposure. Instead of an equity index, Krapl and O’Brien (2012) use bond returns as a control variable, since bond returns do not contain any currency risk exposure. Still, only 11.8% of the firms in their sample show significant currency risk exposure.
In contrast to indirect estimates of currency risk, there exists only very little evi-dence regarding the effect of currency risk on cash flows using the direct approach. Studies of samples of direct estimates of currency risk are scarce due to data un-availability and noise problems. Near-zero and negative observations often make direct estimation of currency risk difficult or impossible. Direct estimates have been found for single companies, for example, by Garner and Shapiro (1984), Ox-elheim and Wihlborg (1995), and Bartram (2008). Studies of samples that employ the direct approach are Bartram (2007), and Martin and Mauer (2003, 2005). The direct approach has the advantage of more directly measuring transaction and eco-nomic exposures.
The application of the direct approach often also gives little significant currency risk exposure. Garner and Shapiro (1986) find only small and statistically insignifi-cant currency risk exposure. The results of Oxelheim and Wihlborg (1995) indicate that changes in the exchange rate only affect cash flows to a modest degree. Bar-tram (2007) finds that the residual net currency risk exposure is economically and statistically small. Using the direct approach, Martin and Mauer (2005) find 157 firms with significant currency risk exposure out of a total of 520 firms, which translates into 30.2% of all firms. Irrespective of which approach is used, in many instances the exposure to currency risk is small and insignificant.
3
Estimating Currency Risk Exposure
Fund (NRF) of APG is a typical long-term investment fund. Its value is computed each month, whereas its investments are in many cases only valued once a year. For this reason this research follows a direct approach using cash flow data for the estimation of currency risk. An important advantage of this approach is that cash flows are not as strongly affected by general market sentiment as stock returns. The illiquid nature of the investments of the NRF is more properly approximated using cash flow data.
The NRF is interested in the determination of the currency risk of its investments and whether or not this risk should be hedged. To decide on possible hedging policies, an indication of the size of the currency risk is to be computed. For that reason the main topic of this research is the determination of the size and signifi-cance of the currency risk of commodity firms. In relation to the existing literature on currency risk, this research differs in that it focuses exclusively on commodity firms.
Applications of the direct approach for samples of firms are given in Bartram (2007) and Martin and Mauer (2003, 2005). In order to investigate the relationship be-tween cash flow changes and the relevant currency risk, Bartram (2007) suggests regressing corporate cash flow variables like earnings on changes in exchange rates. Martin and Mauer (2003, 2005) use operating income before adjustment of depre-ciation. Krapl and O’Brien (2012) use earnings per share as a dependent variable for the estimation of currency risk.
Instead of earnings per share or operating income, this research uses operating expenses as a cash flow variable. The rationale behind this choice will be given in the empirical analysis of the currency risk of firms. Regressions are performed using different versions of a general panel data model. Three models are used, a pooled ordinary least squares model, a fixed effects model, and a seemingly unre-lated regressions model, which are described in detail in the next section. Using these models, the significance and the size of the currency risk is given.
are regressed on changes in the relevant exchange rate. As a control variable, changes in commodity prices are added to the regression. For each firm the relevant commodity price is selected. The significance of the currency risk is determined by means of t-tests. Firms are selected in accordance with the interests of the Natural Resources Fund. The resulting currency risk exposures are summarized per country. Model fits are compared using likelihood ratio tests.
Besides the use of individual firms per country, an ’average’ firm is constructed for each country using a weighted average of operating expenses. These firms are used to compute the currency risk exposure of the average commodity firm of each country in order to give an indication of the size and significance of the currency risk. To test whether different types of firms have different currency risk exposures, firms are split between an exploration and development type and a commodity producing type. For each type and each country an ’average’ firm is again created using weighted averages of operating expenses.
4
Methodology
The general panel data model considered is of the regression form
yit = α + Xit0 δ + uit, (1)
where yit is the dependent variable, Xit is the itth observation on k explanatory
variables, α is a scalar, δ is k × 1 and uit is a disturbance term, i = 1, . . . , n and
t = 1, . . . , T . In this model, observations depend on time t and on individual i. The i subscript denotes the cross-section dimension, whereas t denotes the time-series dimension. Many applications of this general panel data model use a one-way error component model for the disturbances,
uit = ci+ νit, (2)
where ci denotes the unobservable individual-specific effect and νit denotes the
regression is captured by the time-invariant ci. The remainder disturbance νit
varies with individuals and time and can be seen as the usual disturbance in the regression. The Xit are assumed independent of νit for all i and t. Following
Baltagi (2005), model (1) can be written in vector form as
y = αιnT + Xδ + u, (3)
= Zβ + u (4)
where y is an nT × 1 vector of dependent variables, X is a nT × k matrix of explanatory variables, ιnT is a vector of ones of dimension nT , Z = (ιnT, X) is
nT × (k + 1), and β = (α, δ0)0 is a (k + 1) × 1 parameter vector. The disturbances can be written as
u = Dc + ν, (5)
where u = (u01, . . . , u0n)0, ui is a T × 1 vector of disturbances for individual i,
c = (c1, . . . , cn)0, and ν = (ν10, . . . , ν 0 n)
0, where ν
i is a T × 1 vector of remainder
disturbances for individual i. The matrix D is defined by D = In ⊗ ιT, where
In is an n × n identity matrix, ιT is a T × 1 vector of ones, and ⊗ denotes the
Kronecker product. The matrix D is a matrix of individual dummies that may be included in the regression to estimate the ci if these are assumed to be fixed
parameters. The nT × nT covariance matrix of the remainder disturbances νit is
given by Ω = Σ ⊗ IT, with typical element E(νitνjt) = σij. For the general model it
is assumed that the disturbances are heteroscedastic, E(ν2
it) = σi2. The variances
of the error process differ from individual to individual. For any given individual, the error variance is assumed constant over time, E(νitνjs) = 0 ∀i, j and t 6= s.
Let PD = D(D0D)−1D0 be the projection matrix of D. The matrix PD averages
the observations across time for each individual. The matrix QD = InT − PD
contains the deviations from the individual means. The matrices PD and QD are
symmetric, idempotent, and orthogonal, i.e. PD0 = PD, PD2 = PD, similarly for
As the general model contains more parameters than observations, restrictions on the parameters and the covariance matrix of the error terms are required. For the first model the restriction that is imposed on the parameters is that the individual effects ci are the same for all individuals. It is assumed that ci = 0 ∀i. As a
result, the estimators of the parameters α and δ are the same for all individuals. For this particular approach the disturbances νit are assumed independent and
identically distributed with mean 0 and variance σ2
ν. This model is the so-called
pooled ordinary least squares model. It is defined by
y = αιnT + Xδ + u, (6)
= Zβ + u, (7)
where u does not contain any individual-specific effects anymore, hence the uit are
independent and identically distributed with mean 0 and variance σu2 = σ2ν. The OLS estimator of model (7) is given by
ˆ
β = (Z0Z)−1Z0y, (8)
with Var( ˆβ) = σ2 u(Z
0Z)−1. For the estimated covariance matrix of ˆβ, the variances
σ2
u are estimated by s2, which is defined by
s2 = (y − Z ˆβ)
0(y − Z ˆβ)
nT − k . (9)
The second model that is considered is the fixed effects model. Here, the ci are
fixed parameters to be estimated. As noted by Greene (2003), if the ci are
unob-served, but correlated with Xit, then the least squares estimator of δ is biased and
inconsistent as a consequence of an omitted variable. The term ’fixed’ indicates that the individual-specific effect does not vary over time. The fixed effects model is given by
y = αιnT + Xδ + Dc + ν, (10)
with all variables defined as above in the general model. Ordinary least squares is used to compute estimates of α, δ, and the ci.
Alternatively, the fixed effects model can be specified as follows. Define αi = α+ci.
Then for individual i it holds that
yi = αi+ Xiδ + νi, (12)
where yi is a T × 1 vector of dependent variables for individual i, Xi: T × k is the
matrix of explanatory variables for individual i, and νi is the T × 1 disturbance
vector for i. The scalar αi denotes the individual-specific effect for i, whereas δ
denotes the common slope parameter. Stacking the equations of all individuals gives the fixed effects model.
The fixed effects model as given in equation (10) will contain too many dummy variables if n is large. The matrix to be inverted by OLS is of dimension n + k. Using results on partitioned regression the size of the computation can be reduced. The least squares dummy variables (LSDV) estimator of model (10) can be obtained by premultiplying the model by the annihilator matrix QD and
performing OLS on the resulting model
QDy = QDαιnT + QDXδ + QDDc + QDν, (13)
= QDXδ + QDν, (14)
since QDιnT = QDD = 0, as PDD = D. By premultiplying the model by QD the
individual-specific effects are removed. Performing OLS on model (14) requires the inversion of a k × k matrix instead of a (n + k) × (n + k) matrix. The LSDV estimator is given by
ˆ
δ = (X0QDX)−1X0QDy. (15)
For the fixed effects model, the disturbances νit are assumed heteroscedastic, in
line with the assumptions on the νit of the general panel data model. To allow
for a general covariance matrix on the νit as in White (1980), a simple method for
obtaining robust estimates of the standard errors has been described by Arellano (1987). This method assumes that T is small and n is large. The empirical part of this research will show that the sample data does not have a large n. Therefore the Arellano (1987) method will not be applied, but a different computation of robust standard errors is used.
Beck and Katz (1995) have developed a method for computing panel corrected standard errors. This method assumes that T is greater than or equal to n. The covariance matrix of the disturbances is given by Ω = Σ ⊗ IT, with typical element
E(νitνjt) = σij. Beck and Katz (1995) show that the robust covariance matrix of
ˆ
δ is given by
Var(ˆδ) = (X0X)−1(X0ΩX)(X0X)−1. (16) The covariance matrix Ω is an nT × nT block diagonal matrix with n × n blocks of contemporaneous covariance matrices Σ. To estimate the covariance matrix Ω, an estimate of Σ is required. Let eit be the OLS residual of individual i at time t.
A typical element of Σ can be estimated by
ˆ Σij =
PT
t=1eitejt
T . (17)
The estimate ˆΣ is comprised of all these elements. The estimated covariance ma-trix ˆΩ is a block diagonal matrix with diagonal elements ˆΣ.
The third model that is considered is the seemingly unrelated regressions (SUR) model. Take again the general panel data model given in equation (1), where Xit
now contains a constant term and β = (α, δ0)0,
where yit is the dependent variable, Xit is the itth observation on ki explanatory
variables, α is a scalar, δ is ki× 1 and uit is a disturbance term, i = 1, . . . , n and
t = 1, . . . , T . The SUR model as first proposed by Zellner (1962) is defined as follows. Let the set of n equations for n individuals be defined by
yi = Xiβi+ ui, (19)
where yi is a T × 1 vector of dependent variables, Xi is a T × ki matrix of
ex-planatory variables, βi is a ki × 1 parameter vector, and ui is a T × 1 vector of
disturbances. Impose the restrictions that the parameters of the model remain constant over time and assume that E(uitujt) = σij, E(uitujs) = 0 ∀i, j and t 6= s.
The regression relations for the different individuals are only related via the corre-lation of the error terms, but the error covariance across individuals is unrestricted.
The variables in Xi are assumed to be exogenous. Let U = (u1, . . . , un) and assume
that the rows of U are independent and identically distributed with mean zero and contemporaneous covariance matrix Σ = E(Ut0Ut), where Ut is the tth row of U .
If Σ is known up to a scalar factor, βi can be estimated by Generalized Least
Squares. Combining all equations in a single equation gives
y = Xβ + u, (20)
where y = (y10, . . . , yn0)0, β = (β10, . . . , βn0)0, u = (u01, . . . , u0n)0, and let
X = X1 0 · · · 0 0 X2 · · · 0 .. . ... . .. ... 0 0 · · · Xn . (21)
It follows that the covariance matrix of the disturbances is given by
where ⊗ is the Kronecker product. The GLS estimator is given by
ˆ
βGLS=X0 Σ−1⊗ IT X −1
X0 Σ−1⊗ IT y. (23)
For known Σ, the GLS estimator is also called the SUR estimator.
As Σ is unknown in practice, it needs to be estimated. For that purpose feasible GLS is applied. Consistent estimation of Σ is based on OLS residuals for the separate n equations. The matrix Σ can be estimated by
ˆ Σ = Uˆ
0Uˆ
T , (24)
where ˆU consists of the OLS residuals. The feasible GLS estimator is given by
ˆ βSUR = h X0 ˆΣ−1⊗ IT Xi −1 X0 ˆΣ−1⊗ IT y. (25)
The SUR estimator of the parameter vectors is asymptotically efficient relative to OLS, as the disturbances are assumed to be correlated. However, if GLS is numer-ically equal to OLS, there is no gain in efficiency. The greater the correlation of the disturbances, the greater is the efficiency gain accruing to GLS. Also, the less correlation there is between the Xi matrices, the greater is the gain in efficiency
in using GLS.
A number of special cases about efficiency is mentioned by Zellner (1962) and Dwivedi and Srivastava (1978). First, the feasible SUR estimator is asymptoti-cally as efficient as OLS if the matrix Σ is diagonal, i.e. if σij = 0 for i 6= j.
The equations are unrelated and GLS is equivalent to equation-by-equation OLS. Second, if the regressors in one block of equations are a subset of those in another, then GLS gives no efficiency gain over OLS in estimation of the smaller set of equations. Furthermore, if the matrix Xi of regressors is equal for each i, Xi = X
∀i, i = 1, . . . , n, and X is a T × l matrix, then model (20) can be rewritten as
where Y = (y1, . . . , yn) is a T × n matrix of dependent variables, B = (β1, . . . , βn)
is an l × n matrix of parameters, and U = (u1, . . . , un) is a T × n matrix of
disturbances. It follows that
ˆ
βSUR = ˆβOLS, (27)
irrespective of the structure of Σ. Efficient estimation of B is given by ˆBOLS =
(X0X)−1X0Y , and for ˆβOLS it follows that ˆβOLS = vec( ˆBOLS).
To examine the fit of each model, different tests are available. A common test used in testing for fixed effects is the Chow test. The joint significance of the dummy variables is tested by means of an F -test. The null hypothesis of this test is given by H0: c1 = c2 = · · · = cn−1, i.e. under H0 the individual effects are not
significant. If H0 is true, the fixed effects model reduces to the pooled OLS model.
Under H0 the test statistic
F = (R 2 LSDV− R2Pooled)/(n − 1) (1 − R2 LSDV)/(n(T − 1) − k) (28)
follows an F -distribution with n − 1 and n(T − 1) − k degrees of freedom. Here R2
LSDV refers to the residual sum of squares of the fixed effects (LSDV) model and
R2
Pooled refers to the residual sum of squares of the pooled OLS model.
As an alternative to the F -test the likelihood ratio test will be applied. The advantage of using this test is that all three types of models can be compared against eachother, whereas the Chow test only allows for a comparison between the fixed effects and the pooled OLS model. Consider again the SUR model
y = Xβ + u, (29)
where all variables are defined as above. Assume that u follows a multivariate normal distribution with mean vector zero and covariance matrix Ω = Σ ⊗ IT.
covariance matrix Ω, its density is equal to
(2π)−m/2|Ω|−1/2exp(−1 2z
0
Ω−1z). (30)
Using this result, the likelihood function f (y; β, Σ), which is equivalent to the density of y, is given by (2π)−nT /2|Σ ⊗ IT|−1/2exp −1 2(y − Xβ) 0 (Σ−1⊗ IT)(y − Xβ) . (31)
Taking the logarithm gives the log likelihood function `(β, Σ), which can be written as −nT 2 log 2π − 1 2log |Σ ⊗ IT| − 1 2(y − Xβ) 0(Σ−1⊗ I T)(y − Xβ). (32)
Applying the property that the determinant of Σ ⊗ IT is |Σ|T simplifies the log
likelihood function to −nT 2 log 2π − n 2log |Σ| − 1 2(y − Xβ) 0 (Σ−1⊗ IT)(y − Xβ). (33)
Maximizing the log likelihood with respect to the parameters β and Σ gives the maximum likelihood estimators ˆβML and ˆΣML. As GLS with known covariance
matrix amounts to maximum likelihood under normality, it follows that
ˆ β =hX0 ˆΣ−1⊗ IT Xi −1 X0 ˆΣ−1⊗ IT y. (34)
Therefore, if ˆΣ = ˆΣML, then ˆβML = ˆβ. Let the T × n matrix U (β) be defined to
have yi− Xiβi as its ith column. Davidson and MacKinnon (2009) show that the
maximum likelihood estimator of Σ is given by
ˆ ΣML= 1 nU ( ˆβML) 0 U ( ˆβML). (35)
given in equation (34) gives the concentrated log likelihood function `c(β; y) = − nT 2 (log 2π + 1) − n 2 log | 1 nU ( ˆβ) 0 U ( ˆβ)|. (36)
Maximization of the concentrated log likelihood function depends on the data only through the determinant of the covariance matrix of the residuals. Applying exclusion restrictions on the parameters allows the comparison of different models. The likelihood ratio test statistic is defined by
λ = −2(log Lr− log Lu) = −2 log
Lr
Lu
, (37)
where Lr denotes the likelihood of the restricted model and Lu the likelihood of
the unrestricted model. The likelihood ratio test statistic λ is asymptotically dis-tributed as χ2q with q degrees of freedom, where q equals the number of restrictions. The null hypothesis of this test is that the restricted model holds true. The alter-native hypothesis is that the full model holds. If the extra parameters of the full model do not significantly improve the fit, then the null hypothesis is not rejected. In the following section the three models described in this section will be fitted to the data.
5
Estimation of the Currency Risk of Firms and
Countries
There are many ways to model the currency risk of firms and countries. Consider a typical commodity producing firm. The revenue of this firm comes from the sales of commodities. Prices of mainstream commodities are determined on the world market, which are in U.S. dollars. The revenue is therefore assumed to be entirely in U.S. dollars and is hence unaffected by currency risk. As a result, the currency risk is assumed to be only related to the costs of a firm.
Commod-ity mining requires high specialty equipment. Only a small number of producers in the world is able to deliver this type of machinery. The prices of these goods are determined on the world market (U.S. dollars).
Operating expenses contain labour costs, energy costs, and other consumable costs. These costs are typically in local currency, but they can also consist of U.S. dollar costs. For example, a mining firm will use local workers as much as possible, but it will go to the international market to source highly-skilled specialists. The former category of employees is paid in local currency, whereas the so-called expats are often paid in U.S. dollars. The focus of this research is on the currency risk of the operating expenses of commodity firms.
In this paper, currency risk refers to the sensitivity of operating expenses to ex-change rate movements. Operating expenses, abbreviated as opex, are given in U.S. dollars. These items can be found on the financial statements of firms. To model the currency risk of the operating expenses of a firm, it is assumed that the opex of each firm are subject to changes in exchange rates. This assumption implicates that firms face currency risk. Two general approaches are selected to measure the size and significance of the currency risk. From this point on, the currency risk of the operating expenses of a firm is referred to as the currency risk of a firm.
The second approach compares the currency risk of firms between countries. To that end, a weighted average of the operating expenses of all firms within a country is computed as to create a hypothetical ’average’ firm that is representative for each country. Using these average firms, a pooled OLS and a fixed effects model are estimated to determine the currency risk of all average firms of all countries. The pooled OLS model does not differentiate between countries, whereas the fixed effects model allows for differences.
To estimate the currency risk of the average firm of each country, a SUR model is applied. The SUR model assumes that countries are linked in unknown ways. If there is no such link between countries, the SUR model reduces to an OLS model per country. Similar to the first approach, likelihood ratio tests and t-tests are employed to determine which model fits best and what the size and significance of the currency risk is. Additionally the currency risk exposures of exploration & development firms and commodity producing firms are estimated using all three models.
5.1
Data Description
Data on commodity spot prices is obtained from Bloomberg. Monthly data from 2000 to 2012 on prices of the following commodities is used: gold, silver, platinum, palladium, copper, lead, zinc, nickel, iron ore, Brent oil, WTI oil, and natural gas. Besides these commodity price series, monthly spot price data on the Standard and Poor’s Goldman Sachs Commodity Index, a commodity price index, is obtained. Monthly data on thermal coal prices comes from the IMF. All commodity price series are end-of-month observations. As the analysis uses yearly data, a simple average is computed for each year of the monthly commodity price data to come up with yearly commodity price observations.
Monthly data on exchange rates comes from Datastream, where Thomson Reuters is used to collect exchange rate series on the following countries: Argentina, Aus-tralia, Brazil, Canada, Chile, Mexico, Peru, South Africa, and the Eurozone. The currencies of these countries are all taken versus the U.S. dollar. Similar to the commodity price series, simple averages of exchange rate series are computed for each year from 2000 to 2012 for all countries.
In order to compare the firms that are listed on a stock exchange with the firms in the Natural Resources Fund, a number of restrictions is made on the firm data. First, all firms in the dataset are commodity firms according to their SIC code. However, in reality and by the business description by Factset this turns out to be incorrect. Many firms are active in other types of businesses, hence these firms are removed from the data. Next, the NRF is only interested in small to medium-sized firms. For this reason only firms with a market capitalization of 10 million to 1,500 million U.S. dollar in 2012 are used in the analysis. This operation removes the very small firms and the large to very large firms from the data.
substantial revenue. Only countries that the NRF is interested in or has already invested in are used.
In practice many listed firms are active in more than one country. Furthermore, many commodity firms are listed on the Australian or Canadian stock exchange. Many of these firms are actually only listed on these exchanges for financial con-siderations. Their activities can be present in entirely different countries. For example, a firm that is listed on the Canadian stock exchange and develops com-modities in Brazil is indicated as a Canadian firm. In reality this firm only has activities in Brazil, hence it is subject to fluctuations in the USD/BRL exchange rate.
Correcting for the country in which a firm has its activities, the final dataset contains 132 firms with at least 10 years and at most 13 years of yearly data on operating expenses. For the metals and mining firms, commodity firms in Australia, Brazil, Canada, Chile, Mexico, Peru, and South Africa are used. For each country to be included in the analysis, at least 5 firms should meet the required conditions. This results in the removal of Argentina and the Eurozone due to a lack of data. For the oil and gas firms, Australia and Canada are selected. In the analysis these are treated as two separate groups. An overview of the firms is given in Table 1.
5.2
Within-Country Currency Risk
Number of firms Expl. & dev. Prod. Total
Australia 11 14 25
Australia (Oil & Gas) 4 4 8
Brazil 6 0 6
Canada 14 11 25
Canada (Oil & Gas) 4 17 21
Chile 2 3 5
Mexico 9 4 13
Peru 4 7 11
South Africa 9 9 18
All countries 63 69 132
Table 1: Overview of firms. For each country the number of exploration & develop-ment firms (’Expl. & dev.’), the number of commodity producing firms (’Prod.’), and the total number of firms (’Total’) is given.
Let Oit be the operating expenses in U.S. dollars for firm i in year t. The U.S.
dollar price of the commodity produced in year t is given by qit. If a firm produces
more than a single type of commodity, the price of the most important commodity produced by the firm is selected. The exchange rate fit is the amount of U.S.
dollars per unit of foreign currency for firm i in year t. For example, when the USD/CAD exchange rate is applied, the exchange rate is defined as the amount of U.S. dollars per Canadian dollar.
is made. First, the logarithm of the opex, commodity price, and exchange rate is taken. This transformation ensures that percentage changes are applied instead of unit changes. Next, the year-on-year changes of these variables are defined by
Cit = log Oit− log Oit−1, (38)
pit = log qit− log qit−1, (39)
eit = log fit− log fit−1. (40)
Regression models are used to estimate the currency risk of firms. The regression coefficients of commodity prices and exchange rates are referred to as the commod-ity price sensitivcommod-ity and the currency risk sensitivcommod-ity, respectively. The latter term may also be referred to as the currency risk exposure. For ease of explanation, references to changes in the year-on-year changes of the logarithm of opex are ab-breviated as changes in opex. The same holds for changes in prices and exchanges rates.
5.2.1 Model A1: Pooled Ordinary Least Squares
The first model that is considered is the pooled ordinary least squares model. The idea of this model is that commodity producing firms within a certain country face similar currency risk, irrespective of the type of commodity produced. This model implicitly assumes that βit = β ∀i, t. Stacking the observations of all firms for a
single country in a single vector leads to the model
C = α(A1)· ιnT + θ(A1)· p + γ(A1)· e + u(A1), (41)
= X(A1)β(A1)+ u(A1), (42)
where C is an nT × 1 vector of operating expenses, X(A1)= (ι
nT, p, e) is an nT × 3
matrix of explanatory variables, with ιnT an nT ×1 vector of ones, p = (p01, . . . , p0n)0
pooled OLS estimator is given by
ˆ
β(A1)= (X(A1)0X(A1))−1X(A1)0C. (43) Table 2 contains the estimation results for the pooled OLS regression.
The first three columns of Table 2 consist of the estimated parameters ˆα(A1), ˆθ(A1),
and ˆγ(A1) and their standard errors between parentheses for each country. To
determine whether firms in a particular country are subject to currency risk, a t-test is performed to t-test if the estimated parameter of the currency risk sensitivity ˆ
γ(A1) differs significantly from 0. The test statistic S = ˆγ
(A1)− γ(A1)
ˆ σγ(A1)
(44)
is used to test the null hypothesis H0: γ(A1) = 0 against the alternative H1:
γ(A1) 6= 0, where ˆσ
γ(A1) is the standard error of ˆγ(A1). Under the null it holds that
S is asymptotically distributed as a t-distributed random variable with nT − k degrees of freedom, where the number of parameters k equals 3. The final column of Table 2 consists of the p-values of this test.
The results of the pooled OLS estimation show that in general the currency risk exposure of commodity firms differs greatly between countries. The point esti-mations of the currency risk sensitivity ˆγ(A1) vary between -0.929 for Canadian oil and gas firms and 5.429 for Chilean firms. The standard errors of these point estimations, which are given between parentheses, are in some cases very large, up to a value of 2.556 for Chilean firms. The number of companies used for the estimations seems to have a large impact in these values, as for the pooled OLS estimation of Australia 25 firms are used, whereas in the case of Chile only 5 firms are used.
ˆ
α(A1) θˆ(A1) γˆ(A1) p-value
Australia 0.097 0.505 1.540 0.063
(0.085) (0.349) (0.821)
Australia (Oil & Gas) 0.134 0.615 0.156 0.886 (0.093) (0.403) (1.084)
Brazil 0.034 1.615 3.171 0.010
(0.321) (1.910) (1.179)
Canada 0.066 0.443 2.644 0.035
(0.093) (0.445) (1.241)
Canada (Oil & Gas) 0.217 0.526 -0.929 0.324 (0.061) (0.229) (0.936) Chile 0.247 -0.794 5.429 0.040 (0.132) (0.619) (2.556) Mexico 0.304 0.748 1.151 0.375 (0.140) (0.508) (1.289) Peru 0.025 0.606 1.863 0.412 (0.089) (0.267) (2.262) South Africa 0.270 0.616 -0.011 0.981 (0.073) (0.256) (0.478)
Table 2: Results of the pooled OLS estimation of model A1. The regression coeffi-cients of the model are indicated by ˆα(A1), ˆθ(A1), and ˆγ(A1), which are estimated for
Brazilian real versus the U.S. dollar leads to an increase of more than 3% in opex, ceteris paribus. The same holds for Canadian and Chilean mining firms. Appar-ently, the commodity firms in these countries have relatively high costs in local currency and low costs in U.S. dollars. The absolute value of the currency risk sensitivity appears too large to be acceptable. It seems more appropriate to focus only on the sign of the estimates. Except for Canadian oil and gas firms and South African firms all countries have positive currency risk sensitivity, meaning that an appreciation of the local currency versus the U.S. dollar leads to greater opex.
Except for Chile, the commodity price sensitivity ˆθ(A1) of all countries is positive,
which means that an increase of the commodity price of a commodity firm leads to increasing opex. This makes sense, as a price increase makes mining for commodi-ties more profitable. This increases the demand for labour thus increasing local labour costs. For Brazilian firms this effect seems especially large: a 1% increase in the commodity price of the commodity produced gives an increase of 1.6% in opex of Brazilian firms, keeping all other variables constant. Why increasing commodity prices lead to lower opex for Chilean firms is unclear and probably the result of insufficient data.
5.2.2 Model A2: Fixed Effects
The second model that is estimated is the fixed effects model. This model differs from the pooled OLS model in the sense that it allows inference on the behavior of firms in a particular country. In this case, the αi are unobservable firm-specific
effects, which are assumed to be fixed parameters to be estimated. Hence, it is assumed that αit = αi ∀t. Similar to the pooled OLS model, firms are assumed to
face common currency risk, therefore θit = θ and γit = γ ∀i, t. For firm i it now
follows that Ci = α (A2) i · ιT + θ(A2)· pi+ γ(A2)· ei+ u (A2) i , (45)
where Ci is a T × 1 vector of operating expenses for firm i, ιT is a T × 1 vector
of ones, and pi, ei, and u (A2)
i are T × 1 vectors of prices, exchange rates, and
disturbances for firm i, respectively. Let α(A2) = (α(A2) 1 , . . . , α
(A2)
nT × n be defined by D = In⊗ ιT. Stacking the equations of all firms over t results
in the fixed effects model
C = D · α(A2)+ θ(A2)· p + γ(A2)· e + u(A2), (46)
= X(A2)β(A2)+ u(A2), (47)
where C = (C10, . . . , Cn0)0is an nT ×1 vector of operating expenses, X(A2) = (D, p, e) is an nT × (n + 2) matrix of explanatory variables, where p = (p01, . . . , p0n)0 and e = (e01, . . . , e0n)0, β(A2) = (α(A2)0, θ(A2), γ(A2))0 is an (n + 2) × 1 coefficient vector,
and u(A2) = (u(A2) 1
0, . . . , u(A2)
n 0)0 is an nT × 1 vector of disturbances. The estimation
of β(A2) is done by OLS,
ˆ
β(A2)= (X(A2)0X(A2))−1X(A2)0C. (48) The results of the fixed effects estimation are given in Table 3.
The first column of Table 3 consists of the mean value ˆα¯(A2)i of the firm-specific effects ˆα(A2)i , which is computed as the simple average of all firm-specific effects in a particular country. The second and third column of Table 3 contain the estimated parameters ˆθ(A2) and ˆγ(A2)and their standard errors between parentheses for each
country. The standard errors are panel corrected versions of the usual standard errors obtained by OLS in the sense that they allow for correlation between firms. The panel corrected covariance matrix of ˆβ(A2) is estimated by
Varpcse( ˆβ(A2)) = (X(A2)0X(A2))−1X(A2)0(IT ⊗ ˆΣ(A2))X(A2)(X(A2)0X(A2))−1, (49)
where ˆΣ(A2) is the estimate of the matrix of covariances Σ(A2). The panel corrected standard errors are the square roots of the diagonal values of Varpcse( ˆβ(A2)). For
ˆ ¯
α(A2) θˆ(A2) γˆ(A2) p-value
Australia 0.097 0.505 1.539 0.049
(0.089) (0.365) (0.774)
Australia (Oil & Gas) 0.134 0.615 0.156 0.880 (0.088) (0.382) (1.026)
Brazil 0.034 1.615 3.171 0.002
(0.253) (1.508) (0.930)
Canada 0.081 0.317 2.747 0.011
(0.078) (0.391) (1.058)
Canada (Oil & Gas) 0.217 0.526 -0.929 0.260 (0.054) (0.201) (0.819) Chile 0.247 -0.803 5.454 0.092 (0.117) (0.645) (3.160) Mexico 0.311 0.715 1.188 0.425 (0.161) (0.589) (1.481) Peru 0.027 0.588 1.881 0.526 (0.115) (0.334) (2.956) South Africa 0.265 0.665 -0.029 0.949 (0.067) (0.225) (0.446)
Table 3: Results of fixed effects estimation of model A2. The regression coefficients of the model are indicated by ˆα¯(A2), ˆθ(A2), and ˆγ(A2), which are estimated for each
country using a separate model. The regression coefficient ˆα¯(A2)is the mean of the
The results of the fixed effects estimation are in general not very different from the pooled OLS results. The currency risk sensitivities ˆγ(A2) of Brazilian, Canadian, and Chilean firms are also significant in this model, as judged by the respective p-values of a t-test. Australian commodity firms are also found to have significant positive currency risk. The absolute values of the estimated parameters remain roughly the same, implying that adding firm-specific effects does not alter the com-modity price and currency risk sensitivities ˆθ(A2) and ˆγ(A2). This can be checked
by means of a likelihood ratio test for each country. Under the null hypothesis, the pooled OLS model is the correct model, whereas under the alternative hypothesis the addition of firm-specific effects leading to the fixed effects model is the correct model.
The likelihood ratio test statistic is computed as
λ = −2(log Lr− log Lu) = −2 log
Lr Lu
, (50)
where Lr denotes the likelihood of the pooled OLS model and Lu the likelihood of
the fixed effects model. The test statistic λ follows asymptotically a χ2distribution
with n − 1 degrees of freedom. The number of degrees of freedom is determined by the number of additional parameters of the fixed effects model. For every country there are n firms, hence n parameters are added to the model for the n firm-specific effects. One parameter is dropped as the pooled OLS model contains already a parameter α. For each model the value of the log likelihood is computed.
5.2.3 Model A3: Seemingly Unrelated Regressions
The SUR model is the third model that is to be estimated. As a restriction it is assumed βit = βi ∀t, i.e. all firms have their own regression parameters, but these
are restricted to be constant over time. This restriction gives rise to the assump-tion that firms are only related via the correlaassump-tion of the error terms. This makes intuitive sense, as firms in a single country face common risks that are specific for the particular country. Compared to the fixed effects model the currency risk sensitivity may differ among the firms.
A downside of the application of the SUR model is that the number of parameters to be estimated increases sharply. As the time dimension of the data is relatively small, the estimates for the parameters may not be reliable. The model for SUR unit i is given by Ci = α (A3) i · ιT + θ (A3) i · pi+ γ (A3) i · ei+ u (A3) i , i = 1, . . . , n (51)
= Xi(A3)βi(A3)+ u(A3)i , (52)
where Ci is a T × 1 vector, X (A3)
i = (ιT, pi, ei) is a T × 3 matrix, ιT is a T × 1
vec-tor of ones, βi(A3) = (α(A3)i , θ(A3)i , γi(A3))0 is a 3 × 1 vector, and u(A3)i is a T × 1 vector. Combining the opex of all firms of a country in a single equation gives the SUR model
C = X(A3)β(A3)+ u(A3), (53)
Estimation of the parameters is performed by means of feasible GLS. The SUR estimator is given by
ˆ
β(A3) =hX(A3)0 ˆΣ(A3)−1⊗ IT
X(A3)i −1 X(A3)0 ˆΣ(A3)−1⊗ IT C, (55)
where ˆΣ(A3) is the estimate of the matrix of covariances Σ(A3). The results of the
SUR estimation for each country are given in Table 4. The first three columns of Table 4 consist of the simple averages ˆα¯(A3), ˆθ¯(A3), and ˆγ¯(A3) of the estimated
parameters ˆα(A3), ˆθ(A3), and ˆγ(A3) for each country. The last column of Table 4 denotes the number of firms in the particular country that face significant currency risk. The significance of the currency risk for each firm is again determined by means of a t-test. The number of degrees of freedom for the t-test of each firm equals nT −k, where k equals 3n, as each firm i has 3 parameters and each country has n firms. A significance level of 5% is applied to determine whether a firm has significant currency risk.
A limited number of firms is found to have significant currency risk ˆγ(A3). One
country stands out, which is Peru. Of all 10 firms used in the estimation for Peru, 4 are found to have significant currency risk. All in all, for most countries the sign of the currency risk sensitivity is still the same as before. However, the sign of the commodity price sensitivity ˆθ(A3) has reversed in the case of Canada and Mexico. Conducting likelihood ratio tests of the fixed effects model (the restricted model) versus the SUR model (the unrestricted model) does not result in any case to the rejection of the fixed effects model. Similarly, likelihood ratio tests of the pooled OLS model (the restricted model) versus the SUR model (the unrestricted model) does not lead to any rejections of the pooled OLS model. It is very likely that the SUR model suffers from overparameterization, in which case too many parameters are estimated with too little data.
ˆ ¯
α(A3) θˆ¯(A3) γˆ¯(A3) Sig.
Australia -0.042 1.321 1.560 1
Australia (Oil & Gas) 0.134 0.615 0.156 0
Brazil 0.034 1.615 3.171 1
Canada 0.189 -0.412 3.073 0
Canada (Oil & Gas) 0.217 0.526 -0.929 0
Chile 0.509 -1.752 2.859 2
Mexico 0.529 -0.594 1.464 0
Peru 0.153 -0.358 1.105 4
South Africa 0.232 0.773 0.069 2
Table 4: Results of the SUR estimation of model A3. The regression coefficients of the model are indicated by ˆα¯(A3), ˆθ¯(A3), and ˆγ¯(A3), which are the mean values of
the regression coefficients ˆα(A3), ˆθ(A3), and ˆγ(A3) of all firms within a country. The
column ’Sig.’ refers to the number of firms within that country with significant currency risk, as determined by means of a t-test of whether the currency risk sensitivity ˆγ(A3) differs significantly from 0.
countries with many firms the estimates have a smaller standard error as compared to countries with a small number of firms. Furthermore, each firm is given equal weight in the estimation, which seems questionable. For these reasons a second approach is used to come up with estimates of the currency risk. This approach, the so-called between-country approach, is explored in the next section.
5.3
Between-Country Currency Risk
this approach is to give a general impression of the currency risk of firms in a specific country. This approach differs from the within-country approach in the sense that the within-country approach focuses on the currency risk of individual firms within a country, whereas the between-country approach is used to compare currency risk between countries.
For each country a hypothetical ’average’ firm is designed which represents the firms of a country and their average currency risk. The ’average’ firms are con-structed in the following way. Let the number of countries be denoted by N and the number of firms within country j by nj. The operating expenses in U.S. dollars
for firm i of country j in year t are denoted by Oijt. The operating expenses of all
firms are the same figures as used before in the within-country approach. Similar to the latter approach, the percentual changes in year-on-year opex are computed for all firms. The average change of all changes in opex of all firms within a cer-tain country is computed for every year t. This average change in opex, which is denoted by ˜Cjt, represents the changes in opex of the average firm.
For the computation of the average change in opex, a weighted average of opex is used in favour of a simple average. The idea behind this choice is as follows. The operating expenses of exploration and development firms are found to differ substantially from year to year. In contrast, the operating expenses of commodity producing firms are much more stable from year to year. By using a weighted average the percentual changes in opex of the non-producing firms do not cause the opex of the ’average’ firm to fluctuate as much as when a simple average is used instead.
More formally, select country j and compute the year-on-year changes of the log-arithm of operational expenses Oijt of all firms within that country,
Cijt = log Oijt− log Oijt−1, i = 1, . . . , nj; j = 1, . . . , N ; t = 2, . . . , T. (56)
within country j times their relative weight. The relative weight wijt of firm i in
year t is defined as the opex of firm i divided by the sum of the opex of all firms in year t, which is computed as
wijt=
Oijt
Pnj
i=1Oijt
. (57)
For each year the relative weight wijt of the opex of firm i is multiplied by the
year-on-year percentual change in opex Cijt of that firm. Taking the sum of the
weighted changes in opex of all firms gives the average change in opex ˜Cjt of all
firms for year t,
˜ Cjt = nj X i=1 wijtCijt, j = 1, . . . , N ; t = 2, . . . , T. (58)
This average change in opex ˜Cjt of all firms is referred to as the change in opex of
the average firm of country j.
Similar to the within-country approach, a pooled OLS, fixed effects, and SUR model are estimated using the changes in opex of the N average firms. Again, the total operating expenses of commodity firms are explained by the price of the commodity produced and by the exchange rate of the country in which the firm is located. Let ˜Cjt be the change of the average firm of country j, j = 1, . . . , N .
The price of the commodity produced in year t is given by qjt. As not every
firm produces the same commodity, a commodity price index is used to denote the price. The exchange rate fjt is the amount of U.S. dollars per unit of foreign
currency for country j in year t. The year-on-year changes of these variables are given by
pjt = log qjt− log qjt−1, (59)
5.3.1 Model B1: Pooled Ordinary Least Squares
First, a pooled ordinary least squares model is estimated, which is indicated by model B1. This model does not account for any differences among countries. The model basically answers the question if commodity firms all over the world com-bined face significant currency risk. The observations of all average firms of all countries are stacked in a single vector as in model A1, given by equation (41). As a commodity price index the Standard and Poor’s Goldman Sachs Commodity Price Index (S&P GSCI) is used. The estimation results for the pooled OLS re-gression of model B1 are given in panel A of Table 5.
Panel A: Pooled OLS αˆ(B1) θˆ(B1) γˆ(B1) p-value
All average firms 0.029 0.764 0.333 0.397 (0.035) (0.203) (0.392)
Panel B: Fixed effects αˆ¯(B2) θˆ(B2) γˆ(B2) p-value
All average firms 0.028 0.801 0.202 0.630 (0.045) (0.240) (0.418)
Panel C: SUR αˆ¯(B3) θˆ¯(B3) γˆ¯(B3) Sig.
All average firms -0.023 0.967 -0.356 2
Table 5: Results of the pooled OLS, fixed effects, and SUR estimation of models B1, B2, and B3. The first three columns of all panels contain the regression coeffi-cients. Standard errors of the regression coefficients are given between parentheses. The final column of panels A and B denotes the p-value of the t-test of ˆγ(B1) and
ˆ
γ(B2) significantly differing from 0. The column ’Sig.’ refers to the number of
average firms with significant currency risk, as determined by means of a t-test of whether ˆγ(B3) is significantly different from 0.
The first three columns of panel A of Table 5 contain the estimated parameters ˆ
α(B1), ˆθ(B1), and ˆγ(B1) and their standard errors between parentheses. The final column denotes the p-value of the t-test of ˆγ(B1) significantly differing from 0. The
results of the pooled OLS estimation in panel A of Table 5 show that the com-modity price sensitivity ˆθ(B1) and the currency risk sensitivity ˆγ(B1) of all average
an increase of 0.764% in opex on average. As noted before, price increases lead to increased demand for labour and to higher labour costs. Increases in fuel prices give rise to greater fuel costs, thus increasing opex. Since a commodity price index has been used as a regressor, it is not possible to distinguish between the different effects of price increases.
Regarding the currency risk sensitivity ˆγ(B1), on average an appreciation of the
local currency by 1% versus the U.S. dollar increases the opex of the average firm by 0.333%. This effect is insignificant, as the p-value of 0.397 shows. This implies that movements in the exchange rate on average do not affect the operating expenses of a firm significantly. An important point to note is that the effect of currency movements is not significant for the average firm. As found by the within-country approach, the differences in size and significance of the currency risk sensitivity can differ entirely for different firms, even for firms in the same country.
5.3.2 Model B2: Fixed Effects
Next, a fixed effects model is estimated, which allows for country-specific effects. The unobservable country-specific effects α(B2)j are assumed to be fixed parame-ters to be estimated. Using the changes in operating expenses of the average firm
˜
Cjt and equation (46) of model A2, the fixed effects model for average firms is
estimated. The estimation results are given in panel B of Table 5.
The first column of panel B of Table 5 consists of the mean value ˆα¯(B2) of the
country-specific effects ˆα(B2)j , which is computed as the simple average of all country-specific effects. The second and third column of panel B of Table 5 con-tain the regression coefficients ˆθ(B2) and ˆγ(B2) and their panel corrected standard
errors between parentheses. The p-value of the t-test for significant currency risk sensitivity is given in the last column.
sensi-tivity ˆθ(B2) is somewhat larger, whereas the value of the currency risk sensitivity
ˆ
γ(B2) is smaller than in the pooled OLS model. Again, judging by the p-value, the
positive value of the currency risk sensitivity is insignificant, which implies that for the average firm the currency risk does not significantly impact the operating expenses, even after accounting for differences among countries. A likelihood ra-tio test between the pooled OLS model and the fixed effects model results in no rejection of the pooled OLS model.
5.3.3 Model B3: Seemingly Unrelated Regressions
In line with the within-country approach, a SUR model is estimated, which is indicated by model B3. The average firms of all countries are assumed to have their own regression parameters. From this it follows that each country has its own currency risk sensitivity ˆγ(B3). Again, as a drawback this model suffers from a large number of parameters to be estimated, which may turn out to be unreliable. Using the changes in operating expenses of the average firm ˜Cjt, the SUR model
is estimated using equation (53) of model A3.
A summary of the results of the estimation of the SUR model is given in panel C of Table 5. The first three columns consist of the simple averages ˆα¯(B3), ˆθ¯(B3), and ˆγ¯(B3) of the estimated parameters ˆα(B3), ˆθ(B3), and ˆγ(B3) for all average firms combined. The last entry of panel C of Table 5 denotes the number of coun-tries in which the average firm has significant currency risk. As opposed to the pooled OLS and fixed effects model, the average currency risk sensitivity ˆ¯γ(B3) is
found to be negative. There are 2 average firms of countries with significant cur-rency risk sensitivity, namely Canadian oil and gas firms and Mexican commodity firms. The detailed results of the SUR estimation of model B3 are given in Table 6.
Table 6 contains the estimated parameters ˆα(B3), ˆθ(B3), and ˆγ(B3) for the
ˆ
α(B3) θˆ(B3) ˆγ(B3) p-value
Australia 0.088 0.546 0.234 0.585
(0.040) (0.232) (0.427)
Australia (Oil & Gas) 0.064 0.634 -0.039 0.945 (0.084) (0.445) (0.557)
Brazil -0.089 1.985 0.250 0.707
(0.139) (0.747) (0.663)
Canada -0.024 0.450 1.128 0.206
(0.048) (0.312) (0.886)
Canada (Oil & Gas) 0.165 0.061 1.426 0.003 (0.041) (0.228) (0.466) Chile 0.148 0.506 0.209 0.196 (0.029) (0.148) (0.160) Mexico -0.486 3.764 -7.988 0.000 (0.144) (0.710) (0.661) Peru 0.015 0.281 1.748 0.377 (0.087) (0.440) (1.966) South Africa -0.089 0.479 -0.174 0.403 (0.064) (0.322) (0.206)
Table 6: Detailed results of the SUR estimation of model B3. The regression coefficients of the model are indicated by ˆα(B3), ˆθ(B3), and ˆγ(B3). The standard
firm has an extremely large significant negative currency risk, implying that an appreciation of the Mexican peso leads to a large decrease in operating expenses, which are denoted in U.S. dollars. The absolute value of the Mexican currency risk sensitivity seems inappropriately large, which raises doubts on whether the model is overparameterized.
The results in Table 6 also show that the commodity price sensitivity ˆθ(B3) is
positive for all countries, which is to be expected. Increases in prices, either in commodity prices of the commodities sold or in fuel prices, lead to an increase in opex for the average firm. Besides Mexican firms, Australian oil and gas firms and South African mining firms have a negative currency risk sensitivity ˆγ(B3),
im-plying that an appreciation of the local currency versus the U.S. dollar decreases opex. Likelihood ratio tests of the SUR model versus the pooled OLS model and the fixed effects model lead in both cases to the rejection of the reduced model. Hence, according to the likelihood ratio tests the SUR model is preferred to the pooled OLS model and the fixed effects model. In the light of overparameteriza-tion this seems difficult to accept.
Comparing the results of the SUR estimation in Table 6 to the results of the pooled OLS model in Table 2 which are obtained using the within-country approach, the between-country approach shows its advantage. The standard errors of the SUR estimation using the latter approach are much smaller, which gives much more precise point estimates of the commodity price and currency risk sensitivities. Av-eraging the opex of all firms within a country produces more reliable results.
5.3.4 Differentiating Between Two Types of Firms
To investigate whether the currency risk sensitivity is related to the type of firm, the data is split in two categories. The first category contains firms that ex-plore or develop commodities, but that do not produce any commodity. As a zero-production condition firms with zero revenue are selected from the data. A number of these firms has little operating expenses, since they only employ ex-ploration activities. Other firms that are close to production might already have substantial operating expenses. The second category consists of producing firms. These firms are selected according to having a minimum annual revenue of 10 mil-lion U.S. dollar for at least 5 consecutive years.
The currency risk sensitivity of both types of firms is estimated in a similar fashion as before. In line with the idea of constructing an average firm for each country, an average exploration/development firm and an average producing firm is created for every country. For all countries and for each type of firm a weighted average of the change in opex is calculated. The changes in opex of these weighted averages represent the changes in opex of the average firms. Using these average firms, estimates of the currency risk sensitivity of both types of firms are computed for all countries.
5.3.5 Models C1 - C3 for Exploration and Development Firms
Starting with the exploration and development firms, a pooled OLS, fixed effects, and SUR model are estimated. These models are indicated by C1, C2, and C3. As before, next to the currency rates of the different countries the S&P GSCI is added again as a regressor. The estimation results of the three models are given in Table 7.
The first three columns of Panel A in Table 7 give the estimated parameters ˆα(C1),
ˆ
θ(C1), and ˆγ(C1) and their standard errors between parantheses. For the fixed
ef-fects model in Panel B the simple average ˆα¯(C2) of all firm-specific effects ˆα(C2) j
Panel A: Pooled OLS αˆ(C1) θˆ(C1) ˆγ(C1) p-value
All average firms -0.004 0.758 -0.407 0.544 (0.059) (0.347) (0.668)
Panel B: Fixed effects αˆ¯(C2) θˆ(C2) ˆγ(C2) p-value All average firms -0.006 0.849 -0.730 0.368
(0.051) (0.330) (0.807)
Panel C: SUR αˆ¯(C3) θˆ¯(C3) ˆ¯γ(C3) Sig.
All average firms -0.001 0.720 -0.673 5
Table 7: Results of the pooled OLS, fixed effects, and SUR estimation for explo-ration and development firms (models C1, C2, and C3). The first three columns of all panels contain the regression coefficients. Standard errors of the regression coefficients are given between parentheses. The final column of panels A and B denotes the p-value of the t-test of ˆγ(C1) and ˆγ(C2) significantly differing from 0.
The column ’Sig.’ refers to the number of average firms with significant currency risk, as determined by means of a t-test of whether ˆγ(C3) is significantly different
from 0.
Table 7 contains the p-value of the t-test of the currency risk sensitivities ˆγ(C1)
and ˆγ(C2) being significantly different from 0. For the SUR model the number of
countries with significant currency risk is given. The detailed results of the SUR estimation of model C3 are given in Table 8.
The results of the pooled OLS estimation show that the currency risk sensitivity ˆ
γ(C1) of exploration and development firms is negative, but insignificant at the 5% significance level, as the p-value equals 0.544. Compared to the fixed effects model, the currency risk sensitivity ˆγ(C2) is even more negative. The effects is
however insignificant again. A likelihood ratio test of the pooled OLS model ver-sus the fixed effects model results in no rejection of the pooled OLS model. The additional firm-specific parameters α(C2)j do not improve the fit of the model. The pooled OLS model is therefore preferred to the fixed effects model.
ˆ
α(C3) θˆ(C3) ˆγ(C3) p-value
Australia 0.023 1.758 -0.715 0.303
(0.106) (0.559) (0.690)
Australia (Oil & Gas) -0.108 0.057 0.887 0.230 (0.129) (0.671) (0.734)
Brazil -0.041 1.502 1.191 0.000
(0.135) (0.669) (0.158)
Canada 0.031 0.238 1.475 0.101
(0.079) (0.441) (0.890)
Canada (Oil & Gas) 0.185 0.962 -1.609 0.057 (0.111) (0.579) (0.834) Chile 0.297 -1.409 1.340 0.004 (0.197) (0.980) (0.448) Mexico -0.116 1.628 -2.085 0.000 (0.076) (0.374) (0.316) Peru 0.096 1.624 -3.547 0.000 (0.075) (0.371) (0.270) South Africa -0.453 0.121 -2.994 0.000 (0.290) (1.437) (0.484)
Table 8: Detailed results of the SUR estimation for exploration and development firms of model C3. The regression coefficients of the model are indicated by ˆα(C3),
ˆ
θ(C3), and ˆγ(C3). The standard errors of the coefficients are given between
greatly between countries. Using a 5% significance level, the average exploration and development firms in Brazil, Chile, Mexico, Peru, and South Africa are found to have significant currency risk, as can be seen by the p-value in the fourth column. The absolute value of the currency risk sensitivity is huge in the case of Mexico, Peru, and South Africa. Take the average exploration and development firm of Peru for example. A 1% appreciation of the Peruvian sol versus the U.S. dollar leads to a decrease of about 3.5% in opex of the average Peruvian exploration and development firm, ceteris paribus. The average Mexican and South African firms show the same pattern of decreasing opex in the case of an appreciation of the local currency versus the U.S. dollar.
A possible explanation for this pattern is that Mexican, Peruvian, and South African explorers and developers of commodities have relatively high costs in U.S. dollar. Mexican and Peruvian firms can have many expats in their personnel, which are usually paid in U.S. dollars, explaining the high amount of U.S. dollar costs. As noted earlier, South African firms are known to have high U.S. dol-lar costs. An appreciation of the local currency versus the U.S. doldol-lar thus leads to lower costs. However, for Brazil and Chile a significant positive currency risk sensitivity is found. An appreciation of the local currency versus the U.S. dollar leads to greater opex. Exploration and development firms with high costs in local currency suffer from the appreciation of the local currency versus the U.S. dollar.
