country risk and valuation of fdi a real options approach

8/16/2019 Country Risk and Valuation of FDI a Real Options Approach

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Emerging Markets Review

Ž .2 2001 197217

Country risk, country risk indices and valuation of FDI: a real options approach

Kjell B. Nordal

( ) Foundation for Research in Economics and Business Administration SNF , Brei iks eien 40, NO-5045 Bergen, Norway

Received 23 April 2001; received in revised form 18 June 2001; accepted 22 June 2001

Abstract

Country risk, and in particular political risk, may constitute a large part of the total riskinvestors face when investing in emerging markets. It is not a straightforward task to

quantify and include these types of risks in the evaluation and valuation of real investments.We suggest a method involving country risk indices. The approach is based on the realoption approach for valuation of real investments. 2001 Elsevier Science B.V. All rightsreserved.

JEL classifications: G31; G38; G12

Keywords: Country risk; Political risk; Real options; Investments

1. Introduction

The term country risk is often used in connection with cross border investmentsand analyzed from the foreign investor’s perspective. The country risk for a givencountry is therefore the unique risk faced by foreign investors when investing inthat specific country as compared to the alternative of investing in other countries.In this article we address the question of how country risk may be included in the valuation of investment projects. More specifically, we present a methodology where country risk indices are directly included in the valuation of investments.

Corresponding author.

Ž . E-mail address: [email protected] K.B. Nordal .

1566-014101$ - see front matter 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S 1 5 6 6 - 0 1 4 1 0 1 0 0 0 1 7 - 6


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( ) K.B. Nordal Emerging Markets Re iew 2 2001 197 217 198

The main point we make in this article is that country risk indices may bemodeled as stochastic processes and used as state variables when applying thecontingent claims valuation methodology. We do not claim that this approach is

appropriate when valuing all types of investments. We do, however, claim that thisis an alternative that should be considered by the analyst when determining the value of investments and advising on investment decisions when country risk is aprominent risk factor. We present and discuss relevant issues that analysts arefacing when valuing specific investments. This is done by first studying how countryrisk may be defined and analyzed. We then present a specific model, which mayserve as a starting point for analysts considering including country risk indicesdirectly in the evaluation of investment projects.

The contingent claims valuation methodology facilitates the valuation of invest-ments where managerial decision-making concerning the investment is a prominentfeature. The options to abandon the investment or to increase the scale of theinvestment are potentially valuable when investing in emerging markets. Thesedecisions are often closely related to the development of country-specific condi-tions, i.e. to country and political risk. The contingent claims valuation method-ology is based on the same principles used when pricing derivatives written on

Ž .financial securities, as in Black and Scholes 1973 . Our article is an addition to theliterature describing applications of real options. For an introduction to and

Ž .description of the real options literature, see e.g. Amran and Kulatilaka 1999 ,Ž . Ž .Dixit and Pindyck 1994 , or Trigeorgis 1996 . For literature reviewing country and

Ž .political risk analysis, see e.g. Chermack 1992 . An overview of how political riskhas been included in analyses of financial decision-making and valuation is pre-Ž .sented in chapter two in Nordal 1998 . For other uses of country risk indices when

Ž .analyzing financial problems, see e.g. Erb et al. 1995, 1996 and Diamonte et al.Ž .1996 .

The rest of the article is organized as follows. We first describe the term countryrisk and present different information sources used when analyzing country risk.We then discuss possible relationships between risk indices and expected cash flow.In order to implement the contingent claims valuation methodology, a completemodel needs to be specified. We specify a concrete model, test whether the

specifications seem reasonable, and estimate model parameters based on a data setfor a selection of country risk indices for oil producing countries covering the years19841996. The model values oil investments, and the primary factor determiningthe cash flow from the investment, is the oil price. We examine a possiblecorrelation between the oil price and risk indices within the given model specifica-tion. We then present an example, before summarizing the main points in the finalsection.

2. Country risk analysis

Country risk is the unique part of the investment’s risk caused by the location within national borders. Country risk is often meant to measure the possibility of


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loss only, or what we might call downside risk. What we understand by the termcountry risk will to some degree depend on the type of investment. It is common touse three categories when describing foreign investments: lending; equity invest-

Ž . Ž .ment; and foreign direct investment FDI see Fig. 1 . Lending covers directlending or the purchase of bonds from the state, government, or from privatecompanies in a country. Equity may cover investments in companies that may ormay not be listed at the country’s stock exchange. Foreign direct investment coversinvestments in factories and resources, such as mines or oil fields, and other realassets. Regarding lending, the borrowers may be categorized into two groups: thegovernment and government guaranteed borrowing; and borrowing from privatecompanies without public guarantee. When the term country risk is used incross-border lending, and when the borrower is a government, the credit risk isknown as sovereign risk, or sovereign credit risk. Credit risk is the risk that theborrower will not completely fulfill the obligations in the loan agreement such that

Ž .the credit provider, or lender, suffers losses. Calverley 1990 distinguishes betweencountry risk when the bond issuer is a government and country risk when lendingto private borrowers, termed generalized country risk, and this term may also beextended to cover equity investment and FDI. The general use of the term riskcovers both the upside potential and downside risk and may, e.g. be measured bythe variance in return. Country risk may therefore be more properly labeled ascountry effects in return on investments. The downside risk, however, is alsorelated to total risk. This is best recognized by the fact that reduced probabilities

for negative events in most cases will increase the value of the investment.The reasons why a given investment is influenced by country-specific factors aremany, and it is common to analyze country risk by specifying sub-categories of risk.One possible division of country risk is into economic risk, commercial risk andpolitical risk. Economic risk is risk related to the macroeconomic development of the country, such as the development in interest and exchange rates that mayinfluence the profitability of an investment. Commercial risk is risk related to thespecific investment, such as the risk related to fulfillment of contracts with privatecompanies and local partners. The third category, political risk, may in manycountries be the most important one. A country is a political entity, with country-

specific rules and regulations applying to the investment. In addition to the specificregulations, e.g. laws protecting property rights, a government’s willingness andability to change these rules and regulations will constitute a source of risk to theinvestment. Political risk may also be caused by the behavior of the state orstate-owned companies in the market place, or by more extreme situations like war

1 Ž .and civil unrest. Jodice 1985 defined political risk as:

Changes in operating conditions of foreign enterprises that arise out of political process, eitherdirectly through war, insurrection, or political violence, or through changes in government

1 When studying mainly financial assets such as stocks and bonds, the term country risk, andespecially political risk, is in most cases used to describe the possibility of shocks in financial marketscaused by some unforeseen event. The term event risk may also be used.


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Fig. 1. Use of the term country risk.

policies that affect the ownership and behavior of the firm. Political risk can be conceptualized as

events, or a series of events, in the national and international environments that can affect thephysical assets, personnel and operation of foreign firms.

Ž .Root 1972 lists examples of political risk situations, i.e. examples of eventsaffecting real investments. Root distinguishes between three types of political risk:transfer risk, operational risk and ownership control risk. Transfer risk is riskrelated to the transfer of products and services across national borders, or thetransfer of funds such as payments of dividends. Operational risk is risk related tothe operation and profitability of an investment in the host country, such as theoperation of an assembly plant. Examples of operational risk are price controls and

possible requirements that the producer should use sub-standard or expensive localsuppliers. The final category, ownership control risk, is linked to events influencingthe owners’ ability to control and manage the investment. The investment may beexpropriated, or the initial owner may be forced to let local partners get anownership share at a discount price.

The term country risk analysis describes the activity of predicting future condi-tions for the investment in a host country. There are at least three sources of information that the predictions may be based on: written reports; informationdeduced from financial markets; and summary measures like risk indices andratings. Here, we are primarily interested in how these sources of information may

be used when deriving the value of an investment. Because it is often difficult toquantify country risk, all three sources of information used together are likely toprovide the investment analyst with the best estimates. We comment on the first


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two before we turn to country risk indices. Written reports usually containdescriptions of possible future developments in a country. Such reports may beissued by private companies or international organizations like OECD or the

World Bank. Figures from national accounts may be presented in these reports,but in many cases the analysis is primarily qualitative and in textual form. Writtenreports are useful in providing background information, but may often be toogeneral and give little guidance to the numerical evaluation. The second source of information is analyses of prices of assets traded in financial markets. Theprocedure is as follows: A valuation model for the asset is assumed. Based on

Ž . Ž .observation s of price s , one or several parameter values making the theoretical value equal to the actual value are then extracted. Here we are primarily interestedin parameter values reflecting country risk. Consider an example with defaultprobabilities deduced from prices of bonds influenced by country risk. A oneperiod discount bond is issued by a government with principal X . If the loan is1fully repaid, the holder of the bond will receive X . If the country defaults, the1bond holders receive a fraction k. The default probability is p, the risk freeinterest rate is r , and we assume that the default risk does not reflect systematicrisk. The present value of the bond is then:

Ž . E X X X k1 1 1 Ž . Ž .V X 1 p p 10 1 1 r 1 r 1 r

By observing the value of the bond today, V X , observing the interest rate r ,

0 1 Ž .and making an assumption about k, we can solve Eq. 1 with respect to theprobability of default, p. Whether the deduced parameter value is correct dependson whether the observed price is correct and whether the model is correct.2 Insome instances the bond may not be traded every day, so an estimate for the price

Ž .must be made. The valuation model on the right hand side of Eq. 1 depends onthe unobservable recovery fraction k. Depending on the assumption about k, we

Ž . will get different levels of p. The probability of default extracted from Eq. 1 maybe used when finding the expected future cash flow from similar bonds. Beyond thecases where default is caused by major events like war or change of government

leading both to default, and e.g. expropriation, it may be difficult to relate theevent of default to the cash flow from a real investment. In addition to the problemof relevance between the deduced probability from bonds and probabilities of events affecting other types of investments, comes the problem of whether defaultprobabilities are constant over time. If not, it is not possible to deduce theprobability of default at a given future date from the price of a bond. If severalbonds with different maturities are traded, it may be possible to deduce some sortof term structure of default probabilities. It may be the case that the probability of default mainly is linked to a given period, e.g. close to an election date.

Country risk indices are, as the name implies, indices measuring the level of

2 For a discussion of issues related to extraction of information from financial markets, see e.g. BodieŽ .and Merton 1995 .


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country risk. A high level of an index corresponds to either a high or low level of risk, depending on the specification of the index. What is meant by country risk isdetermined by the way the index is constructed. The use of sub-indices is a typical

way of making a risk index. As an illustration we present the rating system of theŽ .International Country Risk Guide ICRG as presented in Coplin and O’Leary

Ž .1994 ; see Table 1. The ICRG composite risk index consists of three sub-indices indices measuring economic, financial and political risk. These sub-indices areagain made up of more detailed indices. We may define three generic types of riskindices and a fourth which is a combination of the first three types. The firstgeneric type of index is a number referring to the current conditions in the country.The ICRG political risk index and the economic risk index is mainly a rating of thecurrent conditions in the country. The second type of risk index refers to theprobability that a specific event will occur during some future time period. Anexample is the sub-index covering the event of expropriation in the ICRG financialrisk index. The third type of risk index is similar to the previous one, but here theevent refers to a situation where the investors experience a worse condition thanthe current one. An example is where an index refers to an increase in a tax rateduring some future time period, but where the size of the increase is not specified.The fourth type of risk index is a weighted average of the three first indices, and isexemplified by the ICRG composite risk rating. The composite risk rating for theICRG is therefore a specific measure of country risk, where the risk is defined bythe structure of the index. Note that the ICRG composite risk index gives twice as

much weight to political risk as to either economic or financial risk.

3. Risk indices and expected cash flow

The variables or parameters in a valuation model may be related to the level of the index, either the present or future level, or to the future path of the index.Consider the case where an investment may be expropriated. The probability of expropriation during the lifetime of the project may be directly related to thepresent level of a risk index. If the ICRG indices are used, lower levels of the index

would correspond to higher risk of expropriation. Whether the project has beenexpropriated at a future date may be related to the future levels of the index. Thisis an example where the probability of expropriation is conditioned on the futurelevel of the risk index. It may, e.g. be more likely that the project has beenexpropriated if the future index is low, as compared to the situation with a highindex level. This approach necessitates that the future development in the indicesis modeled, which again corresponds to an evaluation of the development in thecountry with regard to country risk. Used in this way, the country risk indicesbecome variables like any other variables in the analysis, e.g. like an oil price. Theoccurrence of expropriation may also depend on the future path of the index. If the

risk index has dropped sizably over a short period of time, the analyst may be willing to assume that the probability that the investment has been expropriated islarge as compared to the situation when such a change does not occur. It may also


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Table 1aThe ICRG rating system

Ž . Ž . Ž .Political risk PR Financial risk FR Economic risk ER

Max Max Max points points points

Economic 12 Loan default or 10 Inflation 10expectation unfavorable loan

vs. reality restructuring Debt service 10Economic 12 Delayed 10 as a percent of planning payment of export of goodsfailures suppliers’ credit and servicesPolitical 12 Repudiation of 10 International 5leadership contracts by liquidity ratios

External 10 governments Foreign trade 5conflict Losses from 10 collectionCorruption in 6 exchange experiencegovernment controls Current account 15Military in 6 Expropriation of 10 balance as apolitics private percentage of Organized 6 investments goods andreligion in servicespolitics Parallel foreign 5Law and order 6 exchange ratetraditionRacial and 6nationalitytensionsPolitical 6terrorismCivil war 6Political party 6developmentQuality of 6bureaucracyMaximum 100 50 50possible rating

Ž . Ž .Composite risk rating CRR PR FR ER 2. General principle: the higher the rating, thelower the risk.

a Ž .Source: The Handbook of Country and Political Risk, See Coplin and O’Leary 1994 .

be relevant to relate the probability of expropriation to the time the index spendsŽ .in different risk categories. The ICRG see Coplin and O’Leary, 1994, p. 249

categorized the ICRG composite risk index into five risk categories. The risk levelŽ . Ž .for these categories were named index intervals in brackets : very high 049.5 ;

Ž . Ž . Ž . Ž .high 5059.5 ; moderate 6069.5 ; low 7084.5 ; and very low 85100 . Consider

the example with expropriation. The probability that the project has been expropri-ated at a future date will depend on the levels of expropriation risk the project hasbeen exposed to up to that date. This is illustrated in Fig. 2. At time t the


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Fig. 2. Example of a relationship between the probability of an immediate expropriation of aninvestment and the level of a risk index.

probability that the investment will be expropriated during the next increment of time, provided that it has not been expropriated previously, is p . This probability istsubordinated by the level of a risk index, . The expropriation probability equalst

p if the index level is between L and L , p if the index level is between L and1 1 2 2 2

L , and p otherwise. If higher index levels imply lower risk, it is reasonable to3 3assume that p p p .1 2 3

The exact calibration of the valuation model with regard to country risk is not, of course, a straightforward task. It must be based on a thorough investigation of thespecific investment and the given risk index or sub-indices. In order to secureconsistency, the modeling of country specific conditions based on country riskindices should be in line with the estimates based on the other two sources of information, i.e. written reports and analyses of market data.

4. The model

4.1. Risk index

A risk index may be considered to be, without loss of generality, a transforma-tion of some not directly observable state variable, i.e.:

Ž . Ž . f x 2t t

Ž . where the risk index is a function f of the unobservable state variable x . Thet tŽ .stochastic behavior of the risk index is then given by the choice of f and the

stochastic behavior of x . If the history is relevant when predicting the future, thistmay be considered to be an empirical problem. In addition, in order to facilitate


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Ž .the contingent claims pricing approach, f and x cannot be chosen freely. FortŽ . Ž .technical restrictions, see e.g. Ingersoll 1987 p. 283 .

Ž .In order to implement a valuation model, we need to specify Eq. 2 . We assume

that:

Ž . Ž . Ž . L L L N x 3t MIN MAX MIN t v

Ž . where N is the cumulative distribution function for the unit normally distributed variable, is a non-negative constant, L is the minimum level of the index, v MI N

Ž .and L is the maximum level of the index. The choice of Eq. 3 is motivated byMA Xstudying the situation the country experts are facing when they rate a country.Suppose that the country is either of type L or L . This corresponds to aMIN MAX

Ž . Ž .binary choice problem as, e.g. described by Greene 1993 p. 642 . We consider an

indicator variable, z , equaling one if the government at time t is of type Lt MAXand zero if not. We interpret x , a real number, as the ‘stock of relevanttinformation’ the country expert possesses about the country’s type. If x istnegative, the country is of type L , and otherwise it is of type L . TheMIN MAXcountry expert’s stock of information is, however, influenced by noise . Wetassume that the noise is normally distributed with expectation zero and variance . At time t the country expert’s estimate of the probability that the country is of vtype L is then:MA X

Ž . Ž . Ž . Ž . P z 1 P x 0 P x N x t t t t t t v

where we have used the symmetry of the normal distribution. With this interpreta-Ž .tion the risk index in Eq. 3 is a scaling of the country expert’s estimate of the

probability that the country is of type L . For a given variance of the noise, ,MA X vthe country expert’s future opinion of the country’s type will depend on the arrivalof new information. We assume that the state variable x , reflecting the ‘stock of trelevant country specific information’, will be updated continuously with incrementgiven by:

Ž x . Ž . dx dt dB 4t x x t

where dBŽ x . is the increment of a standard Brownian motion and where and t x xare constants. This model specification does not necessarily fit all countries and allrisk indices. We have here assumed a continuous update regarding the country’stype. For some countries the information may arrive at random times, and may bebetter modeled by a Poisson process.

When using times series of country risk indices to deduce time series of theunobserved variable, the time series of the latter may become censored. The riskindices are only quoted with one or two decimals. This means that a range of values of x will be matched by only one index level, due to rounding of the index.tOr when we deduce the values of x from the risk index, the values will betallocated to a specific number. Censoring is likely to be a problem when and x x

Ž .in Eq. 4 are relatively small, and when the length between the observations is


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small. By increasing the length between observations, we would expect that xt would change more. This would, hopefully, make the problem with censored dataless severe. On the other hand, by increasing the length between observations the

number of observations become fewer. This makes it harder to reject any hypothe-sis due to the smaller sample size.

In order to see whether our specification is reasonable for a large number of Ž .countries, we examined two testable implications of Eq. 4 : the increments of xt

Ž .are independent and normally distributed. We used Eq. 3 and a set of ICRGŽ .indices and Institutional Investor’s country credit ratings IICCR to derive time

series for the unobservable state variable x for 44 oil producing countries. The 44tŽ . 3countries were those listed in the BP British Petroleum Statistical Review 1997 ,

see Table 2. The sample period is covering approximately 12 years, starting in 1984and ending in 1996. One of the main events in the oil market during this period was the Gulf War. Iraq invaded Kuwait on August 2, 1990 and Operation DesertStorm withdrew from Kuwait on February 27, 1991. Events affecting the politicalrisk during this period were, e.g. the fall of the Berlin wall and the opening up inChina with the establishment of free economic zones.

The average of the countries’ ICRG composite risk indices in March 1996 was68.7. The countries with highest composite risk, i.e. lowest CR, were Iraq, Angola, Algeria, Cameroon and Congo. The countries with the lowest risk according toICRG CR were Brunei, Denmark, Norway and the USA. As for the ICRG indices,highlow IICCR-values correspond to situations with lowhigh risk. The highest

possible level of IICCR is 100 and the lowest possible level is zero. The average of the IICCR at the beginning of the sample period was 41.3. The lowest ratedcountries were Iraq, Angola, Congo and Uzbekistan. The highest rated countries were the USA, the UK, Norway and Denmark.

The results of the tests of the increments of the deduced variables are summa-rized in Table 3. For the ICRG indices the tests were based on monthly, quarterlyand half-yearly observations. For the IICCR, only half-yearly observations wereavailable. For the ICRG indices with monthly observations, the case against a

Table 23Oil producing countries listed in BP Statistical Review, 1997

Algeria Canada India Mexico Romania United Arab Angola China Indonesia Nigeria Russian Emirates Argentina Colombia Iran Norway Federation United Kingdom Australia Congo Iraq Oman Saudi Arabia USA

a,b a a Azerbaijan Denmark Kazakhstan Papua New Syria UzbekistanBrazil Egypt Kuwait Guinea Trinidad and VenezuelaBrunei Equador Libya Peru Tobago Vietnam

bCameroon Gabon Malaysia Quatar Tunisia Yemen

a For this country the ICRG indices were not available.b For this country the IICCR was not available.

3 Information related to the BP reports may be found at their homepage www.bp.com.


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Table 3Summary of the numbers of countries rejected when testing for independence and normality of

aincrements of variable deduced for a selection of risk indices

Time between Number of countries Risk index Observations

The ICRG index for InstitutionalPolitical Financial Economic Composite investor’srisk risk risk risk country

credit rating

aMonthly Total in sample 41 40 41 41 N.A.Nos. rejected 41 40 41 41 N.A.

dnormality 30 32 28 33 N.A.

eindep. increments 0 0 0 0 N.A.both normality and 11 8 13 8 N.A.

indep. increments

bQuarterly Total in sample 41 40 41 41 N.A.Nos. rejected 34 37 33 33 N.A.

dnormality 26 25 23 29 N.A.

eindep. increments 2 0 7 3 N.A.both normality and 6 12 3 1 N.A.indep. increments

cBi-annual Total in sample 41 40 41 41 41Nos. rejected 16 29 16 18 27

d

normality 16 23 12 14 10eindep. increments 0 3 2 3 15both normality and 0 3 2 1 2indep. increments

Ž .Data for time period 19841996. From a time series of observations of risk indices , . . . , ,1, 2 N Ž .a corresponding time series of a variable x x , . . . , x is deduced by using the equation L1, 2 N t MIN

Ž . Ž . Ž . L L N x , where N is the cumulative distribution function for the unit normallyMA X MIN t vdistributed variable and was set equal to 1. The reported tests are based on the increments of x, i.e. v

x x .t 1 ta Ž .Number of observations: 152 for all countries, except for the following: 148 Papua New Guinea ;

Ž . Ž . Ž . Ž . Ž . Ž146 Oman ; 145 Quatar ; 141 China ; 137 Congo ; 131 Angola, Brunei, Vietnam ; 53 Russian

. Ž .Federation ; and 45 Yemen .b Ž .Number of observations: 50 for all countries, except for the following: 49 Papua New Guinea ; 48Ž . Ž . Ž . Ž . Ž .Quatar, Oman ; 47 China ; 45 Congo ; 43 Angola, Brunei, Vietnam ; 17 Russian Federation ; and

Ž .15 Yemen .c ŽNumber of observations for ICRG indices: 25 for all countries, except for the following: 24 Quatar,

. Ž . Ž . Ž . ŽOman, Papua New Guinea ; 23 China ; 22 Congo ; 21 Angola, Brunei, Vietnam ; 8 Russian. Ž .Federation ; and 7 Yemen . Number of observations for IICCR: 25 for all countries, except for the

Ž . Ž .following: 8 Russian Federation, Kazakhstan, Uzbekistan ; and 9 Vietnam .d The test of normality is based on the p-value of the BeraJarque test of normality and the

studentized range. The assumption about normality for a country is reported as rejected if we, based onany of these tests, may reject the normality hypothesis at the 5% significance level. The Bera Jarque

Ž .2 Ž .2 test is based on the statistic J n coeff. of skewness 6 excess kurtosis 24 . In case of normal-ity, J is 2 distributed with 2 degrees of freedom.

e The test of independence between increments is based on computing the correlation betweenlagged increments. We lagged the increments one and two periods. If the hypothesis of no correlationcan be rejected at the 5% significance level, the respective country is reported in the table.


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rejection for almost all countries is very strong. For the ICRG CR, all the countriesare rejected. We see from Table 3 that by increasing the time span betweenobservations from monthly to quarterly, the process assumptions for the ICRG

economic risk and composite risk indices cannot be rejected for eight of the 41countries for which there is data. By increasing the length from quarterly tohalf-yearly observations, the process assumptions cannot be rejected for most of the countries, expect for the ICRG FR and for the IICCR.

The majority of countries rejected, are rejected because of the tests of whetherthe increments are normally distributed. This is what we would expect when thedata is censored. The variable will not change for consecutive observations, butthen ‘jump’ when a new level of the risk index is reached. The number of countriesrejected are fewer when the time between the observations are increased, as we would expect when censoring exists. Based on the findings reported in Table 3, weclaim that our model specification may be reasonable for quite a large number of oil producing countries for the given indices. The specification does, however, seemto be better when modeling the behavior of ICRG PR, ER and CR, as compared tothe modeling of the ICRG FR and IICCR. In practical use, when valuing aninvestment in a specific country, the analyst is free to select his own modelspecification. In our opinion the model presented here is a good starting point.

4.2. Spot price of oil and correlation

When evaluating oil investments, the level of the oil price is perhaps the mainfactor determining the level of cash flow from the investment. A possible relation-ship between the oil price and country specific conditions, like tax rates orprotection of ownership rights, may have a considerable influence on expected cashflow. Such a relationship may be modeled as a correlation between a country riskindex and the oil price. If a higher index level implies lower risk, then a positivecoefficient of correlation between the risk index and the oil price means that thecountry risk, as measured by the index, is expected to be reduced when the oil priceincreases. When the coefficient is negative, an increase in the oil price is likely tooccur together with an increase in risk. There are some intuitive explanations for

why the correlation should be positive or negative. If the country is mainlydependent on the production and sale of oil for its revenue, a reduction in the oil

Ž .price may lead to political turmoil, i.e. increased risk positive correlation . A largedrop in the oil revenue combined with a lack of willingness to cut back on publicspending may reduce the country’s credit rating. On the other hand, if the countryis a major oil producer, then a political uncertain situation in the country may leadthe participants in the oil market to believe that there is a chance for a reductionin the supply of oil. This can cause oil prices to rise. In this instance the risk indicesand the oil prices are negatively correlated. A negative coefficient of correlationmay also be expected if the country is a large net importer of oil. An increase in

the oil price will increase the cost of an important input factor and may cause theeconomy to slow down. This may again lead to political instability due to, e.g.unemployment concerns. The credit rating for the country may also drop. In order


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to capture this correlation in our model specification, we first start by modeling theoil price. We use a standard assumption in the contingent claims literature andmodel the spot price of oil as a geometric Brownian motion with constant

parameters, i.e. the increment of the oil price may be written as:

dSt Ž S . Ž . dt dB 5S S tSt

where dBŽS. is the increment of a standard Brownian motion and where and t S Sare constants. The Brownian motions governing the oil price and the risk index may be correlated, i.e. dBŽ S . dBŽ x . dt. The parameter captures the correlationt tbetween the oil price and the risk index.

Having investigated properties of the variables deduced from a set of risk indicesin the previous section, we investigate the properties of the Brent Blend crude oilprice during the sample period 19881996. The statistics for the sample period arereported in Table 4. For the whole period, the coefficient of correlation betweenlagged increments of the log of relative prices, either lagged one or two periods, issignificantly different from zero at a 5% significance level. Also for this period, thetest based on the studentized range statistic indicates that the hypothesis of normally distributed increments can be rejected. By excluding the period for theGulf War, only the coefficient of correlation between the lagged increments for

quarterly data are significantly different from zero. Statistics are also reported forthe period before and after the Gulf War.

For a summary of the estimated coefficients of correlation between the variablededuced from various risk indices and the variable governing the oil price, seeTable 5a. For the sample period, there were more countries with negative esti-mated correlation coefficients than non-negative. The estimated coefficients were,however, rarely significantly different from zero. For Kuwait, not surprisingly, thecorrelation coefficient was significantly different from zero for all indices. The

Ž . Ž .estimates were the following coefficient : ICRG political risk index 0.54 ;

Ž . Ž .ICRG financial risk index 0.68 ; ICRG composite risk index 0.68 ; andŽ .IICCR 0.49 .

4.3. Valuation

The specified processes may be used when computing the expected future cashflow. When, however, using the contingent claims valuation methodology to findthe value of future payments, the drift of these processes must be adjusted. In theBlack and Scholes option pricing formula, the drift of the share price is replaced bythe risk free interest rate. The process for the risk index and the spot price of oil

are, however, not related to actively traded financial instruments. It is thereforenecessary to determine the drift adjustment for these processes. This may be done

Ž .by applying the CAPM, as in Dixit and Pindyck 1994, p. 115 . The required


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Table 4Statistics for sample of the logarithm of relative Brent Blend oil prices

a a,b Period Observations N Mean t-value Variance Coeff of Excess B-J , Stskewness kurtosis P -value ra

Whole Bi-annual 17 0.0239 0.29 0.1170 0.252 2.340 0.13 4. period Quarterly 35 0.0079 0.21 0.0520 1.848 7.331 0.00 5. Monthly 105 0.0026 0.28 0.0095 0.645 3.988 0.00 7.

Excl.Gulf Bi-annual 15 0.0225 0.42 0.0427 0.967 1.635 0.13 4.War Quarterly 32 0.0032 0.13 0.0194 0.339 0.591 0.58 3.

Monthly 98 0.0029 0.39 0.0054 0.102 0.224 0.83 5.Pre-Gulf Monthly 31 0.0022 0.14 0.0083 0.089 0.442 0.86 4.WarPost-Gulf Monthly 67 0.0032 0.41 0.0042 0.314 0.449 0.44 4.War

Whole period: 19881996. Gulf War: August 1990February 1991.a and indicates whether the estimate is significantly different from zero, using a two sided test and a significb Ž .2 Ž The P -value of the BeraJarque test of normality, based on the statistic J n coeff. of skewness 6 excess k

is 2 distributed with 2 degrees of freedom. The reported P -value is the probability of observing a J statistic equal c h indicates that in a normal distribution with n observations, the probability of the observed studentized ra

Similarly, l indicates that the probability of the observed studentized range being this low is less than 0.01.d Coefficent of correlation between observations, where one observation is lagged one or two periods.


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Table 5Summary of the numbers of estimated correlation coefficients and betas

Risk index Estimated Categories forparameter estimated InstitutionalThe ICRG index for

parameters investor’sPolitical Financial Compositecountry

risk risk riskcredit rating

Total number of countries 41 40 41 41

A Coefficient of 0.5 1 0 0 0 1

acorrelation 0 0.5 16 18 16 16 0.5 0 22 20 1 21 23 2

1 0.5 3 3 2 2 4 3 1 1

BbBeta 1 3 1 2 0

0 1 19 1 14 2 17 2 24 2 1 0 19 25 1 22 1 17

1 0 0 0 0

Data for time period 19881996. The estimates were based on half-yearly observations. Number of Žobservations for ICRG indices: 25 for all countries, except for the following: 24 Quatar, Oman, Papua

. Ž . Ž . Ž . Ž .New Guinea ; 23 China ; 22 Congo ; 21 Angola, Brunei, Vietnam ; 8 Russian Federation ; and 7Ž . ŽYemen . Number of observations for IICCR: 25 for all countries, except for the following: 8 Russian

. Ž .Federation, Kazakhstan, Uzbekistan ; and 9 Vietnam .a Ž .From a time series of observations of risk indices , . . . , , a corresponding time series of a1, 2 NŽ . Ž . Ž . variable x , x , . . . , x is deduced by using the equation L L L N x ,1 2 N t MIN MAX MIN t vŽ . where N is the cumulative distribution function for the unit normally distributed variable and 1. v

The coefficient of correlation between the increments of x, i.e. x x , and the log of relative Brentt 1 t Blend oil prices is then estimated. The number in brackets, , corresponds to the number of countries

where the estimated parameter was significantly different from zero at the 5% significance levelb Ž . Ž .The estimation of beta was based on the equation x x r R r , wheret 1 t t t t

r is the 6-month Eurodollar interest rate, R , is the 6-month return on the Morgan Stanley Capitalt t International World Index, and is the error term. The number in brackets, , corresponds to the

number of countries for where the estimated parameter was significantly different from zero at the 5%significance level.

expected return, , from holding a financial asset with an amount of risk equal toi is:i

Ži. Ž . r , i x ,S 6i i

where r is the instantaneous risk free interest rate and Ži. is the risk premium fora financial asset solely influenced by risk of type i. We define the drift adjustment

or convenience yield, , as the difference between the required drift and the actualidrift, i.e. . When is known, we may price claims that are determin-i i i iistic functions of the risk indices and the oil price. Consider the value at time zero


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of a claim paying an amount equal to the index level at time t. The value of thisclaim is given by:

r t Ž . Ž . Ž .V e E L L L N x 70 t MIN MAX MIN t v

where the notation E means that when computing the expectation we use the‘risk neutral process’:

Ž . Ž x . Ž . dx r dt dB 8t x x t

When applying the CAPM to determine the risk premium for the variablegoverning the risk index, it is necessary to determine the beta for this variable. A positivenegative risk premium will follow directly from a positivenegative beta,by using the well-known formula relating the required expected rate of return of anasset to this asset’s beta.

For the sample period 19881996 we estimated the betas for the variablesdeduced from a set of risk indices. As the risk free interest rate we used the6-month Eurodollar rate. We used the Morgan Stanley Capital International

Ž .World Index MSCIWI , measured in US dollars, to represent the market portfolio.MSCIWI is a value weighted index reflecting reinvestment of dividends. The returnon the market portfolio and the Eurodollar interest rate were all end of the monthobservations measured in nominal units. A summary of the beta estimates for thecountry indices are shown in Table 5b. A positive beta means that high excessreturn on the market portfolio is expected to occur at the same time as a reductionin the country’s risk level, as measured by the appropriate index. For mostcountries we expect a beta close to zero. The important fact to be aware of is thatthe variables deduced from the indices are not related in any clear way to prices of actually traded assets. A priori, it does not seem clear that the estimated betasshould be different from zero, unless perhaps for big countries like the USA. Forlarge countries influencing the world economy we would expect that decreasinglevels of risk occur at the same time as we observe high levels of market return, i.e.a positive beta. Most of the estimated betas were close to zero. We see from Table

5b, that almost none of the estimated betas were significantly different from zero.This may indicate that risk related to the changes in the risk index might beconsidered to be unsystematic, i.e. the risk premium for this risk is zero.

5. Example

We provide a stylized example of how risk indices may be included in theevaluation of an investment in an oil field under expropriation risk. The cashpayment from the investment opportunity, provided it has not been abandoned at

time t, is:

Ž . Ž . Ž .C S S k q K 9t t t t t


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where S is the spot price of oil, k is the variable costs per barrel produced, q ist t tthe quantity of oil ready for sale measured in barrels, and the payable fixed costs at

Ž .time t is K . The oil price dynamics is described by Eq. 5 . If the decision to investtis made at time t, the investor will pay an amount I .t

The oil field may be expropriated by the government in the country where the oilfield is located with no compensation to the original owners. The expropriation isan irreversible decision by the government. We facilitate the presentation byintroducing an integer valued stochastic process with jump intensity . Thist tPoisson process starts at zero, and we assume that the oil field is expropriated thefirst time a jump occurs in this process. If the government has not expropriated theoil field at time t, the intensity of the Poisson process during the next increment of

Ž .time, dt, is . This intensity will depend on the level of risk in the country, astmeasured by a country risk index, in the following way:

0.00 if 85 L 100 1 t MAX 0.01 if 70 852 t

Ž . Ž . 0.02 if 60 70 103 tt 0.03 if 50 604 t 0.04 if L 0 505 MIN t

where we have used the same five risk categories for the index, just as an example,

as the ICRG composite risk index. The level and the dynamics of the risk index isassumed to be governed by a state variable, not directly observable, with numericalŽ . Ž . value equal to x at time t, as described by Eqs. 3 and 4 . The correspondingt

levels of this state variable are reported in Table 6. We also report the probabilityfor expropriation during the next quarter and during the next year. These figuresare based on the simplifying assumption that the probability that the project will beexpropriated at time t t, assuming that it has not been expropriated at time t,is given by:

Ž Ž . . Ž . P 1 1 , 0 1 exp t 11Ž .Žtt. 04 t t t

where the time step is t and where the indicator variable 1 1 only if Žtt. 04the project is expropriated at time t t.

Because an option to abandon the investment may be valuable, especially in thepresence of expropriation risk, we include this option in the evaluation. The valueof the investment opportunity, given that the investment is made, with an option toabandon the investment will satisfy the equation:

Ž . Ž . Ž . Ž Ž .. F S , , Max 0,C S V F S , , 1 p t t t t t tdt tdt tdt tŽ . Ž . 1 1 12Žt . 04

Ž . Ž . where F S , , is the value of the oil field at time t and p is the probabilityt t t tthat the investment will be expropriated at time t dt. We have assumed that the


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Table 6Risk indices and probability of expropriation

c dŽ . 4 4Risk Unobservable

P 1

0 1 Annualizedt Ž t ta bcategory variable

85 100 1.036 x 0.00 0.000 0.000t t70 85 0.524 x 1.036 0.01 0.002 0.010t t60 70 0.253 x 0.524 0.02 0.005 0.020t t50 60 0.000 x 0.253 0.03 0.007 0.030t t

0 50 x 0.000 0.04 0.010 0.040t t

a Corresponds to the categories given for the ICRG composite risk index, see Coplin and O’LearyŽ .1994 , p. 249.

b Ž . Ž . Ž .Derived by using the equation L L L N x , where N is the cumula-t MIN MAX MIN t vtive distribution function for the unit normally distributed variable and 1. v

c Rounded to three decimals. t 0.25.d Ž Ž ..1 t Approximated by the formula 1 1 P 1 1 , rounded to three decimals.Ž t t . 04

salvage value in case of abandonment is equal to zero. When deriving the value Ž .Ž Ž .. Ž .V F S , , 1 p in Eq. 12 , we use the ‘risk neutral processes’t tdt tdt tdt t

for the oil price and the state variable governing the risk index, as implied by Eq.Ž .8 . This formulation also assumes that no risk compensation is required for theexpropriation risk.

We calibrated the model and solved it numerically by using discrete time stepsand a two-dimensional binomial tree. For an explanation of this procedure, see e.g.

Ž .Clewlow and Strickland 1998 . We used a time step of 0.25, i.e. 3 months. WeŽ .selected a production quantity of one barrel per time step four barrels per year

for 10 years. The fixed and variable costs were set to, respectively, USD 2.5 perquarter and USD 8 per barrel. The volatility of the spot oil price was set to 0.2 andthe convenience yield to 0.05. The risk premium for the volatility of the processgoverning the risk index was set equal to zero, and the correlation coefficientbetween this process and the oil price was also zero. The risk free interest rate wasassumed to be 6% per year, and the investment amount was USD 100. Based on

these assumptions we computed the value of the investment if it were done today.We also computed the value of delaying the investment decision 1 year. Thebreak-even spot price of oil if the investment is made today, time t, or never is S N

.tThe spot price of oil that makes investing today preferred to waiting is S W

. Wetdefine the relative hurdle for the spot price of oil at time t, H , to be the relativetrelationship between these break even prices, i.e. H S W

S N

. The number H t t t tis a measure of the incentive to wait compared to the alternative of investing now.

The relative investment threshold for different combinations of expected devel-opment and volatility of the variable governing the risk index, i.e. and , are x xshown in Table 7. The incentive to wait is lower for lower levels of the index, i.e.

when the risk is high. The lowest level of H is 1.35 and the highest is 1.52. ThetŽ .intuition behind this result is that if the risk level is high low index level , then it is

more likely that the project will be expropriated sooner or later. The investor is not


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Table 7Investment threshold for the numerical example for different combinations of present index level,expected development and volatility

Level of Expected Volatility, xindex today change, x 0,05 0,1 0,15 0,2

90 0.05 1.47 1.47 1.47 1.460.00 1.52 1.50 1.50 1.490.05 1.52 1.52 1.51 1.51

70 0.05 1.38 1.39 1.39 1.390.00 1.44 1.43 1.43 1.420.05 1.47 1.47 1.47 1.46

50 0.05 1.35 1.35 1.36 1.370.00 1.37 1.38 1.38 1.39

0.05 1.41 1.41 1.42 1.42

expected to learn more about the probability of expropriation by waiting, and the value of waiting is therefore relatively low making the investment thresholdsmaller. The same reasoning may be used when explaining that the investmentthreshold tends to be reduced when the expected change in the risk index, hererepresented by , is reduced. The effect of increased volatility depends on the xindex level. At low index levels, an increase in the volatility, represented by , x

Ž .makes it more likely that the risk is reduced in the future higher index levels . Theinvestment threshold may therefore be increased. The opposite effect will apply with an initial high index level.

6. Summary

In this article we discuss and present relevant issues related to the use of countryrisk indices in project evaluation. We specified a model which, even though weused oil investments as an example, may serve as a starting point when evaluating a

variety of investment projects. Based on data covering a selection of country riskindices for oil producing countries, we examined the properties of the model. Wemade the following observations:

When deducing a time series of a not directly observable state variable fromtime series of a risk index, censoring of data may become a problem. Eventhough we faced this problem, we argue that our model is a reasonable startingpoint for the majority of the countries when modeling the ICRG PR, ER andCR indices. The model’s assumptions do, however, to a lesser degree match thebehavior of the ICRG FR and the IICCR indices.

A possible relationship between a risk index and the underlying cash flow mayhave a large impact on expected cash flow and value. When we estimated thecoefficient of correlation between changes in the risk index and changes in the


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oil price, we found that there were slightly more negative estimates thanpositive. For oil investments a negative correlation implies that an increase in

Ž .cash flow from the investment higher oil price is likely to occur together with

an increase in country risk. Few of the estimated correlation coefficients were,however, not significantly different from zero.

We used the CAPM to estimate betas for the state variables deduced from therisk indices. Applying estimated betas is one way to determine the risk premiumfor risk related to the development of the risk index. Most of the betas were notsignificantly different from zero, which indicates that we in many instances mayconsider the risk related to the indices themselves as unsystematic.

We ended our presentation with a numerical example. In this example wecomputed the incentive for the investor to delay the investment decision. This

incentive was dependent on, among other elements, the current level, the expecteddevelopment in, and the volatility of a risk index. In this way, risk indices may beused to communicate difficult concepts related to country risk.

Acknowledgements

Financial support from The Center for Monetary and Financial Research, Oslo,is gratefully acknowledged. I thank Campbell R. Harvey, Duke University andNBER, for letting me access his data on the risk indices of International Country

Ž .Risk Guide ICRG and the country credit ratings of Institutional Investor. I alsothank Delphi Economics, Oslo and Statoil, Stavanger, for their data support.

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