Damodaran’s Country Risk Premium: A Serious Critique
Lutz Kruschwitz∗Andreas Löffler†& Gerwald Mandl‡ , Version from July 31, 2010

Contents
1 Introduction 2 2

2 CRP concept

3 Critique of the CRP concept 7 3.1 The theoretical foundation of Damodaran’s equations – built on sand 7 3.2 Damodoran’s empirical basis – a hotchpotch of ad hoc ideas . . . . . 12 4 Conclusion 19

∗ Freie Universität Berlin, Germany, Chair of Finance and Banking, E-Mail LK@wacc.de. † Universität Paderborn, Germany, Chair of Finance and Investment, E-Mail AL@wacc.de. ‡ Universität Graz, Austria, Chair of Accounting and Auditing, E-Mail Gerwald.Mandl@uni-graz.at.

1

Electronic copy available at: http://ssrn.com/abstract=1651466

1 Introduction
For several years, when setting discount rates Damodaran has advocated more consideration of country risk premiums (CRP ) when it comes to assessing companies with activities in emerging markets. We have to acknowledge that his approach is enjoying growing support among investment banks and auditing firms. At the same time, it is to be noted that Damodaran’s concept has failed to resonate sufficiently with the academic community. This is reason enough to perform a systematic analysis and critical discussion of his country risk premium concept. Damodaran’s initial considerations concerning a country risk premium can be found in Damodaran (1999a) and Damodaran (2003), with further essentially unchanged mentions in his more recent publications. In our contribution we will concentrate on the two aforementioned sources.

2 CRP concept
In the following, we intend to give a neutral, that is, non-judgmental description of Damodaran’s country risk premium concept (CRPC). We will also attempt to provide a detailed reconstruction of Damodaran’s thought process which led to this approach. Risk-return models The cost of capital for risk-return models can be categorised as expected returns. Damodaran begins his considerations by concluding that within the framework of capital market models with J risk factors, the relationship
J

expected return = rf + j=1 RP j · βj

(1)

applies at all times, where rf represents the risk-free interest rate, RP j the risk premium for the j-th factor and βj the j-th beta factor. In the special case of CAPM, which is a single-factor model, this can be simplified to expected return = rf + MRP · β, (2)

where MRP is referred to as the market risk premium. On the condition that the risk-free interest rate is known, risk premiums and beta factors must be estimated for all J risk factors. Damodaran generally defines a risk premium RP j as an excess return which investors achieve when they have to accept an average rate of risk for the j-th factor.

2

Electronic copy available at: http://ssrn.com/abstract=1651466

What should be measured and what is actually measured Damodaran focusses on risk premiums and, in the CAPM context, discusses what ought to be measured to later be able to compare it with what is typically measured. Under CAPM, one of the concerns is to determine the market risk premium (MRP ), which is the premium that investors demand when they invest in a well diversified portfolio of risky assets (the market portfolio). How is the MRP estimated? Normally, one looks at long time series to work out the historical premiums associated with investing into stocks as opposed to risk-free securities. According to Damodaran, such an approach can yield reasonable MRP estimates when working with US data, as the US stock market is large and diversified and both the stock market and the bond market enjoy a long history. If, however, smaller, younger markets are used, the results are meaningless. Damodaran justifies this line of argumentation by referring to the fact that the shorter the time series, the greater the standard error. Modified historical risk premium To address the described problem Damodaran proposes a modified process, beginning with the basic proposition equity risk premium = equity risk premium for a mature market + country risk premium and continuing with two questions: 1. How should one determine the first component (the equity risk premium for a mature market)? 2. Furthermore, should one also use a country risk premium? And if so, how should it be determined? Damodaran’s answers are as follows: 1. To determine the equity risk premium in a mature market, he proposes using US data, taking the period 1926 to 1998 as a baseline1 , using the geometric mean and – with respect to the risk-free interest rate – using Treasury bonds.2 2. In regard to country risk premiums Damodaran points out that some scholars believe it is possible to diversify country risks.3 He explains that this
1 The relevant article by Damodaran was published in 1999, so we can conclude that today he would recommend using the period 1926 to 2009. 2 Treasury bonds are US bonds with a minimum term of 10 years that normally have half-yearly coupons and are taxable at the federal level only. 3 He indicates no source.

(3)

3

could be the case provided the stock markets of different countries do not correlate. In reality, however, they do correlate positively, he states, so it is not possible to eliminate a major part of the country risk through diversification. In order to estimate the country risk premium, states Damodaran, three problems must be solved: a) The country-specific risk must be measured. b) The country-specific risk must be converted into a country-specific risk premium. c) A given firm’s exposure to that country-specific risk must be assessed. Measuring country-specific risk Damodaran establishes that there are various ways to assess country risks. The simplest approach would be to use the ratings of relevant agencies (S&P, Moody’s, IBCA). While their ratings always relate to the risk of default, these risks are essentially driven by the same factors that drive equity risks: currency stability, trade balances, political stability and so forth. An additional advantage of such ratings, he continues, is that they relate directly to spreads over US Treasury bonds. To illustrate, he uses a table with various Latin-American countries (from Argentina to Venezuela) that has three additional columns: – one for currency risks (from A– for Chile to BBB– for Colombia and Uruguay), – another for spreads over US corporate bonds (“corporate spreads”) – and finally one for spreads over Treasury bonds (“country spreads”). Damodaran believes that country spreads potentially reflect the market’s risk assessment more precisely than corporate spreads, yet still advocates measuring country risks via corporate spreads since the market for corporate bonds is far more liquid than that for government bonds. Finally Damodaran touches upon other possibilities to measure country risks, casually mentioning their pros and cons without describing alternatives in more detail. Reading this section conveys the impression that, all things considered, using corporate spreads is the best or at least, a workable method. Estimating the country risk premium Measuring country risks is just an interim step towards assessing the country risk premium. Country risk initially only measures default risk. According to Damodaran it makes intuitive sense for the

4

country risk premium for equity positions to be higher than the default risk for outside capital positions. The likely reason is the fact that lenders of outside capital generally take priority over lenders of equity whenever financial surpluses are distributed. To allow for this fact, Damodaran compares the stock market volatility of a given country to the volatility of the bond market in the same country, producing the following equation for estimating the country risk premiums: σstock . (4) CRP = corporate spread · σbond Usually stocks are more volatile than bonds. Accordingly, the CRP is – usually – higher than the corporate spread when following the proposal described here. Valuating corporations with country risk premiums To determine the cost of capital for a company exposed to country risks, Damodaran distinguishes three different alternatives: The bludgeon approach: Provided all companies in a country are exposed to the country risk in an identical manner, Damodaran recommends the approach expected return on equity = rf + MRP · β + CRP . (5)

Here, the risk-free interest rate rf equals the US interest rate for Treasury bonds and the MRP equals the market risk premium of a mature market – specifically, the US market. The beta approach: Here, it is assumed that the company’s country risk is proportional to the market risk, that is, it can be measured using the beta factor. In this case Damodaran recommends expected return on equity = rf + (MRP + CRP ) · β, without commenting further. The lambda approach: The broadest approach, Damodaran’s preferred method, allows for a company to be exposed to market risk and country risk in different ways. While this leads to cost of capital of expected return on equity = rf + MRP · β + CRP · λ, (7) (6)

Damodaran (1999a)’s work offers no further explanations on how to establish λ.4 Damodaran (2003) is more informative in this respect.
4 Damodaran himself refers to Damodaran (1999b) for details. There, however, he states merely that for emerging markets, it is not possible to collect data that would allow a reliable assessment of beta factors.

5

Damodaran stresses that the lambda method is not a single-factor model like the standard CAPM, but rather a two-factor model. In light of equation (1), equation (7) could therefore be written as expected return on equity = rf + MRP · β1 + CRP · β2 Damodaran (2003) provides the following information about the lambda method: – Like beta, lambda has a value of around 1 where λ = 1 represents an average country risk, while λ > 1 (λ < 1) reflects a company that is exposed to a higher (lower) than average country risk. – Most investors would accept that corporations have different lambdas. – Damodaran describes various ways to determine a corporation’s lambda factor. 1. A turnover or sales based approach would be one of the most obvious methods. A corporation that generates 30 % of its turnover in Brazil is less exposed to the associated country risk than a corporation generating 70 % of its turnover in Brazil. 2. However, a corporation may also be exposed to country risk if it does not generate any turnover in that country but has production plants there. This is particularly true if these production plants cannot be moved easily (e.g., mines). 3. It may be possible to mitigate or even eliminate country risks using suitable instruments (insurance, derivates etc.). However, Damodaran believes that corporations would probably hesitate to apply such lambda-reducing instruments because a) there are always costs associated with risk management and b) they would eliminate risks, but also opportunities. According to Damodaran the crucial factor is the difficulty associated with obtaining reliable information on a corporation’s production plants and/or risk management strategy. By contrast, general information about a corporation’s sources the turnover is easily available. Therefore, to determine a corporation’s (j) lambda factor he suggests λj = share of turnover generated by corporation j in a country share of turnover of an average corporation in that country

To calculate lambda this way, information is needed on both the numerator and the denominator. To estimate the denominator Damodaran suggests looking at export statistics.

6

Furthermore he discusses the use of yardsticks of profitability rather than turnover, as well as market prices. Concerning the latter, he suggests regressing a corporation’s earnings per share to the country’s bond returns and to use the incline of the regression line as the lambda factor. Formally, this procedure is very similar to the one used to determine the beta factor; however, one would have to expect a considerable standard error. We herewith conclude our analysis of Damodaran’s country risk concept and turn to a systematic critique.

3 Critique of the CRP concept
3.1 The theoretical foundation of Damodaran’s equations – built on sand
Equation (1), which Damodaran uses as a starting point for his deliberations, merits several notes. In the case of J = 1 we are dealing with a one-factor model, e.g. the CAPM. Looking at the CAPM, it is proven that within the limits of a neoclassical equilibrium model consisting of definitions and logical, consistent assumptions, the equation (2) is valid. This would at least put equation (2) on a scientifically demonstrable basis. By contrast, when using the arbitrage price theory (APT) by Ross (1976), we are dealing with a multi-factor model where it is possible to prove that it possesses the linear structure indicated in equation (1). Here, J > 1 can apply. However, it is in the nature of the model that none of the risk factors can be interpreted conceptually. We are hence not allowed to pick out one of these factors and interpret it as a country risk factor. Furthermore, for any multi-factor model it is possible to prove that it can get by with just one single factor.5 However, this demonstrates that equation (1) has no scientific justification. Further, if one interprets equation (1) as a multi-factor model in the sense of an empirical model based on multiple linear regression, its linear structure is not proven as it is in the CAPM or the APT. Rather, it is simply assumed. Those who work with it without furnishing this proof later (in whatever way) are hence using unscientific arguments.6 Damodaran’s deliberations may therefore be justified if they relate to a CAPM framework. As he explicitly differentiates between mature and emerging countries and their specific risks, he may have a CAPM in mind that distinguishes between at
5 The details are described in Gilles und LeRoy (1991). 6 We shall deal with this aspect in greater detail in the next chapter.

7

least two countries with specific risks. Therefore we first devote ourselves to the question of whether two different risky asset classes (A and B) can be examined in a CAPM and what implications this has. For this reason we concentrate on the usual model world of a CAPM with one period.7 Investors should be able to make risky investments in countries A and B. There is no reason to assume that the investors in question can only invest in their respective countries of residence. In a capital market model such as the CAPM, the entirety of available investment opportunities plays an important role. Described here with the letter M, they comprise the sum of all risky assets in both country A and country B and are usually referred to as the market portfolio. Besides investing in risky assets a CAPM offers the possibility to trade risk-free securities. The CAPM is without any doubt an equilibrium model. Usually, in such models one assumes that the risk-free securities are in “zero net supply”. This means that the sum of all risk-free investments equals the sum of all risk-free credits. If we assume a world with two countries, “zero net supply” means that market portfolio M contains neither risk-free securities from country A nor any from country B. The risk-free securities yield country specific returns which are denominated by A B rf and rf . There are two cases that need to be distinguished: Different currencies: The countries may have different currencies that can be merged through an exchange rate. The exchange rate between A and B shall be set at f0 . The future currency rate f1 is assumed to be uncertain. Identical currencies: We also want to examine a case where both countries have the same currency and only the risks associated with the respective government bonds are different. This is, for instance, the case in the euro zone. We assume that country A’s return is risk-free. Both cases will now be discussed more precisely. Different currencies Assuming different currencies in countries A and B, we A can conclude that the rate of return rf for investors in country A and the rate B of return rf for investors in country B is risk-free. If, however, an investor in B country A opts to invest at rf , his rate of return becomes contingent upon the future exchange rate and is hence no longer safe unless he hedges it. The opposite also applies. For the sake of clarity, we focus on an investor in country A and assume that he invests in bonds of both his own country and a foreign country. Within the
7 For details of modelling a CAPM, cf., e.g., Duffie (1988, pp. 93 ff).

8

framework of a standard CAPM, is it possible to alter the known securities market line in such a manner that a country risk premium becomes discernible? No. For the investor based in country A, the classic CAPM remains valid; in his case, the expected return of a risky asset j is
A A E rj = rf + E[rM ] − rf

Cov[rj , rM ] . Var[rM ]

(8)

Since market portfolio M contains no bonds of country B (“zero net supply”), it is not discernible how a country risk premium could arise here. On the contrary, the standard CAPM is applicable without any modification when assuming the perspective of an investor based in country A. Nor does this change when switching perspectives to consider an investor based in country B. For this market participant the same standard CAPM applies, and this investor now regards the bonds issued by his home country as risk-free. His riskB free return therefore amounts to rf . From this perspective, the CAPM assumes the form8 E f1 (1 + rj ) − 1 = f0 =
B rf

f1 B + E (1 + rM ) − 1 − rf f0

Cov

f1 f0 (1

+ rj ), f1 (1 + rM ) 0 f1 f0 (1

f

(9)

Var

+ rM )

If specific assumptions are made regarding the correlation between exchange rates and asset returns, equation (9) can be simplified. We consider that it is not unreasonable to assume that exchange rates and share returns are independent of one another. While this assumption is certainly a restriction, it is by no means totally unrealistic; exchange rates are generally far more influenced by transactions
8 To follow this line of argumentation note that within the framework of equation (8) payments for all assets, bonds, etc. must be converted into the currency of country A. To find out how the equation changes if we take the perspective of an investor based in country B, the currency of country B has to be used for all calculations; a currency exchange risk must hence be considered. Generally, the return on a title j, which today carries a price tag of p(Xj ) and over the course of one year will generate uncertain cashflows of rj =
Xj p(Xj )

− 1. Taking the currency exchange risk

into account, asset j will yield (in a foreign currency) the uncertain amount of f1 Xj and has a price of f0 p(Xj ). The return in the foreign currency will therefore amount to f 1 Xj f0 p(Xj )

−1 =

f1 f0 (1+rj )−1.

9

on bond markets than by corresponding securities transactions.9 However E f1 f1 B (1 + rM ) − 1 − rf = E f0 f0
B E[1 + rM ] − 1 − rf

B ≈ E[rM ] − rf + E

f1 −1 . f0

In the CAPM equation, then, the market risk premium in one country’s currency must be replaced by the market risk premium in another country’s currency plus expected changes in the exchange rate. This replacement is economically sensible since because it makes a difference whether worldwide GDP growth is measured in yen, dollars or euros. However, it is not justifiable to speak of a country risk premium in this context. The beta is also subject to change. Unfortunately, these correlations are not as obvious so the numerator and the denominator of the new beta are presented seperately. If we assume again that exchange rates and asset returns are independent of one another, after a fairly complex calculation we obtain Cov f1 f1 f1 (1 + rj ), (1 + rM ) = Var f0 f0 f0 E[(1 + rj )(1 + rM )]
2

f1 +E f0 Var f1 f1 (1 + rM ) = Var f0 f0

Cov[rj , rM ], f1 f0
2

E (1 + rM )2 + E

Var[rM ] .

Neither in the beta factor can we recognise any kind of country risk premium. Identical currencies Let us assume now that countries A and B use the same currency. If the bonds of country A and of country B are riskless, every deviation A B from the equation rf = rf would imply arbitrage opportunities, because one would only need to borrow money in the country with the lower return and invest it in the country with the higher interest rate. The CAPM equations of both countries are identical in this case. Alternatively, we consider a situation where the bonds of country A are riskless A but those of country B are risky. In this case, one must assume that E[r B ] > rf . Admittedly, even under these assumptions there is no place for a country risk premium in a typical CAPM. For the investor residing in country A, equation (8) is B still valid. Since rf does not exist the investor in country B would have a CAPM
9 This is borne out by the fact that bond market turnover is far greater than capital market turnover.

10

without a risk-free asset. He can nevertheless buy government bonds of country A. Therefore, the typical CAPM without any country risk premium applies to him. To put this in a more current and drastic context: All investors use German government bonds to assess Greek securities and as a market portfolio use an index composed of German and Greek shares. Finally, some fundamental considerations are advisable. To this end, we examine the typical shape of the debate within the scientific community and look at under which circumstances it is fair to say that a new theory, such as the country risk premium concept, is gaining popularity or even has taken hold. Among economists it is common to begin by discussing new insights in journals before moving on to publishing monographs. After the end of the Second World War a system of peer-review began to develop, one that has both its strengths and its weaknesses.10 There is justified criticism regarding this purely quantitative way of assessing scientific achievement. In any case, there is consensus within the scientific community that these days, the truly crucial debate on new insights is conducted via the journals. While other disciplines prefer to hold conferences (e.g. computer sciences) or prefer to conduct their debates by publishing monographs (e.g. some of the humanities), economists prefer to debate via scientific journals. Here, too, the majority principle applies. It is fair to claim that a new theory can be considered to have taken hold once the majority of economists cited in the journals has accepted it. Where the country risk premium concept is concerned we observe that although Damodaran has presented his approach in the manner described above, it has yet to elicit a positive response from the scientific community. It has been neither criticised nor accepted; in fact, no one has taken notice. In fact, in none of the articles quoted above does Damodaran refer to the work of other scientists. Interestingly, then, this disregard appears to be mutual. The Journal of Applied Finance, where Damodaran (2003) was published, does not enjoy recognition in the scientific community.11 The Journal of Applied Finance claims that its goal is “to be the leading bridging journal between practitioners and academics”.12 The editorial board includes no high-ranking personalities. Damodaran (2009) appeared in Financial Markets, Institutions and Instruments,
10 Regarding the weaknesses, cf. the very valuable work of Gans und Shepherd (1994) or http://www.unifr.ch/wipol/assets/files/PhD%20Course/gans shepherd1994.pdf. 11 There is no reference to it in the journal rating of the Vienna University of Economics, nor in any other international ratings of scientific periodicals (cf. http://vhbonline.org/service/jourqual) nor in the Jourqual of the German Academic Association for Business Administration. 12 Its mission statement reads, “The mission is to publish well-crafted papers of interest to practitioners (including those without PhD-level training) and of use to academics in stimulating research and in their teaching function.”

11

which is published by Anthony Saunders at the NYU Salomon Center, who is a faculty colleague of Damodaran’s.13 Jourqual gives this publication a relatively low ranking at C (6.80), while the ranking of the Vienna University of Economics does not consider it at all. The same is true for other rankings.14 Damodaran’s other articles on the country risk premium are either discussion papers or SSRN publications as this one, so they have never been subject to an assessment. Summing up, it is fair to claim that Damodaran’s idea of introducing a country risk premium is not scientifically justified within a CAPM. We can also claim that Damodaran’s country risk premium concept is not part of the regular scientific debates. He appears to write primarily for practitioners. Scholars from American or European universities have (so far) taken no notice of the concept described in this paper. It is therefore inappropriate to consider Damodarans’s concept of the country risk premium an acknowledged theoretical model.15

3.2 Damodoran’s empirical basis – a hotchpotch of ad hoc ideas
Additional points of criticism are presented in the following. It will emerge that while Damodaran has plenty of imaginative ideas on how to determine country risk premiums, all of them turn out to be problematic at second glance. Lack of a formal definition of CRP When determining country risks it is fair to expect that there exists a clear definition of a CRP . Yet Damodaran fails to provide such a definition. It is unclear what exactly must be measured in order to calculate the CRP . To avoid any misunderstandings we take another look at the classic standard CAPM: E[rj ] = rf + MRP · βj . (10) The left side shows the costs of equity of an enterprise j in the sense of an expected return; to the right are the risk-free interest rate, the market risk premium and the beta factor. Each of these three quantities is defined in such a way that it
13 The mission statement reads, “Financial Markets, Institutions and Instruments bridges the gap between the academic and professional finance communities. With contributions from leading academics, as well as practitioners from organizations such as the SEC and the Federal Reserve, the journal is equally relevant to both groups.” 14 See the Keele 4-4-2-list, University of Leicester and others. 15 During a recent legal dispute where two of the authors were involved, representatives of a highly respected auditing firm referred to Damodaran’s concept as a “well recognised theoretical model”.

12

is clear what is meant. The MRP is defined as MRP = E[rM ] − rf , (11)

so we can state that it represents the difference between market yield and the risk-free interest rate, where the market yield is the return an investor can expect if he invests in a diversified portfolio of risky assets (the market portfolio). We do not deny that estimating the market risk premium is a challenging affair, but with a view to equation (11) it is at least possible to state that there is a precise formal definition of this term. Unfortunately, this is not the case for the country risk premium. However, in connection with his equation (1) Damodaran claims that a risk premium is generally a surcharge that investors demand on top of the risk-free interest rate if they have to accept an average risk concerning the relevant factor. When trying to see matters from Damodaran’s perspective, one needs to distinguish between mature and emerging markets, for which we will use A und B. Now Damodaran leaves no doubt that with MRP he fully concentrates on A markets, while the CRP is all about B markets. In analogy to equation (11) one could assume that it were possible to follow Damodaran by using definitions such as
A MRP = E[rM ] − rf B CRP = E[rM ] − rf

and

(12) (13)

Yet these two definitions are by no means as clear as the definition of the market risk premium according to equation (11). 1. When equation (11) refers to the market portfolio, at least it is on principle clear that it includes all risky assets in the world. However, when using definitions (12) and (13) all risky assets must be divided into two classes, namely those which can be attributed to the A market, and those which belong to the B market. In this context it must be borne in mind that Damodaran fails to draw a clear dividing line between the A market and the B market. Also, there may be further markets with risky assets that can be attributed neither to A nor to B. Damodaran fails to indicate how to deal with titles belonging to such a C market. 2. It is striking that definitions (12) and (13) work with a uniform risk-free interest rate. If A and B represent two countries (or country groups) each with their own currency, and if one also assumes that both countries’ govA B ernment bonds are (virtually) risk-free, rf = rf does not necessarily apply. Damodaran does not state how to deal with the resulting problems.

13

Practical estimation of CRP In order to estimate the MRP according to equation (12), Damodaran suggests using the usual method. He recommends falling back on market data drawn from the mature A market and analysing long time series. To him, it is not possible to similarly estimate the CRP according to equation (13) using data drawn from the B market since he believes there to be insufficient data on emerging markets. He therefore has to choose an alternative and recommends two steps, both of which contain plenty of arbitrary elements. Estimating country risk: The first step concerns the determination of country risk. This is generally understood to represent the risk of default in foreign trade and payments, which threatens the settlement of accounts receivable between foreign contracting partners. Normally, a distinction is made between original and derivative default risks, depending on whether the foreign government or a borrower residing in a foreign country (foreign company) is considered the debtor. Damodaran prefers to use derivative default risks, arguing that markets for corporate bonds are more liquid than government bond markets. However, he does not exclude the use of data on original default risks, providing the user of the Damodaran concept with ample scope for action, considering that original and derivative default risks may correlate negatively. Original or derivative country risks are reflected in credit spreads, that is, in interest markups for loans or bonds granted by a given country to a country with a triple A rating.16 The fact that default risks associated with foreign corporate bonds are not subject to the same forces as the risks associated with foreign shares is mentioned by Damodaran, but he deemphasizes this fact. This is hardly surprising, since he is preoccupied with finding pragmatic “solutions” rather than with developing a well-founded theoretical model. Identifying country risk premiums: In the second step Damodaran attempts to derive the CRP using company specific credit spreads. To address these relationships formally and unambiguously, we assign the symbol CS to the credit spreads. We are therefore looking for a functional relationship between CS and CRP . In this context it must be remarked that the risks associated with shares and bonds have little to do with one another. Knoll, Vorndran und Zimmermann (2006) provide ample proof that these risk categories are essentially incommensurate.
16 This kind of information is available from rating agencies such as Fitch Ratings, Moody’s and Standard & Poor’s.

14

However, our criticism goes beyond that. Damodaran establishes the relationship between CS and CRP without reference to a clear theoretical foundation that is logically verifiable by third parties. Rather, he relies on the fact that shareholders usually take a more risky position than lenders, and pragmatically suggests converting the credit spread to the desired country risk premium using a simple rule of three. As a conversion factor he recommends the ratio between the volatilities, that is asset volatility CRP = . CS bond volatility His recommendation is a problem for two reasons: 1. Since Damodaran’s model is not based on a sound line of argumentation, there are no clear rules on how to measure volatility. He himself uses the standard deviation. Yet by the same token one could also apply the variance or another dispersion measure, and σ2 σstock = stock . 2 σbond σbond applies as a general rule. Using variances instead of standard deviations would therefore, all else being equal, lead to entirely different country risk premiums. Without a model-theoretical foundation we once again observe arbitrary results. 2. The volatilities must be estimated on the basis of empirical data, regardless whether they are measured with standard deviations or variances. We assume that in order to do so one has to fall back on capital market data of emerging markets. Yet according to Damodaran these do not constitute a reliable basis, and it is precisely this fact that caused him to develop his country risk concept. This is clearly an instance of a vicious circular statement. Standard error and structural changes Damodaran duly describes the procedure to be followed in order to estimate the CAPM’s MRP . He considers long time series. He also correctly points out that the shorter the considered time series, the greater the standard error. He distinguishes between fully developed markets on the one hand and emerging markets on the other, asserting that MRP s which are evaluated using data from emerging markets are useless owing to the too short time series.

15

However, this does not imply that MRP s which have been evaluated using data from mature markets are more reliable. Yet this is exactly what Damodaran suggests. He overlooks or at least omits the fact that time series can have structural breaks, and it is fairly certain that the time series between 1926 and 1998 contain several such breaks.17 Damodaran is not concerned about that. Independently of (presumed) structural interruptions, he recommends a time series of this length in order to evaluate the MRP for the mature US market. From this angle, it cannot be excluded that MRP which have been evaluated using data from emerging markets are statistically more reliable than MRP based on data from mature markets. Diversifiability of country-specific risks Damodaran justifies the necessity of country-specific risk premiums by arguing that diversification does not significantly diminish country-specific risk. In order to successfully support this line of argumentation we see two possible avenues: Either one shows that such attempts at diversification are technically impossible, as e.g. the trade with certain financial instruments is unlawful; alternatively, one can demonstrate that financial instruments from two different countries (or groups of countries) correlate in such a manner that diversification would not realistically lead to a meaningful risk reduction. Damodaran does not bring forward arguments of the first type. Also, they would be hard to confirm in this day and age. He instead uses arguments of the second variety, explaining that diversification is only possible if the markets of two different countries are “uncorrelated”. This is not a very precise statement. We interpret it in such way that the correlation coefficient between the assets of country A and those of country B would have to be ρA,B = 0. This is a very odd view of things. It is at least possible to show that even a positive correlation allows for the set-up of portfolios that are less risky than if one were to invest solely in the lowest-risk asset. The only precondition would be that ρA,B < 1, so only a perfect positive correlation is to be avoided.18 Naturally, the effects of diversification increase as the correlation effect diminishes. Yet it remains a mystery why one needs to postulate ρA,B = 0 to assert substantial diversification. Also, Damodaran makes absolutely no reference to how strongly one has to diversify in order to eliminate the need for a countryspecific risk premium. His views regarding this aspect, too, need to be considered
17 This can be properly analysed by using models of structural interruption. There is hence no need to rely on “anecdotes” about the global economic crisis, the Korean war, the banking crisis or other similar events. 18 It is worth pointing out that even a perfect positive correlation allows for complete risk obliteration if short selling was permitted.

16

arbitrary. Incidentally it has to be clarified what correlations there are between assets from different countries. Damodaran fails to provide concrete figures based on verifiable empirical studies. He limits himself, again, to qualitative generalised assumptions. Cost of capital and CRP Damodaran names three possibilities for integrating country risk premiums into a company’s equity cost of capital. All three are difficult. First of all, we observe that the choice of procedure seems to be at the discretion of the person performing the valuation. None of the three possibilities is logically derivable from a theoretical model. They are merely the product of their inventor’s imagination. In the following we limit ourselves to the beta and the lambda approach, without considering the option that Damodaran refers to as the bludgeon approach. Beta method: This concept is formally based on E[rj ] = rf + (MRP + CRP j ) · βj
MRP ∗ j

(14)

in other words, it basically consists in raising the market risk premium by a country risk premium.19 The questionable nature of this concept is exacerbated in that Damodaran claims to depart from CAPM only once he introduces the (subsequent) lambda method. The fact that he makes no such statement concerning the beta method could mislead practitioners, especially, into thinking that this concept leaves them within the bounds of CAPM. This, however, is not the case. Why not? Within the framework of CAPM a market risk premium is an entity that is wholly independent of the company under review. The MRP has the exact same value for all companies under review. Yet this is precisely not the case for the country-specific risk premium. After all, it only becomes relevant for companies with activities in emerging markets.20 If this were not the case, there would be no compelling reason to raise the cost of capital by a country-specific risk premium and to compute a “market risk premium” MRP ∗ .21 In contrast to MRP the modified MRP ∗ is always a j j
19 It should be mentioned here that, following Damodaran’s concept, the magnitude of the market risk premium should be assessed based on data from a developed capital market. 20 To make this unmistakably clear, in equation (14) we have marked the country-specific risk premium with the company index j. 21 For the reason mentioned in footnote 20 this variable, too, is marked with index j.

17

company-specific value, and this is simply irreconcilable with the traditional CAPM. The assumption that CAPM is the foundation for determining the cost of capital leads to a logical contradiction, to the extent that Damodaran’s beta method is used. Even if one were to ignore this major problem there is still one further question. In order to clarify it, we assume that the company’s activities abroad account for aj of its overall activities.22 We further assume that an average ¯ proportion of foreign activity a is typical of all participants in this emerging market. This produces three conceivable cases. Either the foreign activity of ¯ the company in question is above the average (aj > a), or it corresponds to ¯ ¯ the average (aj = a), or it is below the average (aj < a). Which procedure ought to be used when employing the beta method? Damodaran remains silent on this. Intuitively it may seem reasonable to apply a risk premium in the first case, to dispense with a country-specific risk-premium in the second and to apply a risk discount in the third. However, such a solution would seem entirely ad-hoc and, like the entire CRP approach, lacks a stable theoretical foundation. Lambda method: In the same way Damodaran fails to provide a formally clear definition of the CRP , he fails to provide a corresponding definition of the lambda factor. He merely provides the equation23 E[rj ] = rf + MRP · βj + CRP · λ and states that, on average, lambda is equal to one. This is a largely uninformative statement, merely allowing for lambda to be greater or smaller than one. For instance, nothing is said as to whether lambda can also be negative or whether it has an upper limit. It is hence entirely open what λ is supposed to be. This is very different when it comes to the beta factor. Everyone familiar with the CAPM knows that it represents the ratio between a covariance and a variance, namely βj = Cov[rj , rM ] . Var[rM ]

Those wishing to know how to determine a lambda factor can only employ the examples supplied by Damodaran in this particular context. They will
22 How this proportion is measured is of no concern to us at this point. We address this in the context of the lambda method. 23 In “proper” terms this would probably have be rewritten as E[rj ] = rf + MRP · βj + CRP · λj .

18

want to base their calculations on quantitatively measurable entities that describe a company’s level of economic activity in an emerging market. These entities could be turnover, production costs, or even key financial indicators (cash flow, net profit), so once again there is a pronounced risk of arbitrariness since using turnover to estimate lambda will not produce the same figures as using EBITDA. When Damodaran primarily argues in favour of using turnover-related figures, he does so merely in the interest of pragmatism, not on the basis of a convincing theoretical foundation.

4 Conclusion
We are aware that practitioners often pose questions whose answers require complicated academic analysis. Practitioners tend to lack the time and sometimes also the necessary theoretical foundation to tackle these issues in a scientifically convincing manner. It is entirely understandable if, under the circumstances, they make assumptions that in an ideal world would attract strong criticism, or if they take recourse to simple ad-hoc solutions. Accordingly, it is possible that practitioners propose country risk premiums simply to deal with certain problems. Damodaran is, however, not a practitioner in the field of valuation but a professor at a well-respected university. He thus has the necessary resources and time to give thorough consideration to challenging problems in this field. In particular, it is fair to expect him to adhere to strict scientific principles. It is precisely these virtues that we feel are lacking here. Scholars who, endowed with the status of a university professor, propagate solutions to problems that do not stand up to scientific criteria, act recklessly since they create the impression that their ad-hoc solutions are based on a theoretical foundation. Unfortunately, this is the criticism that we feel we have to level at Damodaran: 1. Damodaran’s concept of a country risk premium (CRP ) is of no relevance in academic circles. 2. It is not fair to claim that the country risk premium concept has a strong theoretical basis. Indeed, this is impossible within the framework of a traditional CAPM. Neither is the country risk premium concept empirically supported, where “empirical” means based on a sound econometric methodology. 3. Since Damodaran’s country risk premium can be neither theoretically nor empirically supported, the rates of return on capital that are derived by such methods are highly arbitrary.

19

The observation that his concept is making inroads among both investment banks and auditing firms is therefore cause for considerable concern.

References
Damodaran, Aswath (1999a) Estimating equity risk premiums, Working Paper, Stern School of Business, New York University, New York. — (1999b) Estimating risk parameters, Working Paper, Stern School of Business, New York University, New York. — (2003) “Country risk and company exposure: theory and practice”, Journal of Applied Finance, 13, 64–78. — (2009) “Equity risk premiums (ERP): determinants, estimation and implications; a post-crisis update”, Financial Markets, Institutions and Instruments, 18, 289– 370. Duffie, Darrell (1988) Security Markets: Boston. Stochastic Models, Academic Press,

Gans, Joshua S. und Shepherd, George B. (1994) “How are the mighty fallen: rejected classic articles by leading economists”, Journal of Economic Perspectives, 8, 165–179. Gilles, C. und LeRoy, S.F. (1991) “On the arbitrage pricing theory”, Economic Theory, 1, 213–229. Knoll, Leonhard; Vorndran, Philipp und Zimmermann, Stefan (2006) “Risikoprämien bei Eigen- und Fremdkapital - vergleichbare Größen?”, FinanzBetrieb, 8, 380–384. Ross, Stephen A. (1976) “The arbitrage theory of capital asset pricing”, Journal of Economic Theory, 13, 341–360.

20