metadata: authors: 0: author: Melecky,Martin
count: World
docna: 0: docna: Choosing the currency structure for
            sovereign debt : a review of current approaches
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Economic Adjustment and Lending,Public Sector Economics,Strategic Debt Management,External Debt,International Trade and Trade Rules,Macroeconomic Management,Public Finance Decentralization and
            Poverty Reduction,Financial Structures,Debt Markets
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,International Economics and Trade
abstracts: cdata!: This paper acknowledges the fact that
            some countries have to borrow in foreign currencies due to
            the various constraints they face. Starting from this point,
            the author reviews approaches for trying to determine the
            currency structure for sovereign debt, and discusses some
            issues inherent in these approaches. The analysis mainly
            focuses on the correlations of domestic fundamentals with
            the actual versus equilibrium exchange rate in light of the
            long-term perspective of a debt manager and changing
            exchange rate regimes. In addition, the author makes some
            observations on the characterization of exchange rate
            volatilities in the existing approaches.
repnme: repnme: Choosing the currency structure for
            sovereign debt : a review of current approaches
display_title: Choosing the currency structure for
            sovereign debt : a review of current approaches
listing_relative_url: /research/2007/06/7694702/choosing-currency-structure-sovereign-debt-review-current-approaches
topicv3: Government Expenditure m1326649 1112,Trade m1326924 698,Debt Management m1327211 451,Central Banks m1327453 1235,Monetary Policy m1327609 444
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,International Economics and Trade
no_of_pages: 36
author_keys: 0: author_key: 915923
model_extractions: WPS4246

# Choosing the Currency Structure for Sovereign Debt

A Review of Current Approaches*

## Martin Melecky<sup>†</sup>

Banking and Debt Management Department World Bank

### Abstract

This paper acknowledges the fact that some countries have to borrow in foreign currencies due to the various constraints they face. Starting from this point, the paper reviews approaches for determining the currency structure for sovereign debt, and discusses some issues inherent in these approaches. The review mainly focuses on the correlations of domestic fundamentals with the actual versus equilibrium exchange rate in light of the long-term perspective of a debt manager and changing exchange rate regimes. In addition, the paper makes some observations on the characterization of exchange rate volatilities in the existing approaches.

Keywords: Sovereign Debt Management, Foreign Exchange Risk, Risk Management, External Shocks, Fiscal Sustainability JEL Classification: H63, F37, G11.

World Bank Policy Research Working Paper 4246, June 2007 _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._

*I thank David Bolder, Alessandro Missale, Otavio Ladeira de Medeiros, Phillip Anderson, Lars Jessen, Eriko Togo and Antonio Velandia for their suggestions and comments on earlier drafts of this paper.

† Banking and Debt Management Group, World Bank, 1818H Street NW, DC 20433, USA, email: mmelecky@worldbank.org.
# 1 Introduction

Sovereign borrowers often have large funding needs owing to their e¤ort to stabilize income over time and across circumstances, increase income faster than it is possible when relying only on their own resources, support monetary policy, and develop domestic capital markets.<sup>1</sup> If the funding needs cannot be met by issuing debt denominated in the domestic currency, the government is forced to issue debt in a foreign currency and as a result can be exposed to foreign exchange (FX) risk by possibly having currency mismatches on its balance sheet. The currency mismatches could arise if, after matching the cash ‡ows from assets<sup>2</sup> and liabilities denominated in similar currencies, there still remains an open position in any foreign currency. There are at least four candidate explanations for the constraints forcing sovereigns to borrow in foreign currencies.

First, the inability of developing countries’governments to issue desired amounts of debt denominated in domestic currencies can be attributed to the unwillingness of foreign investors to hold sovereign debt denominated in currencies of small developing countries. In this regard, the literature on the "original sin", see e.g. Eichengreen et al. (2003), Hausmann and Panizza (2003) and Chamon and Hausmann (2005), highlights the role of path dependence and international factors in foreign exchange borrowing while downplaying the importance of institutional and macroeconomic factors. This implies that there is not much leeway left for many emerging market economies in need of ...nancing, as policy makers cannot alter the initial conditions, and improvements in policies and institutions do not seem to a¤ect their ability to issue domestic currency debt o¤shore. In contrast to the evidence from the "original sin" literature, which ...nds mainly the country size explaining the sovereign debt’s currency structure, Claessens et al. (forthcoming) ...nd that institutional and

> 1The reason for government borrowing can be also more opportunistic by simply taking advantage of favorable market conditions for ...nancing.

> 2Usually the most important asset of a government is the present value of its future revenues. As the revenues are most often denominated in the domestic currency borrowing in foreign currencies creates currency mismatches in government’s balance sheet. In the case where the revenues are denominated in foreign currencies, e.g. oil revenues or royalties, borrowing entirely in domestic currency would also create currency mismatches.

2
macroeconomic factors are related to the currency composition of government bond markets when controlling for country size.<sup>3</sup> Second, sovereigns can be constrained in issuing desired amounts of debt in domestic currency due to partial dollarization of the domestic economy. Dollarization is usually ascribed to decreasing monetary credibility, an argument put forth by e.g. Jeanne (2005). Low monetary credibility is then often an outcome of de...cient independence of monetary policy and interference of ...scal policy with the way monetary policy is conducted. A lack of independent monetary policy implies higher in‡ation expectations and in‡ation volatility due to the possibility of the government trying to in‡ate the debt away (Togo, 2006; Burnside, 2003; Blinder, 1983; Sargent and Wallace, 1981). Monetary policy has long been considered an important determinant of debt composition in the literature on OECD countries - see e.g. Bohn (1990a) on debt currency composition and monetary policy, or Falcetti and Missale (2002) on debt currency composition and central bank independence.

The third explanation of the fact that sovereigns issue foreign currency debt is that this borrowing simply appears as less expensive when assuming that the FX risk is comparable to the interest rate risk or emphasizing the cost perspective in the cost/risk trade-o¤. Broner et al. (2007) o¤er an explanation of the emphasis of cost considerations in borrowing programs of emerging market economies. Such rather an opportunistic approach is not uncommon even among the OECD countries, see e.g. Wolswijk and de Haan (2005), where e.g. Austria, Finland and Sweden have more than 10 percent of sovereign debt denominated in foreign currencies. It is therefore the cost-risk perspective of the debt management authority, its debt management capacities, and the degree of government’s preference for risk that are critical in this respect.

The fourth reason for a government not to issue as much domestic currency debt as possible, and rather opt for foreign-currency debt, can derive from its attempt to avoid crowding out domestic ...rms from domestic currency borrowing. This attempt

> 3More speci...cally, Claessens et al. ...nd that economies with deeper domestic ...nancial markets issue less foreign currency debt, and that increasing demand from foreign investors for foreign currency debt and less ‡exible exchange rate regimes are associated with more foreign currency issuance.

3
can stem from the recognition that in case the private sector has limited capacity to manage FX risk an elimination of the direct FX risk from a government’s balance sheet can shift the FX risk to private sector’s balance sheets and possibly increase the value of government’s contingent liabilities.

The obvious solution to the problem of eliminating the FX risk from sovereign balance sheets is development of domestic government bond markets. This would entail gradual elimination of the constraints due to e.g. the lack of benchmark issues, institutional investors, and a liquid secondary market. Institutional factors are crucial in this respect, see. e.g. Burger and Warnock (2004), Santos and Tsatsaronis (2003), and Turner (2002), who stress among others the role of creditor-friendly policies and laws, sound debt management and public governance for domestic government bond market development. Since institutional factors show high persistence it is not likely that the sovereigns and debt managers in particular could eliminate FX risk inherent to their balance sheets in a rapid manner.<sup>4</sup> Moreover, the potential size of the domestic market might still not su¢ ce for accommodating the demand for funds from the government and other entities in the domestic economy. The practical experience regarding relaxation of the domestic market’s constraints in selected countries<sup>5</sup> is summarized in World Bank (2007).

This paper focuses on management of the FX risk in a government debt portfolio by choosing the optimal currency composition for the unhedged sovereign debt. The latter refers to an open, short position of a sovereign in a foreign currency. Such position occurs if the sovereign, after matching the ...nancial characteristics of its asset and liabilities, is exposed to FX risk. The FX risk is usually considered one of the major risks in EMEs. It is also signi...cantly higher than in industrialized economies, as the EMEs are more exposed to external shocks, such as those relating to the terms of trade and the cost of ...nancing, in addition to ...nancial contagion or natural disasters, see Caballero and Cowan (2006), and Claessens (2005). The importance of ...nding optimal currency benchmarks for sovereign debt portfolios has

> 4There are also transitional issues for many economies, relating to macroeconomic policies, that impact on exchange rates and overall monetary conditions.

> 5These are the 12 countries selected by the WB’s Treasury for piloting its debt management diagnostic and associated advisory work.

4
been stressed by work of Caballero and Cowan (2006), Claessens (2006), and Bordo and Meissner (2006) who pointed out that although the FX risk in EMEs is high, the use of derivatives for hedging is limited and other types of hedging are costly (accumulation of FX reserves; foreign trade diversi...cation). Although the use of derivatives among EMEs is increasing in recent years, their still de...cient utilization in debt management stems from laws (rules) restricting instruments that can be used for debt management, a lack of leading examples, low sta¤capacity, and also a lack of markets for many EMEs currencies.<sup>6</sup> In this paper, we take a long-term perspective, as the debt managers should, in thinking about the foreign currency structure of sovereign debt portfolios, so as to minimize the FX risk of the benchmark portfolio and the use of add-on hedging products. What concerns the connection of our paper to existing literature, we acknowledge the fact that some countries have to borrow in foreign currencies due to the constraints they face. Taking o¤ from this point we review approaches that one might want to use when trying to determine the optimal currency structure for sovereign debt, and discuss some issues inherent in these approaches. Hence, we do not attempt to contribute to the literature on the "original sin" or explain how currency mismatches come about, we take these circumstances as given.

Section two complements and follows up on the work of Bolder (2005) by reviewing recent analytical and numerical approaches that can be employed in choosing the optimal currency structure for sovereign debt. Section three discusses and points to some issues related to the concepts and parameters underlying those approaches. Section four concludes, and o¤ers some policy implications and directions for future work.

> 6The limited use of derivatives also derives from the type and structure of the derivatives. Although, swapping one hard currency for another is readily available the feasibility of swapping a foreign hard currency into the domestic currency of a developing country can be limited due to much larger costs or constrained external convertibility of the domestic currency. Further, the structure of swaps can be seen as less convenient for budgeting purposes than e.g. options as the swap is settled in future whereas the premium for options is paid up-front.

5
# 2 Applicable Approaches

The current methods dealing with currency allocation of foreign debt applied by practitioners comprise but are not limited to (i) the minimum variance portfolio, (ii) matching the currency structure of FX reserves, foreign trade or capital ‡ows, or (iii) relying on the promise of the national central bank to maintain a peg against chosen currency. Employing the minimum variance portfolio approach for the currency choice is limited in its success as this approach is aiming at optimal diversi...cation and does not consider the link to government revenues and the time-varying ability of government to service its debt. Matching of currency structure of foreign reserves, foreign trade or capital ‡ows goes beyond e¢ cient diversi...cation and embraces the idea of an asset and liability management (ALM) approach. Nevertheless, it is hard to see through the interplay of foreign trade and capital ‡ows so that in practice the guidance is limited. Further, mimicking the structure of foreign reserves has its limitations due to the fact that most countries do not apply de facto free-‡oating exchange rate regime, intervene in the FX markets, and thus alter the free-‡oat level and composition of FX reserves. A more sophisticated methods combining optimal portfolio allocation and the ALM approach have been developed the literature.

To discuss the substance and implications of the theory underlying the choice of currency denomination of the sovereign debt we review in this section selected analytical approaches that have been recently adopted to support or justify policy decisions and deliberations<sup>7</sup> . Namely, we extend the approaches proposed by Licandro and Masoller (2000) and Giavazzi and Missale (2004) for choosing optimal weights of domestic in‡ation indexed debt, domestic nominal debt and foreign currency debt in a sovereign debt portfolio (the benchmark portfolio). These two approaches were recently applied in the cases of Uruguay and Brazil, respectively. We amend these approaches so that they solve the problem of choosing the optimal weights for debts in several foreign currencies. The approaches of Licandro and Masoller (2000) and Giavazzi and Missale (2004) di¤er in several aspects. Licandro and Masoller consider

> 7Note that there are other approaches in spirit similar to those that we review in this paper see for instance Missale (1999, chapter 5) or Bohn (1990a).

6
tax smoothing as the government’s (debt manager’s) objective while Giavazzi and Missale employ stabilization of the debt-to-GDP ratio as the objective function in their setup. However, both approaches emphasize the role of the exchange rate risk (variation) and co-movements of domestic fundamentals and exchange rates as the key concepts in determining the optimal portfolio weights. In addition, Giavazzi and Missale ...nd covariances between the returns (costs) of di¤erent debt instruments as being vital for determination of their weights in the debt portfolio, where positive covariance of the returns characterizes the related debt instruments as substitutes.

In a nutshell, the two approaches discussed below emphasize the importance of co-movements of the exchange rate with determinants of government revenues, negative correlation of an exchange rate with government expenditure, and the overall riskiness of a given foreign currency - the exchange rate’s variance.

# 2.1 The Approach of Licandro and Masoller

In this section we extend the approach of Licandro and Masoller (2000)<sup>8</sup> to a multicurrency case. When deriving the optimal decision rule for choosing the currency structure of sovereign debt Licandro and Masoller set up a two-period problem<sup>9</sup> in which the government wants to smooth out the variation in future tax rates, where � is the relative weight given to the local-currency nominal debt, �<sup>�</sup> is a vector of relative weights given to di¤erent foreign-currency nominal debts, and � is the tax rate. Et represents expectations conditional on an information set available to agents at time t. The latter implies that all variables dated t are known with certainty in this problem whereas variables dated t + 1 are uncertain (stochastic). The government is subject to the following constraints:

> 8Licandro and Masoller build on Calvo and Guidotti (1992), Goldfajn (1998) and Missale (1997) when setting up their optimization problem.

> 9We will denote the ...rst and the second period in their problem as t and t + 1, respectively.

7
where Gt is the government expenditure-to-GDP ratio, wt the growth rate of real government expenditure, yt is the real GDP growth rate, Bt is the debt-to-GDP ratio, Rt is the interest rate on the local-currency debt, �t is the in‡ation rate, R<sup>�</sup> t<sup>is a vector</sup> of interest rates on foreign-currency debts, et is a vector of exchange rates, and Rt<sup>Iis</sup> the real interest rate on the local-currency debt (in‡ation indexed debt). Constraint (2) states that the future tax has to be equivalent to future government expenditure plus future servicing costs of the government’s debt all expressed as percentages of GDP. Constraint (3) is an arbitrage condition that makes the borrowing cost of nominal debt in local currency, nominal debt in foreign currencies, and in‡ationindexed debt in local currency equivalent. For the arbitrage condition to hold two types of risk premia are introduced. F P is a vector of risk premia the government has to pay on local-currency nominal debt relative to nominal debt in foreign currencies. Similarly, IP is the risk premium the government has to pay on nominal debt in local currency relative to in‡ation-indexed debt in local currency. Expression (4) constrains the weights on di¤erent borrowing instruments to be between 0 and 1.

Licandro and Masoller solve the problem speci...ed in equations (1)-(4) using the 8
# Lagrangian method and arrive at the following solution

where and qt is a vector of real exchange rate de...ned as qt = et � �t and V ar(:) and Cov(:) denote variance and covariance conditional on information available at time t . We focus in our interpretations of the solution results on the choice among di¤erent currency denominations of foreign debt and refer the reader to the original work of Licandro and Masoller (2000) for interpretation of remaining parts of the solution, i.e. those for the domestic debt<sup>10</sup> . Our main quantity of interest is thus �<sup>�</sup> a vector of weights put on foreign debt denominated in foreign currencies relative to local-currency in‡ation-indexed debt. Note that �, i.e. the weight on local-currency nominal relative to in‡ation-indexed bonds, is still part of the solution for �<sup>�</sup> . However, we condition on the value of � and take it as identical for all foreign currencies. Recall at this point that we seek the optimal allocation of debt that is constrained to be issued in foreign currencies. Further, this foreign currency

> 10Licandro and Masoller further simplify the solution by disregarding the possibility of issuing nominal debt in local currency. This is based on their empirical argument that local-currency nominal bonds are prohibitively costly due to low credibility of macroeconomic policies and past crises episodes. We keep the framework general and at the theoretical level.

9
debt cannot be naturally hedged and hedging using ...nancial derivatives is costly or not available. Equation (7) states that the expectations about future developments in foreign interest rates and exchange rates determine the optimal currency structure of foreign debt. One can derive from equation (6) that the variance of an exchange rate V ar (qt), and the covariances of an exchange rate with domestic fundamentals, here in‡ation �t, output growth yt, and growth of government expenditure wt, are key in determining the optimal currency structure. Finally, there is also a role for the risk premia on the domestic nominal debt relative to the debt denominated in various foreign currencies, F P .

All the later quantities are likely to vary across di¤erent currencies. The expectations about future foreign interest rates and exchange rates can be usually obtained from national central banks and market participants that put a considerable e¤ort into producing successful forecasts.<sup>11</sup> The variances and covariances can be readily estimated from observed data, but we argue that those are critical for determining the optimal currency allocation of the foreign debt and that the estimations should respect the medium- to long-term perspective of debt managers. Regarding the foreign currency risk premia F P we claim that these are most likely endogenous to the exchange rate volatility V ar (qt), as seen in (3), and the covariances of exchange rates with domestic fundamentals. In a nutshell, if the domestic economy converges to foreign economy A, i.e. the covariances of domestic and foreign fundamentals are generally positive, idiosyncratic shocks hitting the domestic economy will become less likely and the volatility of exchange rate, the most ‡exible price relating the domestic and foreign economies, will be decreasing and so will be the risk premium. On the other hand, a currency exchange rate with unrelated foreign economy B, will be more volatile and the foreign exchange premium high since all the shocks hitting the domestic economy will be idiosyncratic with respect to foreign economy B: We will discuss and elaborate on the role and estimation of the covariances and the exchange rate variance in section 3.

In addition, we will concentrate on the nominal costs of debt servicing and gov-

> 11For recent research on the predictive ability of economic fundamentals in exchange rate models see. e.g. Engel and West (2005).

10
ernment revenues and thus work with the nominal exchange rate. This is mainly due to di¢ culties with practical implementation of the real cost approach as the relevant de‡ator for each quantity of interest can di¤er, especially in high in‡ation environments. Further, the government budget is composed and planned in nominal terms.

# 2.2 The Approach of Giavazzi and Missale

Also the approach of Giavazzi and Missale (2004) can be readily extended to a multicurrency case. Giavazzi and Missale start from assuming that the objective of the government (the treasury) is to minimize the probability that debt stabilization efforts fail. In general, this can occur due to revenues falling short of the expected ones or the inability to cut expenditures. More formally, the government chooses the relative proportions of the nominal interest rate debt, s, foreign currency denominated debt, q; and domestic in‡ation index debt, h, in its total borrowing (debt) in order to where X and At+1 are the uncertain and expected components of the ...scal adjustment, and Bt<sup>T</sup> +1<sup>is the trend debt ratio.At+1�4B</sup> t<sup>T</sup> +1<sup>is therefore the planned reduc-</sup> tion in the debt-to-GDP ratio, and � (X) denotes the probability density function of the random variable X: In short, the government wants to minimize the probability that the planned reduction in the debt-to-GDP ratio, At+1 �4Bt<sup>T</sup> +1<sup>; falls short of the</sup> actually needed reduction X which is uncertain (stochastic). While choosing s; q and h to achieve its objective the government is a subject to the following constraints. First, the budget accumulation equation, where It+1Bt are the interest rate payments, et is the log of the nominal exchange rate, St<sup>T</sup> +1<sup>isthetrendprimarysurplus,yt+1isthelogofoutput,and�t+1isthe</sup> in‡ation rate. The debt-to-GDP ratio (at market values) is thus determined by 11
the interest payments on the outstanding debt, the size of the domestic currency depreciation, the trend in the primary surplus, and the growth of nominal GDP. Second, the interest payments are equal to where it+1 is the domestic interest rate, Rt<sup>�is the foreign interest rate, RPtis the risk</sup> premium, Rt<sup>Iis the real return on the in‡ation-linked bonds, and Rtis the long-term</sup> interest rate (of 1 year maturity). (Rt<sup>�+ RPt)istheapproximationofthereturnon</sup> foreign currency bonds (Rt<sup>�+ RPt) (1 + 4et+1),and</sup> �Rt<sup>I+ �t+1</sup> � is the total return on the in‡ation-indexed bonds.

Third, the ratio of the trend primary surplus to GDP, St<sup>T</sup> +1<sup>,isuncertainbecause</sup> it depends on cyclical conditions and the in‡ation rate as follows When solving this optimization problem for s; q and h Giavazzi and Missale introduce several risk premia. Namely, these are the term premium on ...xed-rate bonds, TPt, that makes the terms structure of interest rates hold, i.e.

the exchange rate risk premium, FPt that completes the uncovered interest parity (UIP) condition and the in‡ation risk premium, IPt, that equalizes the interest payment on priceindexed and ...xed rate bonds (the Fisher condition) 12
When using the linear approximation<sup>12</sup> of � (X) for a range of bad realizations of the ...scal adjustment, i.e. when X > 0; Giavazzi and Missale arrive at the following solution of the optimization problem described in (8)-(14). In the solution we use vector notation (in bold) to emphasize the extension to the multi-currency case: where V ar(:) and Cov(:) denote variance and covariance conditional on the information available at time t and Pr is the probability of a debt crisis as perceived by the government.

When interpreting the problem solutions we again focus on the part that deals with foreign currency debt<sup>13</sup> , namely, optimal distribution of the foreign debt across di¤erent currencies. This implies that our main quantity of interest is q<sup>�</sup> , i.e. how much of the foreign debt should be denominated in a given currency. We again con-

> 12The linear approximation of � (X) implies triangular probability density function equal to

> where X > 0 and X is the worst possible realization of the ...scal adjustment.

> 13We refer the reader to Giavazzi and Missale (2004) for further discussion of the solution results.

13
dition upon the other choice variables, i.e. s<sup>�</sup> and h<sup>�</sup> , in the sense that we treat them as if they were determined ...rst, and then think about the elements of the vector q<sup>�</sup> . From the practical point of view this implies that the debt manager determines ...rst the amount of local-currency debt that will be issued and then thinks about how to divide the foreign debt into planned currency denominations. We can observe in (16) that the key measures for determination of the optimal currency structure of foreign debt are the covariances of exchange rates with domestic fundamentals, namely output, Cov (yt+1et+1) ; in‡ation, Cov (�t+1et+1), and the interest rate, Cov (et+1it+1) ; the variance of exchange rates, V ar (et+1), and the forward premia F P t. We again claim that F P t can be to a large extent endogenized with respect to the covariances and the exchange rate variance. What we intend to discuss further in section 3 is the estimation of the covariances and how to look at them, and possibly a better way of employing the exchange rate variance in risk analysis. Our discussion is motivated by the fact that both measures are intended as predictors of future developments and that the perspective of a debt manager is medium- to long-term rather than short-term.

Before we proceed with a review of other related approaches it is worth pointing out that the reviewed theoretical approaches employ a number of simplifying assumptions so that their results may not apply as directly as implied by the models. In particular, these approaches assume bonds of one-period tenor which results in debt charges being determined entirely by contemporaneous values of relevant ...nancial variables whereas in reality the debt charges will depend on both current and past values of relevant ...nancial variables. The numerical approaches reviewed in the next section try to overcome this limitations, but at the cost of requiring much more detailed information and structure to be imposed. As consequence the range of insights one can acquire from the numerical approaches is limited by the latter.

# 2.3 Other Related Approaches

There are other, numerical approaches that deal with minimization of a government loss function while taking into account the structure of the government balance sheet 14
and possible shocks the government may face. The numerical approaches do not provide an explicit analytical solution that would guide one conceptually in the choice of the currency structure for foreign debt, and thus serve as a base for a more judgemental analysis. These approaches provide one with "exact" numbers as an output from the numerical optimization encompassing simulations out of macroeconomic or econometric models and ...nancial accounting. In order to make our literature review comprehensive we broadly group the recent numerical approaches according to the indicators they produce and brie‡y discuss their substance, insights and limitations. The indicators each numerical method produces constitute key inputs into the government’s candidate objective function as their values should be minimized or maximized in accord with government preferences. We look at the following broadly speci...ed indicators: (i) cost at risk (CaR) or value at risk (VaR), (ii) default probability based on speci...ed government’s debt-to-GDP default ratio, and (iii) default probability based on a distress barrier. Although the indicators ultimately look at the same risk we prefer to draw a slight distinction among the three groups with regard to the structures of the numerical approaches.

(i) The ...rst group includes work conducted at, for instance, the Bank of Canada, see Bolder (2002, 2003); Danmarks Nationalbank, see Danmarks National Bank (2006); Korea, see Hahm and Kim (2004); the UK DMO, see UK DMO Annual Review (2006) and Pick (2005); Swedish DMO, see Bergstom and Holmlund (2000); or Peruvian Ministry of Economy and Finance, see Peru Ministry of Economy and Finance (2005). The main indicator of interest that concerns this group is the CaR measure. The latter expresses the risk as the percentile distance, typically between the 50th and 95th percentile of the simulated cost allocation<sup>14</sup> . The larger the percentile distance, the higher the risk of the government liability portfolio. The cost is typically measured as a ratio to GDP and can be expressed either in nominal or real terms. The standard parts of the simulation underlying the CaR computation is a model simulating the paths of the underlying economic/...nancial variables, such as interest rates, output growth, in‡ation, exchange rate etc., and a ...nancial accounting framework for computation of the cost measure for each generated scenario. Since

> 14For a detailed exposition of this method see Danmarks Nationalbank (2000).

15
the ...nancial accounting framework is deterministic and ...xed for each model<sup>15</sup> the crucial part in this case is the model simulating the paths of the underlying economic variables. The work at the Bank of Canada, Danmarks Nationalbank focuses on simulation of the term structure of interest rates as the interest rate risk is of a major focus there. Korean model combines the concept of the e¢ cient frontier and CaR penalties to derive the optimal benchmark portfolio for government debt. In the Peruvian model the process used to generate discrete-time observations of ...nancial variables is derived from a multivariate continuous-time model. On the other hand, the Swedish model is a discrete-time model based on univariate autoregressive processes with regime switches characterizing the data generating processes (DGPs) of the economic variables. Finally, the UK model uses a reduced form of an implicit structural model in combination with regime switches to generate the likely paths of economic variables.

(ii) The second group includes work of e.g. Garcia and Rigobon (2004), or Xu and Ghezzi (2004). In general, this approach again uses simulated paths of economic variables and the debt structure to compute the corresponding government debt-toGDP ratios. The numerous possible paths of the variables give rise to a distribution of the debt/GDP realizations at each point in time. The probability mass in the tail of these distributions cut o¤ by the speci...ed debt/GDP default threshold is then used as a measure of the probability that the government ...nances will be considered unsustainable at a given point in time. The two referenced approaches di¤er mainly in the aspect of using discrete- and continuous-time model speci...cations, respectively. Garcia and Rigobon (2004) use an unrestricted vector autoregressive (VAR) model to simulate the economic variables whereas Xu and Ghezzi (2004) use a system of Brownian motions as the basis for their simulation.

(iii) Gapen, Gray, Lim and Xiao (2005), Gray, Merton and Bodie (2005) work with an explicit measure of sovereign credit risk derived from a contingent claim analysis. The latter uses option pricing formulas to capture possible non-linearities in the relationships of interest. They start from determining a distress barrier analogous to

> 15The ...xed structure can however di¤er across models depending on the selected level of aggregation of the borrowing instruments (categories).

16
the default threshold in (ii) which is to some extent endogenized in this framework. The distress barrier is determined based on seniority of the consolidated government’s liabilities. More speci...cally, Gapen et al. (2005) assume that the distress barrier is equal to the book value of the short-term external debt plus interest and one-half of the long-term external debt<sup>16</sup> . The value of domestic currency liabilities is then modelled as an implicit call option on sovereign assets in this framework. In a nutshell, the distance to distress and the measure of sovereign credit risk is derived from the probability mass in the tail of the distribution for the value of assets at a given point in time. The tail containing probability of default is cut o¤by the distress barrier. The derived indicator corresponds to default (credit) risk and appears to well track the EMBI time-variations.

One can use the methods in (i)-(iii) to set up an optimization that would estimate the optimal weights on each currency considered for denomination of foreign debt. Proceeding along these lines one can take the calibrated model structures of the frameworks in (i)-(iii) as a set of constrains and minimize the value of a relevant indicator, say probability to default, while varying (optimizing over) the weights of individual currencies in the foreign debt portfolio. Such numerical approaches can provide a complementary insight to that of a more analytical or judgemental approaches so that the complex questions of debt managers are tackled using alternative modeling avenues. Although not so apparent as in the case of the analytical approaches the results from the numerical frameworks will hinge upon how the model structures that generate the economic variables are calibrated. The most crucial parameters in this respect will be again the covariances of variables or basic shocks generating those variables and their volatility. If the parameters are estimated then the assumption about conditional means of the modelled variables may considerably in‡uence the estimates of shocks’covariances.

It is crucial that in practice the development of numerical models for supporting the decision-making process of debt managers follows a top-down route, i.e. responding to the questions raised at the managerial levels rather than introducing 16Although this approach treats fundamentally the distress barrier as ...xed or deterministic (...xed for a certain period) from a practical point of view it can be also random and have a distribution.

17
unnecessary complexity and detail from the very start. In addition, given the limited capacity of debt management o¢ ces in developing countries we do not see the numerical procedures as the mainstream approach. Instead, we would suggest that forecasts of the expected paths for economic fundamentals, such as output growth, interest rates, in‡ation, exchange rates etc., including the associated con...dence intervals are taken from the national central banks which have usually much higher capacity in this respect and put a considerable e¤ort into forecasting of such variables. This can enable the debt managers to construct some baseline scenarios and perform a sensible scenario analysis. The use of macroeconomic predictions from the national central banks is also advisable in order to ensure consistency of macroeconomic policies and the assumptions on which they are based.

# 3 Issues with Current Approaches

Typical economic problems dealing with optimal allocation of sovereign debt portfolios imply that the optimal currency structure of foreign debt is to a large extent determined by magnitudes of covariances between domestic fundamentals and the considered exchange rates, and variances of the considered exchange rates - see section 2. In this section we aim to further discuss (i) the economic concept underlying the variances and covariances in the aforementioned economic problems, (ii) their empirical measures, and (iii) their role in risk analyses of sovereign debt portfolios.

## 3.1 Covariances of Exchange Rates and Domestic Fundamentals

Following the outlined structure we (i) discuss the economic concept underlying the role of the covariances in problems dealing with optimal currency denomination of foreign debt. The covariances appear in the solution results since the variables characterizing servicing costs of the debt and performance of the domestic economy are uncertain (random variables) and so is the economic structure relating all the economic variables in question. The main purpose of the covariances is thus to capture 18
in a possible scope the structural links among the economic variables of interest. Essentially, one would like to capture a structure that is coherent in terms of available theory and stable over time. Nevertheless, especially in developing and emerging market economies the structural links between economic variables are evolving over time, and on occasions change substantially as the economies adjust their production, new economic policies are implemented, and the transition process to market economies is underway. Moreover, the covariances employed for characterization of the structural links among economic variables should re‡ect the perspective and decision (investment) horizon of a debt manager which usually cover the period of at least 3 to 5 years. The estimated covariances are thus intended to be sustained and forward looking, although most often higher frequency and historical data are used to estimate them.

This leads us to (ii) the discussion of empirical measures used to capture the covariances. There are essentially two ways how to proceed in this respect. First, one can work with the economic variables themselves or the underlying structural shocks driving those variables. Both approaches have their pros and cons. When working with the variables themselves one has to be careful about how the individual time-series components impact on the big picture one would like to obtain. The most basic characteristic of each variable over time would include a trend component (both deterministic and stochastic) and a cyclical (short-term) component<sup>17</sup> . The trend components will commonly dominate the cyclical components in estimations involving longer time-series although the cyclical components may deliver very di¤erent and sometimes more important story about the economic structure. The trend components mostly arise due to the transition and catching-up processes the developing countries are experiencing and its dominance is often valid not only from statistical but also an economic point of view.

Employing the economic variables themselves for estimation of covariances has the disadvantage of assuming that the conditional mean of the variables is constant and not putting any economic structure on the estimation. The latter refers to the

> 17We ignore seasonality in our discussion as this component is usually eliminated from the data before it is employed in analysis.

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fact that ideally one would want to capture the underlying forces (structural shocks) that drive each variable and leave out the systematic component. The main challenge associated with this approach is the structural identi...cation of the underlying shocks. Both Licandro and Masoller (2000) and Giavazzi and Missale (2004) do not apply structural identi...cation of the underlying shocks and thus fail to capture the covariances of interest in their estimations. Licandro and Masoller (2000) use one-step ahead forecast errors from a VAR model to characterize the underlying shocks while Giavazzi and Missale (2004) use a reduced form<sup>18</sup> of an implicit structural model to do the same. In both cases the authors identify the structural shock as the estimated (forecast) error attached to a given variable, e.g. a demand shock as the residual from the output equation of their VAR. In fact, in both cases the identi...ed shocks appear to be a combination of the structural shocks so that the estimated covariances among the shock do not provide the information the authors sought. It is essential to employ methods that allow structural identi...cation of the underlying shocks in this respect such as structural VAR models or micro-founded models featuring rational expectations. However, in those models the structural shocks are often assumed to be uncorrelated for identi...cation purposes so that any estimated empirical covariances should be zero to avoid contradictions with the a priori estimation assumptions.

Moreover, from an empirical point of view estimating the covariances between the exchange rates and the domestic fundamentals will most likely provide very little information that would help the debt manager decide on how to optimally allocate the foreign debt among various currencies. This is due to the fact that the covariances are usually very low or not statistically di¤erent from zero - see e.g. Bohn (1990b; Table 4, columns 2-3). This might be due to the failure of the fundamentals to predict exchange rates (Meese and Rogo¤, 1983). On the other hand, Engel and West (2005) argue that although exchange rates cannot be predicted by economic fundamentals exchange rates themselves have some power in predicting the fundamentals. The 18One can object to this classi...cation and claim that Giavazzi and Missale use a structural model. What is considered as structural model here is a system of equations in which the covariance matrix of endogenous variables is not simply an identity matrix, as in the case of Giavazzi and Missale where the structure would purely derive from lag selection. The classi...cation used here is thus in line with the forms of structural VAR and New Keynesian models.

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latter would su¢ ce to produce at least some correlation between an exchange rate and the fundamentals that would guide debt managers in their decisions. What we see as a main problem is the use of relatively high frequency data and the actual exchange rate for estimation of the covariances between the model variables, here exchange rates and economic fundamentals, of the theoretical framework. This is due to the fact that the exchange rate observations carry substantial amount of noise<sup>19</sup> that blurs the information one strives to retrieve from the covariances. To illustrate this point consider the following example. Assume that the DGP for the exchange rate, st; is e where st is the fundamental (equilibrium) value of the exchange rate given by where �t and �<sup>�</sup> t<sup>arethedomesticandtheforeignin‡ation,respectively,following</sup> simple AR(1) processes, i.e.

Finally assume that the domestic output growth is generated as i.e. by a combination of the supply and demand shocks. We set var("AS;t) = var("IS;t) = 1; var("<sup>�</sup> AS;t<sup>)=0:5; var("s;t)=10usingthecommonknowledgethat</sup> ‡exible exchange rates are usually more volatile than other economic fundamentals; further, � = �<sup>�</sup> = 0:8 and �y = 0:6. We generate 10; 000 observations of the variables

> 19In the short run the trading in the exchange rate markets is not based on currencies’fundamentals and is driven largely by trends in the trade set by chartist. Fundamentalists come to trade only if there is a sizable adjustment needed to bring the exchange rate to its fundamental value see de Grauwe and Grimaldi (2005).

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and compute the correlation of both the domestic output growth, yt, and in‡ation, e �t, with the actual and equilibrium exchange rates, st and st: Table 1: Exchange Rates Simulation

||st|est|
|---|---|---|
|yt|0:0090|0:1208|
|�t|0:0666|0:5003|

The results illustrate our point that the large noise the actual exchange rate contains precludes the investigator to retrieve the desired information on structural links between the variables. Given this and the fact that the decision horizon of debt managers is medium- to long term one should employ some measure of an equilibrium exchange rate when trying to estimate the covariances between an exchange rate and domestic fundamentals to be used in the theoretical model. There are various concepts of the equilibrium exchange rate<sup>20</sup> . One of the most popular and suitable for EMEs would be the behavioral equilibrium exchange rate (BEER) discussed by e.g. Clark and MacDonald (1998). This concept is relatively simple and allows more empirically driven selection of the equilibrium exchange rate determinants.

Concerning (iii) the risk analysis, one should work, in addition to the concept of equilibrium exchange rate, with future scenarios that allow to bring in information on likely developments in the structure of foreign trade, intended utilization of comparative advantages, strategic diversi...cation of exports and imports, possible ...nancial markets integration and its impact on the currency structure of capital ‡ows, or economic integration, such as accession to a trade or currency union. Further, working with equilibrium exchange rates allows the debt manager to carry out comprehensive risk analysis even when the local currency is pegged against certain foreign currency. Consider for example the Russian 1998 debt crises before which the government was happy to expose its balance sheet to potential movements in the RUB/USD rate since at that time the ruble was pegged against the dollar. How-

> 20NATREX, FEER, DEER, BEER etc. see MacDonald (2000) or Driver and Westaway (2005) for an overview.

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ever, a severe misalignment of the RUB/USD exchange rate had developed and the 1998 debt crises was triggered by a currency crisis as the needed adjustment of the pegged rate towards the shadow market rate was exercised by the markets. More generally, if debt managers use the pegged rate in their analysis they focus entirely on risk minimization and ignore the covariance between the ...nancing cost of foreign debt and domestic fundamentals of government primary balance altogether, as the covariance of domestic variables with a hard peg is essentially zero. The covariances can be deceiving under a peg in general, since the rate is rather sustained by central bank’s interventions than market forces and fundamentals. Debt managers are thus interested in relative expected covariances of domestic fundamentals with exchange rates against candidate currencies for FX debt denomination. Employing equilibrium exchange rates<sup>21</sup> to perform such a relative comparison of the covariances across candidate currencies has the clear advantage of exercising an equal treatment.

# 3.2 Exchange Rate Variance

(i) Another important parameter for the decision on currency denomination of foreign debt is the degree of uncertainty concerning future movements in exchange rates. This uncertainty is often approximated by estimated volatility (standard deviation) using historical data. Unlike the covariances that are intended to capture the economic structure and help in thinking about future trends in the economic development, i.e. the central tendency of variables, the exchange rate volatility is intended to capture the magnitude of likely deviations of the exchange rates from their future central tendencies. Similar to the covariances the exchange rate variance is intended to be forward-looking. Since the historical data of developing countries often cover relatively tranquil periods and periods of currency crises there appear to be large spikes in the data mostly in the direction of large depreciation. Apart from the possible isolated spikes in the exchange rate series of developing countries the

> 21The use of equilibrium exchange rate is probably not the ultimate solution due to the lack of a general agreement on a suitable model for equilibrium exchange rates. It is rather a step forward in the direction towards a more structural approach to FX risk management that is being currently developed in a companion paper.

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series often show clustering of volatility in addition (see Figure (1)). This stems from the fact that one crisis is often followed by another, or triggers major restructuring or resetting of macroeconomic policies which themselves induce swings in the economic performance of a given country.

Figure 1: Historical Changes in Selected Exchange Rates <!-- Start of picture text --> 270<br>250<br>230<br>210<br>190<br>170<br>150<br>130<br>110<br>90<br>70<br>50<br>30<br>10<br>-10<br>1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005<br>-30<br>-50<br>UYU/USD BRL/USD GBP/USD<br><!-- End of picture text --> Note: Quarter-to-quarter percentage changes of the UYU/USD, BRL/USD and GBP/USD exchange rates over the period 1975Q1-2006Q3; calculated using the end-of-period local currency to USD markets rates from IMF’s International Financial Statistics.

For determination of the currency benchmark for the foreign debt portfolio one requires an overall measure of riskiness of each currency, i.e. the overall measure of relevant exchange rate volatility. The estimation of volatility can be revised on a yearly basis and so can the currency benchmark for foreign-currency debt. However, one has to make a choice in regards to what period is to be covered in the estimation.

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The estimation period can cover crises periods, di¤erent exchange rate regimes and macroeconomic policies. The estimation based on historical data can therefore be deceptive and one has to make some judgemental decisions when thinking about how risky each foreign currency is likely going to be in future. We illustrate how the choice of the estimation period matters by computing standard deviations for the three exchange rate series plotted in Figure (1) for di¤erent periods. The results are shown in Table (2) where uyu/usd, brl/usd and gbp/usd denote exchange rates of the Uruguayan peso, Brazilian real and British pound against the US dollar.

Table 2: FX Risk Estimation and the Time Span

||stan|dard deviation|s of|
|---|---|---|---|
|as of|4 (uyu/usd)|4 (brl/usd)|4 (gbp/usd)|
|1975|14:9205|49:4310|5:1868|
|1985|7:6615|57:9931|4:9470|
|1995|7:6051|13:1201|3:3610|

Lower cases denote logs and 4 is the ...rst di¤erence operator Furthermore, if currency peg is exercised with respect to certain currency and not others the extremely low volatility in the case of the pegged rate can be deceptive since the central parity can be severely misaligned with respect to the equilibrium exchange rate that would restore external balance. If such a misalignment exists the potential realization of contingent liabilities in case of large depreciations constitutes risk that the debt manager is not taking into account when working with the actual as opposed to the equilibrium exchange rate. For the purpose of risk considerations we argue that one is better o¤ working with some measure of equilibrium exchange rates as this ensures more conservative and comprehensive treatment of the FX risk and does not bias the relative magnitudes under di¤erent exchange rate regimes both across currencies and over time.

When it comes to (iii) the risk analysis, the current practise is to stress-test the scenarios involving possible future trends in domestic fundamentals and the exchange rates by generating disturbances from assumed Normal distributions of the relevant 25
variables where the parameters of the distributions have been estimated on historical data. We do not think that this approach to stress testing of a debt portfolio or an entire balance sheet generates the insights one would like to acquire from such an exercise. Instead we would suggest following the argument started in the previous section on the covariances that also the variances employed to establish a currency benchmark for foreign debt are computed using some equilibrium measure of exchange rates. This addresses two possible misperceptions in estimations of expected exchange rate risk (volatility). First, a misperception could arise in regard to the choice of foreign debt denomination under ...xed exchange rate regimes. If the debt managers rely on the promise of the national central bank to sustain the announced peg at all times they ignore the risk of mismanagement of the exchange rate regime, possible emergence of exchange rate misalignments and consequently speculative attacks. However, if equilibrium exchange rate is employed the debt managers get a better picture about the underlying forces behind medium-term exchange rate movements and their volatility relative to other foreign currencies. Second, if currency crises emerged and the exchange rate peg was abandoned one would not want to include into his expectations this period of excessive volatility and assume that the same event can occur under more ‡exible exchange rate regimes. Again, the equilibrium exchange rate can serve as a useful ...lter so that the expected volatility (risk) is measured consistently across candidate currencies. It is thus not the observed volatility per se that the debt managers want to get handle on, it is rather the relative expected volatility across exchange rates with respect to candidate currencies for FX debt denomination.

Further, the stress testing of a debt portfolio, if the capacity of the debt management o¢ ce allows, could be performed by generating disturbances using more realistic processes.<sup>22</sup> What we mean by realistic are processes which can generate

> 22In the actual simulation two approaches can be adopted. The ...rst one, a more simple, would involve just adding the suggested processes to univariate models of simulated variables. This is not di¤erent from shocking individual variables used to compute the baseline scenario e.g. for the expected future ...nancing cost. The second approach involves covariance matrices of the variables being simulated or some endogenous transmission mechanism in which case the proposed "more realistic" processes for exchange rate shocks would be added as disturbances to the exchange rate equation in the model and transmitted through the system accoding to the assumed endogenous

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infrequent spikes in the series of disturbances (the noise) and volatility clustering. Although such processes can be sometimes challenging to estimate we see them as much more comprehensive and insightful for the purpose of stress testing and risk analysis. Two classes of processes are at hand in this respect. Namely that of timevarying volatility or mixtures of distributions. The former class comprises DGPs such as generalized autoregressive conditional heteroscedasticity (GARCH) models, see Bollerslev (1986), or models of stochastic volatility, see e.g. Hull and White (1987). The latter class of processes features mixtures of distributions, see e.g. McLachlan and Basford (1988). Both classes of processes are well established in the ...nancial econometrics literature and practice. We provide two simple examples to visually illustrate potential advantages of employing such processes. The upper panel of Figure (2) shows arti...cially generated series using a GARCH(1,1) model with t-distributed errors where the coe¢ cients where set arbitrarily so that the generated series resembles patterns of the series in Figure (1). Similarly, the bottom panel of Figure (2) shows arti...cially generated series using AR(1) process with disturbances being a mixture of Poisson and Normal distributions; again all coe¢ cients are set at arbitrary values.

structure.

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Figure 2: Simulated Series of Exchange Rate Volatility <!-- Start of picture text --> 2<br>1.5<br>1<br>0.5<br>0<br>-0.5<br>-1<br>-1.5<br>0 100 200 300 400 500 600 700 800 900 1000<br>GARCH(1,1)<br>2<br>1.5<br>1<br>0.5<br>0<br>-0.5<br>0 100 200 300 400 500 600 700 800 900 1000<br>Mixture Poisson+Normal<br><!-- End of picture text --> Note: Generated arti...cial series using a GARCH(1,1) model with Student’s t-distributed errors, and an AR(1) process with disturbances being a mixture (a weighted sum) of Poisson and Normal distributions.

The two snapshots of processes of time-varying volatility and a mixture of distributions illustrate how the combination of volatility clustering and arrivals of infrequent large shocks can be incorporated into the risk analysis or more speci...cally the stress testing. In practice this process can be estimated on historical data or calibrated. Calibration might be preferred especially in the case of mixed distributions since estimation of distributions for infrequent large shocks can be challenging given the 28
low number of observations on those events in typical real data samples.

# 3.3 The Covariances and the Variance

In this section we discuss possible interdependencies between the covariances of exchange rates with domestic fundamentals and the variances of exchange rates, the FX risk. In order to look into this relationship we take more macroeconomic approach. Consider ...rst an exchange rate between a domestic and foreign currency and the shocks driving these currencies. Assume that the exchange rate is driven by domestic and foreign structural shocks where the exchange rate determination can be based on the UIP condition, the purchasing power parity or the monetary model of exchange rate determination. In either case the value of the domestic currency will rise with favorable domestic shocks (e.g. supply or demand shocks) and fall with unfavorable shocks. The same is true for the foreign currency value which rises with favorable shocks and fall with the unfavorable ones. Consider now three scenarios. (i) if the domestic and foreign economies are converging in the sense that the shocks hitting both the economies are becoming more correlated the relative value of the two currencies, the exchange rate, is becoming less volatile. This is because the value of domestic currency is rising at times when the value of the foreign currency is rising as well. (ii) if however the economies are not linked at all, shocks either in the domestic or foreign economy will be purely idiosyncratic and fully re‡ected in the relative price of the domestic and foreign currency, the exchange rate. (iii) if the shocks are in general negatively correlated the domestic economy is hit by an unfavorable shock and the domestic currency value is falling at times when the foreign economy is hit by a favorable shock such that the foreign currency is increasing in value, and vice versa. The relative value of the domestic and foreign currency will be signi...cantly more volatile than in the case of (i) or (ii). In future research we plan to follow this avenue when proposing an alternative framework for FX risk management.

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# 4 Conclusion

In this paper we have started from the observation that some countries are constrained to issue debt in foreign currencies and that debt managers have to choose or have the choice on the denomination of foreign debt. From the point of view of the World Bank’s classi...cation, IBRD countries have to choose the currency in which they want to borrow from the World Bank, whereas IDA countries have to borrow in SDRs. Nevertheless, even in the case of IDA countries the World Bank is not the sole lender and the countries often borrow from other sources in addition, such as bilateral donors. The latter often lend funds in certain currencies. If there are enough borrowing opportunities (donors) for an IDA country on similar terms the choice on the currency structure for external debt is e¤ectively made.

The literature that would guide debt managers in their choice of the currency structure for foreign debt is rather inconclusive in its practical recommendations. In this paper, we have tried to review and discuss the relevant approaches that have recently appeared in the literature. The theoretical approaches point to the crucial role of exchange rate volatilities, and covariances of exchange rates and domestic fundamentals in determination of the optimal currency structure for foreign debt. We have thus focused on these two parameters and discussed their empirical measures.

We suggest based on the arguments discussed in this paper that the debt managers work with equilibrium exchange rates when employing the reviewed theoretical frameworks in practice. This suggestion is based on the fact that actual exchange rates carry a lot of noise which precludes the debt manager to get any useful guidance (information) from the data. Also, the concept of an equilibrium exchange rate is more consistent with the medium- to long-term perspective of debt managers. Further, both the covariances between domestic fundamentals and the exchange rates, and exchange rate volatility can be deceptive when a ...xed exchange rate regime is being maintained since the risk of possible large depreciations of the domestic currency is not explicitly considered and the currency structure of the foreign debt thus not adequately diversi...ed. Finally, when it comes to stress testing of a potential currency benchmark for foreign debt a scenario analysis considering likely future de30
velopments is often accompanied by a stochastic simulation that hinges on shocks generated from Normal distributions with constant volatility. We think that this approach does not provide the insights one would like to get from stress testing as the most important attributes of exchange rate shocks that one would like to capture are the possibility of infrequent large shocks and volatility clustering. Hence, we suggest that, for the purpose of stress testing, processes involving time-varying volatility or mixtures of distributions be adopted.

The direction for future work will include development of a simple framework(s) that EMEs can use for FX risk management, and which is based on the idea that exchange rates between currencies of economies that converge or co-move are less volatile, and therefore less risky, than the exchange rates between currencies of economies that are not linked at all or negatively correlated. While developing this simple framework for FX risk management one might also want to look into the role of diversi...cation in this context.

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