4 Foreign Currency Liabilities in Debt Management

D. Folkerts-Landau, and Marcel Cassard
Published Date:
July 2000
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Patrick de Fontenay and Philippe Jorion 

For governments (or firms) that borrow, as most do, whether to issue foreign currency denominated debt, how much, and in which currencies seem to be separate decisions, subject to different considerations. Indeed, this is how many countries have approached foreign borrowing. For example, a central bank may decide it needs to replenish its stock of foreign exchange reserves and how much it should borrow abroad. The choice of currency or currencies in which to borrow is then decided separately.

Historically, for many developing countries, the choice of currencies in which to denominate their foreign debt was imposed by the lenders, and in the absence of easy access to the swap market that choice could not be changed. For a second category of countries, the necessity of borrowing abroad was imposed by the balance of payments or official reserve situation, or by the narrowness of the domestic market for government debt, either in terms of volume, liquidity, or choice of maturities. Governments were also able to borrow on better terms than public enterprises and private firms to which they would lend the proceeds of their foreign borrowing. For those countries, the choice of currencies is an important decision to be taken as part of their external debt management. Finally, there is a third category of countries, which includes most industrial countries and several developing countries. In those countries, governments are not compelled to issue debt denominated in foreign currencies, and some choose not to. Of course, from a balance of payments standpoint, sales to nonresidents of government bonds denominated in local currency represent foreign borrowing.

The first part of this paper discusses the currency composition of foreign debt, largely from the standpoint of the countries in the second category. The second part discusses the role of foreign currency debt in sovereign liability management and reviews the different approaches to this issue. The third part is a numerical application of modern portfolio theory to a country case.

Currency Composition of Foreign Debt

For countries whose governments (or central banks) need to borrow abroad, the traditional advice to match foreign assets and liabilities was often impractical. This was often because foreign assets were too small or because the management of foreign assets (that is, official reserves) and that of foreign debt was done by different entities and in accordance with different sets of principles and guidelines. Another standard piece of advice was to borrow in the currency or currencies of the main trading partner(s). Intuitively, this seems to make sense as debt payments would be in the same currencies as export receipts, and cash flows would match. However, this may not be the best advice.

As an example, Argentina, whose currency is pegged to the U.S. dollar, would seem a perfect candidate for denominating its foreign debt in dollars. However, if the dollar appreciates, Argentine exports both to the United States and to third markets will lose their competitiveness relative to nondollar countries. Export receipts are likely to decline and the debt service-to-exports ratio is likely to rise. In this case, some borrowing in currencies other than the U.S. dollar would have stabilized the debt-service ratio.

For primary producers, the currency in which the main exports is denominated may be different from that of their main trade partner. Indonesia, for example, sells oil priced in U.S. dollars to Japan. In 1986 and 1987, it was hit by the depreciation of the dollar and the fall in oil prices, while a substantial share of its foreign debt was in Japanese yen and European currencies. As a result, the debt-service ratio rose from about 20 percent in 1984 to 28 percent in 1987. Borrowing in the currency in which the main export is priced is not necessarily optimal, however, as commodity price movements do not always offset exchange rate changes. In 1993, for example, the appreciation of the U.S. dollar was more than offset by the decline in the price of oil, and oil exporters would have benefited from having borrowed in currencies other than the U.S. dollar.

A more sophisticated approach consists in determining the currency composition of external debt so as to minimize the variance of a country’s terms of trade or debt-service ratio as a result of exchange rate fluctuations. By borrowing in foreign currencies, a country can hedge against changes in net foreign exchange receipts expressed in the national currency if those changes are positively correlated with movements in the exchange rates of those currencies. Thus, if the appreciation of a country’s trade partner’s currency is associated with an improvement in its trade balance or terms of trade, the country could stabilize its debt-service ratio, if it borrowed in that currency.1 The rise in the debt-service obligations resulting from the appreciation would be offset by the improvement in the trade balance (both expressed in domestic currency). In the simplest form of this model, the currency composition of the external liabilities depends only on the covariances among exchange rates and the covariances between exchange rates and net foreign exchange receipts. Borrowing costs (and the covariances between these costs) can, however, be integrated into the model—as in Claessens (1992). The practical limitations of the approach result from the fact that the relationship between exchange rate changes (or borrowing costs) and terms of trade changes are for many countries weak or unstable.

One still hears occasionally the view that currency selection is irrelevant, as domestic inflation rates are reflected in local interest rates and exchange rates adjust to offset the interest rate differential for (unhedged) foreign investors or borrowers—that is, the high interest currency is expected to depreciate relative to the low interest currency (this expectation being reflected in forward exchange rates). The experience has been otherwise, however, as for lengthy periods since the collapse of the Bretton Woods exchange rate regime, forward exchange rates have overestimated changes in the spot rate and actual exchange rate changes have not fully offset the interest rate differentials. Indeed, a popular strategy for many debtor countries has been to borrow in those countries where lending rates were the lowest. Sometimes, the main motivation has been to reduce the short-term impact of the debt-service payments on the government budget. Even if the benefit of the favorable interest differential in the low-cost countries is subsequently offset by the cost of currency appreciation, the recognition of the capital loss can be postponed and even entered “above the line” in the budgetary accounts. More frequently, such a currency selection strategy has reflected its success. It is a risky strategy, however, as its popularity among investors and borrowers in selecting the currencies participating in the European Monetary System (EMS) and the heavy losses incurred when the EMS broke down in 1992 readily demonstrate.

The case for currency diversification of external debt remains strong, both on theoretical and practical grounds, as it is for international investing. For many developing countries, its main benefit is to reduce the risks associated with the impact of interest rate and exchange rate changes or their ability to meet their external debt obligations. In other words, the cost minimization aspect of diversification may be less important than the prevention of a debt crisis. Ideally, the diversification process should take account of the main factors that affect a country’s ability to service its debt, including any “natural hedges” that may exist, with a view to minimizing the variance of the debt-service ratio.

Role of Foreign Currency Debt2

By contrast with the group of countries that is forced to incur debt denominated in foreign currencies, there is another group for which foreign currency debt is an option but not a necessity. With the dismantlement of capital controls and the global integration of financial markets, it is possible for countries in that group to tap foreign investors and lenders by issuing debt instruments denominated in the national currency. They have a foreign debt but it is not expressed in terms of foreign currencies. Governments in the United States, Germany, and Japan only issue debt denominated in local currency (except for the so-called “Carter bonds”). Recently, New Zealand has stopped borrowing in foreign currencies. Australia does not issue public debt denominated in foreign currencies but swaps part of its public debt into such debt. The private sector is of course free to borrow in any form and denominations it chooses.

Why do some countries’ governments choose to have some of their debt denominated in foreign currencies? Some of the main considerations are the following.

Size of Market and Availability of a Wider Range of Debt Instruments and Maturities

This has been a major factor in the past, but much less relevant today with global financial integration.

Macroeconomic Hedging

In theory, the choice between domestic and foreign debt could be made on the basis of which one provides the better hedge against macroeconomic risk, such as output fluctuations or terms of trade shocks, and results in smoother consumption flows. If terms of trade losses are associated with a depreciation of the domestic currency and a rise in the price level, the decline in the real value of the debt in local currency held by foreigners will offset some of the income losses caused by the fall in the terms of trade. There would be no offset in the case of foreign currency debt. But such an association is uncertain and domestic interest rates could rise and offset the effect of the devaluation.

Other shocks will have different implications for the economy depending on the denomination of the debt. Real interest rate shocks are more easily diversified away for foreign currency debt than for domestic debt. Foreign borrowing can provide a hedge against inflation in the creditor country or a rise in import prices, if the debtor country cannot insulate itself completely through the exchange rate, and its debt is at a fixed interest rate.

Foreign currency debt can make a country more vulnerable to capital outflows—as the role of tesobonos in the 1994-95 Mexican crisis amply demonstrates. The degree of vulnerability depends, however, on other factors such as the current account position (which is related to private sector decisions) and the responsiveness of capital flows to changes in domestic interest rates, as well as the maturity structure of the debt. In a crisis, a government can reduce the value of its domestic debt through inflation; for foreign debt, default is the ultimate escape.

From a more narrow standpoint, the choice between domestic and foreign currency debt could be made dependent on which one minimizes the variability of the budget balance. If budgetary outlays on account of foreign currency-denominated public debt are negatively correlated with other government spending or positively correlated with government revenue, debt in foreign currencies would stabilize the budget balance and avoid the negative impact on the economy of a larger deficit or of higher taxes. For the group of countries under consideration in this section, this may be much less important than for the other countries. Their economies are more resilient and their income levels high enough to sustain some fluctuations in real income. Nevertheless, those countries in the group that are heavily dependent on energy or raw material exports, like Australia and Canada, may welcome greater stability in the current account if it could be achieved through appropriate selection of currencies for foreign borrowing. If there were, for example, a robust tendency for the prices (in U.S. dollars) of their primary exports to fall when the dollar appreciates, but by more than the dollar strengthens, then borrowing in nondollar currencies would stabilize the current account of the balance of payments—in contrast with borrowing in dollars only.3 The considerations are the same as those discussed for currency composition of external debt in the first part of the paper.

Policy Signal

The issuance of public debt denominated in a foreign currency can provide a signal that the authorities will not attempt to reduce the value of debt through inflation. It gives credibility to the government’s anti-inflation program and may reduce the cost of borrowing if domestic interest rates incorporate an “inflation risk premium,” which the authorities do not regard as justified in view of their determination to reduce inflation. The same result could be achieved, however, by issuing inflation-indexed bonds denominated in local currency.

Indexed bonds do not carry an exchange rate risk, and given that government revenue is positively correlated with inflation, the issuer is also protected against an inflationary stock. By “selling protection’’ against inflation to investors, the authorities can expect to lower the cost of their borrowing. They also provide investors with a new financial instrument, which may have a favorable effect on the savings rate. But from the standpoint of liability management, indexed bonds are not a substitute for foreign currency debt, as they provide limited diversification.

Cost and Risk Minimization

For countries in this group, this is the most relevant consideration. Like a corporate treasurer, the agency responsible for public debt management will seek to reduce borrowing costs without taking undue risk. Despite its well-known limitations, the mean variance approach is a useful starting point. According to this approach, the share of foreign debt in total debt and the currency composition of foreign debt are determined simultaneously.

The optimization process uses as inputs the cost of borrowing in the various financial markets (including the domestic market) and the covariances between the various interest rates, exchange rates, and the whole debt portfolio (see Jorion, 1994). Currency returns can be based on historical data or assumed to be zero. The process produces an efficient frontier of optimal risk-return combinations of interest rates and currencies. It is important to note that the inclusion of currencies in the portfolio does not depend on their having positive expected returns.4

The selection of a point on the frontier can be made on the basis of the Sharpe ratio, or the level of risk aversion. Given the benefits of international asset diversification,5 it is not clear why some countries eschew foreign currency borrowing, which is the flip side of international investing, as the same arguments for investing internationally apply to borrowing internationally. Possible reasons include extreme risk aversion, or the view that foreign lenders do not assess correctly the country’s economic prospects and insist on a “risk premium,” which the authorities regard as unjustified. The largest industrial countries may want to encourage the use of their currencies and the development of their own financial markets by issuing public debt only on the domestic market. The size and the efficiency of their domestic markets, relative to the rest of the world, also limit diversification benefits.

The Case of Australia

Cost and Risk of Borrowing in Australian Dollars

As an illustration, consider the case of Australia. Table 4.1 presents data on the cost and risk of borrowing in Australian dollar bonds as well as in five other major markets from 1978 to 1995. These performance numbers are taken from the Salomon Brothers World Bond Indices, which cover all bonds with remaining maturities above five years. The value of each bond index is marked to market each month, includes capital appreciation and coupon payment, and is translated into Australian dollars. These data can be given two interpretations: the usual one is that of investment performance numbers for an investor; the other is that of cost of capital numbers from the viewpoint of sovereign borrowers.

Table 4.1.Cost and Risk: Major Bond Markets in Australian Dollars(Annual returns in percent, 1978-95)






Unhedged bonds
Hedged bonds
Currencies (long)
Source: Salomon Brothers World Bond Indices.
Source: Salomon Brothers World Bond Indices.

The return, or cost, on an unhedged bond incorporates movements in the local currency price P* and in the spot rate price of the foreign currency S. Considering two time periods, 0 and 1, this return is:

The top part of the table shows that, over this period, costs would have varied between 11.42 percent annually (for Swiss francs-denominated bonds) to 16.16 percent (for yen-denominated bonds). Borrowing in Australian dollars would not have been too expensive, with an all-in nominal cost of 11.87 percent. The reason for this low cost is that, even though Australia had high interest rates over the period, the Australian dollar slid from a U.S. dollar value of 1.14 to 0.75 from 1978 to 1995. This depreciation more than offset interest rate differentials and created a relatively low total borrowing cost.

In terms of risk, the month-to-month volatility of Australian dollar bonds was about 9 percent. Foreign currency-denominated bonds, however, exhibited much greater risk, with volatility varying from 13.85 percent (for U.S. dollar bonds) to 17.63 percent (for British pound bonds). Perhaps this explains why some countries prefer not to issue foreign currency-denominated bonds, as they appear more risky.

Separating the Currency and Bond Market Decisions

Positions in foreign bonds involve the same exposure to both the foreign bond market and to the foreign currency. But there is no need to do so. There is no reason to assume that the same position will create the lowest borrowing cost. Long-term yields in one currency, for example, could be viewed as relatively low but the currency itself could be expected to appreciate over the short term. One strategy to take advantage of these views would be to borrow long term in this market while buying a short-term forward cover. In other words, this is a short position in a currency-hedged bond. More generally, the two components can be separated through the use of derivative contracts such as forwards, futures, or swaps.6

The cost of a hedged bond is composed of that on an unhedged bond plus the payoff on a long forward contract. Defining the initial forward rate as F0, the return can be defined as:

As the amount hedged is the same as the exposure to the foreign market, this can be called “unitary hedging.” The second set of rows in Table 4.1 displays the cost and risk of currency-hedged bonds. These represent the pure “bond” component of foreign bonds. While differences in returns are relatively small, the risk of foreign currency bonds is dramatically decreased. For Swiss franc bonds, for instance, the volatility drops from 16.33 percent to only 4.50 percent. This remaining volatility is that of the Swiss bond market, which in fact turns out to be much more stable than the Australian bond market. Thus, if the goal is to provide a stable long-term source of capital, the local bond market may not be the best choice. More generally, however, there is no reason to believe that unitary hedging is optimal, especially in the context of a large portfolio.

Table 4.1 also shows that most of the risk of foreign bonds is actually due to movements in exchange rates. The third set of numbers in the table displays the volatility of returns on forward contracts, which represent short-term movements in exchange rates. The table shows that this risk is quite substantial. For the Swiss franc, for instance, the A$/SwF exchange rate has a volatility of 15.46 percent, which is nearly as large as that of the Swiss bond itself.

One of the basic tenets of portfolio theory is that a diversified portfolio will generally have lower risk than individual assets, provided correlations are less than unity. Correlations are presented in Table 4.2 The table shows correlations of hedged bonds with other hedged bonds and with currencies, as well as correlations between currencies. Correlations between hedged bonds are generally low. The lowest number is 0.13, between Australia and Switzerland. The highest is 0.59, between Germany and Switzerland. As a result, we would expect that portfolio risk could be substantially reduced by spreading risk among many hedged bond markets.

Table 4.2.Correlation Coefficient
Correlations of hedged bonds with:






Hedged bonds
Australian dollar1.00
U.S. dollar0.321.00
Deutsche mark0.210.511.00
Japanese yen0.150.390.551.00
Pound sterling0.150.410.460.391.00
Swiss franc0.130.340.590.420.411.00
U.S. dollar-0.240.00-0.06-0.04-0.02-0.03
Deutsche mark-
Japanese yen-
Pound sterling-
Swiss franc-
Correlations of currencies with:
U.S. dollar1.00
Deutsche mark0.511.00
Japanese yen0.480.711.00
Pound sterling0.470.780.611.00
Swiss franc0.460.930.720.751.00
Correlations of unhedged bonds with:
Unhedged bonds
Australian dollar1.00
U.S. dollar0.061.00
Deutsche mark-0.040.541.00
Japanese yen-0.040.460.691.00
Pound sterling0.000.480.630.551.00
Swiss franc-0.040.500.910.700.601.00

Table 4.2 also shows correlations between hedged bonds and currencies, and within currencies. The former correlations help to determine the risk of unhedged bonds. Define V(Ru) as the variance of an unhedged bond. Going back to the hedged return plus currency return decomposition in (2), this variance is also:

For instance, Table 4.2 shows that the correlation between Swiss franc hedged returns and the Swiss currency is 0.05. The components of unhedged Swiss franc returns are shown in Table 4.3.

The variance components translate into a total risk of unhedged bonds of 16.3 percent, precisely the number in Table 4.1. These correlations are small, but slightly positive, implying that, for instance, an appreciation in the Swiss franc is associated with decreasing Swiss franc interest rates. This positive correlation magnifies the risk from foreign currency borrowing. Thus, unit hedges may not be optimal.

Table 4.3.Components of Unhedged Swiss Franc Returns
Variance Components
Risk of hedged Swiss franc bonds4.5020.3
Risk of Australian dollar/Swiss franc15.46239.0

Optimal Portfolios

More generally, the currency position should take into account all interactions between currencies and interest rates. All of this information about costs, risk, and correlations can be translated into portfolio positions using modern portfolio theory. Figure 4.1 presents the traditional “efficient set,” which plots the locus of portfolios that minimize risk for given cost levels. In the usual application of mean-variance analysis, the goal is to move up and to the left, which implies selecting a point on the upward-sloping portion of the curve. For borrowers, the goal is to minimize a function of the portfolio cost and risk, which implies selecting a point on the lower part of the efficient set.

Figure 4.1.Optimal Portfolio Choice: Unhedged Bonds Cost

(Percent per year)

Source: Author’s calculations.

From Table 4.1, we know that the bond market with the lowest cost is Switzerland. Therefore, the efficient set starts at the bottom with the Swiss market. As the Australian market had similar cost, but lower risk, the efficient set is relatively flat on its bottom part, which means that there is little room for cost reduction relative to borrowing in Australian dollars. The exact allocation depends on the risk aversion. For simplicity, assume that the function to be minimized involves the expected return E(R) and the variance V(R) as in:

The borrower trade-off between low cost and low risk is expressed by the parameter g, which we assumed arbitrarily to be 3.7

The top part of Table 4.4 shows the optimal allocation with unhedged bonds only. The total cost amounts to 11.74, a gain of 13 basis points relative to borrowing in Australia only, with a risk level of 7.74, which is a gain of 125 basis points.8 The position has perforce the same allocation on bonds and currencies, with 73.2 percent on the Australian dollar and 26.8 percent on the Swiss franc.

Table 4.4.Optimal Allocations






Optimal allocations: unhedged bonds only
Cost: 11.74
Risk: 7.74
Net position
Optimal allocations: bonds and currencies
Cost: 11.57
Risk: 4.27
Net position

Next, Figure 4.2 presents the efficient frontier with unhedged and hedged bonds. This is equivalent to considering a menu of assets consisting of bonds and currencies, with only positive positions on bonds and limits on currency positions. The new line moves sharply to the left relative to that in Figure 4.1. The optimal portfolio is detailed in the bottom part of Table 4.4. Relative to the first allocation, costs are further reduced from 11.74 percent to 11.57 percent, and risk is sharply lower, from 7.74 percent to 4.27 percent. The optimal allocation between bonds and currencies is now decoupled, with 10 percent in Australian dollar bonds, 90 percent in Swiss franc bonds, but essentially 100 percent in Australian dollars. For the risk aversion we selected, the portfolio achieves diversification across bond markets without incurring foreign currency risk.9

Figure 4.2.Optimal Portfolio Choice: Bonds and Hedges

Cost (Percent per year)

Source: Author’s calculations.


This example was presented for the purpose of demonstrating the usefulness of the mean-variance framework. More generally, the optimization can be based on the Treasurer’s exchange rate and interest rate forecasts. If necessary, constraints can be added. A major advantage of this framework is that it generates portfolio allocations that are consistent with the objective function, market projections, risk, and correlations.

This approach is also consistent with recent developments in risk management based on the concept of value-at-risk (VAR). VAR addresses the question, “What is the worst possible loss over a monthly horizon at the 95 percent level of confidence?” Computing the portfolio VAR is useful for a number of purposes, including effectively communicating the downside risk of the portfolio to a nontechnical audience, understanding the components of portfolio risk, and establishing a systematic procedure to control risk and plan for worst-case scenarios. With the assumption of jointly normal distributions underlying the mean-variance approach, VAR is simply related to the overall portfolio standard deviation.

The framework presented here can be easily generalized. For instance, our analysis is based on monthly data. If the reporting interval, over which the portfolio is marked to market, is different, this can be adjusted easily. Also, we only considered prices in the domestic currency, in nominal Australian dollars. If the goal is macro-economic hedging, the numéraire can be adjusted easily. For instance, assume that the Treasurer wishes to stabilize the volatility of the portfolio value relative to that of output fluctuations. As explained earlier, hedging is beneficial if states of the world where the economy grows strongly are associated with situations where borrowing costs are higher, because these are precisely the situations where the country can afford greater costs. Conversely, when output is low, the goal is to have lower debt costs. The exercise can then be repeated by measuring costs relative to the desired index.

Finally, this framework can be adjusted to implement market views. By now, there is an abundant literature on “anomalies” in the foreign exchange markets.10 One notable anomaly is the failure of “uncovered interest parity,” which states that the advantage of currencies with low nominal interest rates should be fully offset by currency appreciation. Table 4.5 presents a simple implementation of this result. Every month, a decision is made whether or not to hedge in the foreign bond market. If the forward premium is negative, implying that the foreign short-term interest rate is higher than the domestic rate, the decision is to hedge, or buy the foreign currency. Table 4.5 shows the resulting cost from borrowing on an unhedged basis, on a hedged basis, and using active hedging. The last line shows that the gain from active hedging relative to an unhedged position can be substantial, on the order of 1 percent a year.

Table 4.5.Cost and Risk of Various Strategies(Annual returns in Australian dollars, 1978-95)









Active hedging
Gain of active
versus unhedged1.272.190.740.62-0.24-0.710.601.05

Of course, this strategy is not without risk. As explained before, it is subject to devaluation risk (although all of these are positions relative to a floating dollar). Model risk is also an issue, which is why it would be useful to repeat this exercise using simulations based on prior information only.

Similar strategies can be used for the active management of global bond portfolios. Ilmanen (1996), for instance, shows that international bond returns can be forecasted using a number of variables, including business cycle indicators, real bond yields, and term spreads. He also simulates a dynamic trading strategy that appears to add substantial value. In practical terms, a borrower can use this information to identify periods of time when yields in one particular country are abnormally low.

More generally, we realize that active strategies, both for currencies and bond markets, must be approached with caution. Our advice would be to diversify not only across market risks, but also across active strategies. Diversification should therefore be viewed in a wider context than the traditional mean-variance framework.


This paper has provided a survey of approaches to sovereign debt management. We argued that modern portfolio theory, which is traditionally applied from the viewpoint of maximizing returns to investors, can equally serve to minimize costs to borrowers while not assuming undue risks. A major advantage of this approach is that it provides a consistent framework for dealing with the objective function, projected returns, risks, correlations, and user-specified constraints. Active views can be explicitly taken into account.

This approach, however, presents some disadvantages. First, this is a one-period model that does not deal well with traditional asset and liability management issues, such as covering a known stream of cash outflows. The one-period model is also myopic in that it ignores long-term issues such as mean-reversion in exchange rates as well as the possibility that today’s actions may be corrected by future actions. Finally, the mean-variance optimization model makes full use of model parameters. The question must be asked whether the parameters used in the optimization process are stable enough to serve as a basis for sovereign liability management. With these limitations in mind, we should recognize that modern portfolio theory, which is now increasingly applied to the investment process of global investors, can be equally useful for the management of sovereign debt.


    ClaessensStijn1988“The Optimal Currency Composition of External Debt,”World Bank Policy Planning and Research Working Paper (Washington: World Bank).

    ClaessensStijn1992“The Optimal Currency Composition of External Debt: Theory and Applications to Mexico and Brazil,”World Bank Economic Review. Vol. 6No. 3 (September) pp. 50528.

    de FontenayPatrickGian MariaMilesi-Ferretti and HuwPill1995“The Role of Foreign Currency Debt in Public Debt Management,”IMF Working Paper 95/21 (Washington: International Monetary Fund).

    FrootKenneth and RichardThaler1990“Anomalies: Foreign Exchange,”Journal of Economic PerspectivesVol. 4 (Summer) pp. 17992.

    GlenJack and PhilippeJorion1993“Currency Hedging for International Portfolios,”Journal of FinanceVol. 48 (December) pp. 186586.

    IlmanenAntti1996“When Do Bond Markets Reward Investors for Interest Rate Risk?”Journal of Portfolio Management. Vol. 22 (Winter) pp. 5264.

    JorionPhilippe1994“A Mean-Variance Analysis of Currency Overlays,”Financial Analysts JournalVol. 50 (May) pp. 4856.

    JorionPhilippe1997Value at Risk: The New Benchmark for Controlling Market Risk (Chicago, Illinois: Irwin Professional).

    KritzmanMark1993“The Minimum-Risk Currency Hedge Ratio and Foreign Asset Exposure,”Financial Analysts Journal. Vol. 49 (September) pp. 7778.

    KronerKenneth and StijnClaessens1989“Improving the Currency Composition of External Debt: Applications in Indonesia and Turkey,”World Bank Working Paper 150 (Washington: World Bank, International Economics Department).

    KronerKenneth and StijnClaessens1991“Optimal Dynamic Hedging Portfolios and the Currency Composition of External Debt,”Journal of International Money and FinanceVol. 10 (March) pp. 13148.

    MichaudRichard1989“The Markowitz Optimization Enigma: Is Optimized Optimal?”Financial Analysts JournalVol. 45 (January) pp. 3142.

    OdierPatrick and BrunoSolnik1993“Lessons for International Asset Allocation,”Financial Analysts JournalVol. 49 (March) pp. 6377.

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