In Chapter 16, the fundamental steps in the investment management process were explained. These steps include:

To provide a broad overview of the many aspects of international fixed income investing in one chapter implies that many topics do not receive the depth of discussion they deserve. For example, the topic of currency management is extensive and we provide only the fundamental principles here. However, the same principles involved with currency management apply equally to international equity portfolio management.

While many of the examples and illustrations in this chapter apply to international investing from the perspective of a U.S. manager investing in bond markets outside of the United States, it is important to keep in mind that the principles apply to any cross-border manager investing outside of his or her domestic bond market. The same issues faced by U.S. managers regarding currency management apply to managers throughout the world when they invest in bonds in which the cash flows are not denominated in their local currency.

Broadly speaking, investor specifications include:

Global bonds are usually a small part of an overall portfolio added for both return and diversification. The strategic asset allocation for the portfolio is made up of benchmarks that both define the asset class and provide a performance target that each investment manager strives to outperform. Return objectives are often expressed in terms of the benchmark return, e.g., benchmark return plus 100 basis points over a market cycle. The return objectives and risk tolerances will indicate not only the most appropriate benchmark, but also the most suitable investment management style. Investors who are primarily concerned with diversification may wish to place tight limits on the size of positions taken away from the benchmark to ensure diversification is not weakened. A total-return oriented investor might be far less concerned with diversification and focused on absolute return rather than on benchmark relative return.

Investment policy statements should be flexible enough to allow the portfolio manager sufficient latitude for active management while keeping the portfolio close enough to the benchmark to ensure that the portfolio remains diversified. The policy statements should address allowable investments including:

The time horizon for investment performance is also important. A short-term time horizon, such as a calendar quarter, may encourage more short-term trading which could diminish the natural diversification benefit from international bonds as an asset class. Investors who emphasize the risk reduction, or diversification aspect of international bond investing, should have a longer time horizon of perhaps three to five years. As differences between economic cycles can be prolonged, this provides enough time for a full economic cycle to add any diversification benefit.

The most frequently used fixed-income benchmarks are the Citigroup World Government Bond Index (WGBI) and the Lehman Global Aggregate. As discussed above, the benchmark often provides both the return objective and the measure of portfolio risk.

Many managers are attracted to active currency management because of the large gains that can be attained through correctly anticipating currency movements. As currency returns are much more volatile than bond market returns, even modest positions in currencies can result in significant tracking error (see Chapter 17). Traditionally, the bond manager has handled currency exposures assuming the same fundamental economic factors (identified later in this chapter) influence currency levels. However, many managers are hiring foreign exchange specialists because bonds and currencies can behave quite differently in reaction to the same stimulus. Both the risks and opportunities posed by currency movements suggest that some specialization in currency is warranted and that a joint optimization of the bond and currency decision provides better risk-adjusted returns.³²⁴ Research has also shown that active management by currency specialists can consistently add to returns.

The first task is to determine the neutral or strategic foreign currency exposure appropriate for the investment objectives. Most of the academic research on currency hedging for U.S. dollar-based investors suggests that a partially hedged benchmark offers superior risk-adjusted returns as compared with either a fully hedged or unhedged benchmark.³²⁵ This research has led some to recommend a 50% hedged benchmark for either a passively managed currency strategy, or as a good initial hedged position for an active currency manager. Once the benchmark has been selected, a suitable currency hedge position needs to be determined. For example, a U.S. dollar-based fixed income manager whose primary goal is risk reduction might adopt a hedged or mostly hedged benchmark which has historically shown greater diversification benefit from international bonds. Despite a higher correlation with the U.S. bond market than unhedged international bonds, hedged international bonds offer better risk reduction due to a lower standard deviation of bond returns than an only U.S. bond market portfolio.³²⁶ In addition, this lesser volatility of hedged international bonds results in more predictable returns. Conversely, an investor who has a total return objective, and a greater risk tolerance, would be more likely to adopt an unhedged, or mostly unhedged benchmark, and allow more latitude for active currency management.

From the perspective of a U.S. investor, Exhibit 1 shows that for the 18-year period 1985 - 2002 the currency component of investing in unhedged international bonds accounted for much of the total return volatility. The international bond index used is the Citigroup WGBI excluding the United States (denoted by “non-U.S. WGBI”). Investing in international bonds on a hedged basis reduced the return in most periods, but also substantially reduced the return volatility. As can be seen in Exhibit 1, over the 18-year history of the WGBI, hedged international bonds returned less than unhedged international bonds and even lagged the U.S. component of the WGBI slightly. However, the volatility of the hedged non-U.S. WGBI was one third that of the unhedged index, and three quarters that of the U.S. component.

To compare returns on a risk-adjusted basis we can use the Sharpe ratio.³²⁷ Despite the higher return of the unhedged non-U.S. WGBI, its risk-adjusted return was lower than the hedged index and the U.S. bond component alone for the 1985 through 2002 period.

As noted above, using a 50% hedged portfolio offers a compromise in that its return is virtually midway between the return of the unhedged non-US WGBI and the U.S. bond component with substantially lower volatility than the unhedged index, giving it a higher Sharpe ratio than the unhedged index. Of course the relative performance of the hedged versus the unhedged index depends upon the performance of the home currency (here the U.S. dollar) which can experience long cycles of strength or weakness.

The advantage of using a partially hedged benchmark versus a fully hedged or fully unhedged benchmark is illustrated in a mean-variance framework in Exhibit 2. The 50% hedged portfolio offers better diversification with some small reduction in return when a modest allocation to international bonds is added to U.S. bond portfolios.

Bond markets can be divided into four trading blocs:

The trading bloc construct is useful because each bloc has a benchmark market that greatly influences price movements in the other markets. Investors are often focused more on the spread level of, say, Denmark to Germany, than the absolute level of yields in Denmark. (Since the beginning of the European Monetary Union (EMU) in 1999, the euro zone bond markets have traded in a much tighter range.)

Limits on investment in countries outside the benchmark should also be specified at the outset. Despite the pitfalls of using duration to measure interest rate risk across countries, risk limits on duration are nonetheless useful and should be established. Typically, the range of allowable exposures is wider for bond exposures than currency exposures.

Credit risk limits, usually a minimum weighted average credit rating from the major credit rating agencies, and limits on the absolute amount of low or non-investment grade credits, should also be included. Apart from default risk, the illiquidity of lower rated securities may hamper a manager’s ability to alter exposures as desired. In the past, due to the lack of a liquid corporate bond market in many countries, and the relative illiquidity of Eurobonds compared to domestic government bond markets, most credit risk in international bond portfolios was concentrated in U.S. and emerging market bonds. However, this difference in liquidity between U.S. corporate bonds and those in other countries has diminished significantly in recent years due to strong growth in the European corporate bond market since European Monetary Union.

Since the performance of most portfolio managers is judged against a benchmark return, managers are constantly seeking opportunities to outperform a benchmark. There are a number of means by which portfolio managers can add to returns; however, the bulk of excess returns relative to the benchmark comes from broad bond market and currency allocation decisions. A disciplined investment approach, based upon fundamental economic factors or market indicators of value, facilitates the market and currency selection process. Because of the historical high volatility of currency returns, the approach to currency management should be a primary concern.

International bond managers also utilize one or more different management styles. These can be divided into four general categories:

International bond portfolio managers would do well to maintain a disciplined approach to buy and sell decisions. This would require each allocation away from the benchmark to have a specified price target (or more often yield spread or exchange rate level), and stated underlying rationale. Depending upon the management style, the size of the position should reflect the strength of the investor’s conviction or model’s signal. As long as the investment rationale that supported the initial decision remained unchanged, the position would be held, or potentially increased, if the market moves in the opposite direction. Each trade should be designed with consideration for the relevant bond yield or exchange rate’s behavior through time. For example, an exchange rate that exhibits a tendency to trend will require a different buy and sell discipline than one that tends to consistently revert back to an average exchange rate.

However, as the volatility of currency returns is generally higher than that of bond market returns, the incremental returns gained from currency exposures must be evaluated relative to the additional risk incurred. For an active currency management strategy to consistently provide superior risk-adjusted performance, a currency forecasting method is required that can predict future spot rates (i.e., future exchange rates) better than forward foreign exchange rates (i.e., rates that can be locked in today using the market for forward contracts). As shown later, forward foreign exchange rates are not forecasts of future spot foreign exchange rates, but are determined by short-term interest rate differentials between currencies.

Academic studies have shown that several strategies have been successful in generating consistent profits through active currency management. The fact that forward foreign exchange rates are poor predictors of future spot exchange rates is well established. Historically, discount currencies (i.e., those with higher interest rates than the investor’s local currency) have depreciated less than the amount implied by the forward rates, providing superior returns from holding unhedged positions in currencies with higher interest rates. Overweighting currencies with high real interest rates versus those with lower real interest rates has also been shown to provide incremental returns.³²⁹

In addition, some currency movements are not a random walk, but exhibit serial correlation (i.e., currency movements have a tendency to trend).³³⁰ In a market that tends to trend, simple technical trading rules may provide opportunities for incremental currency returns.³³¹ These findings in several academic studies demonstrate that excess currency returns can be generated consistently, providing a powerful incentive for active currency management.

Duration management has become easier in international markets in recent years. Many countries have concentrated their debt in fewer, more liquid, bond issues. Official strip markets (which separate government bond cash flows into individual interest and principal payments) now exist in at least nine countries. Interest rate futures, available in most markets, offer a liquid and low-cost vehicle for changing duration or market exposure quickly. The interest rate swaps market, used extensively by large institutional investors, is generally very liquid across international bond markets. Following European Monetary Union, the swap curve, rather than individual country yield curves, has increasingly been used as a reference for some markets. Increasingly, countries have set up professional debt management offices that are independent from both central banks and finance ministries. These debt management offices have become significant users of derivatives themselves to minimize borrowing costs, alter the maturity structure or currency composition of outstanding debt, and to promote liquidity in their domestic market.³³³

The process for selecting an out-of-index market is similar to that followed by an active manager for a domestic bond portfolio manager when deciding whether or not to construct a portfolio with allocations different from the benchmark index and whether or not to invest outside the index. The manager will assess the potential performance on a total return basis of the markets outside of the index relative to that of the markets to be underweighted in order to allocate funds to out-of-index markets. An international bond portfolio manager, however, must also take into account the affect of currency movements and hedging decision of an investment outside or within the index.

As we saw above, exposure to emerging markets can significantly add to returns. For example, a portfolio composed of 80% exposure to the Citigroup Non-U.S. Government Bond Index and 20% exposure to the J.P. Morgan EMBI + Index from 1994 through 2002 would have added 120 basis points to the return of the international index and reduced the standard deviation of returns by 12%. A 20% allocation to emerging markets in an international bond portfolio that was half-hedged against foreign exchange rate changes would have increased returns by 223 basis points while decreasing the standard deviation of returns by 37%.

The strategic decision of which bond markets and currencies to overweight usually begins with an economic outlook and bond and currency forecasts in each of the markets considered for investment. The long-run economic cycle is closely correlated with changes in bond yields, and trends in both the economic cycle and bond yields tend to persist for a year or longer. The millions of dollars spent each year by money management firms, banks, and brokerage houses in forecasting economic trends is testimony to the potential returns that can be achieved by correctly forecasting economic growth or turning points in the economic cycle.

Forecasting interest rates, however, is extremely difficult. Academic literature generally holds that interest rate forecasts are unable to generate consistent risk-adjusted excess returns. This is partly because market prices can deviate substantially over the short term from the level consistent with the economic fundamentals. Economic fundamentals impact bond and currency prices over the medium to long term. Also, the volatile nature of certain economic data series may result in exaggerated market reactions to individual data releases that may be different from the actual trend in the economy. These deviations may persist for several months until either the initial figure is revised, or several subsequent data releases reveal the error in the initial interpretation.

The creation of an independent economic outlook can be useful in several ways. First, it can help identify when market interpretations of the economic data are too extreme, or add value through correctly anticipating economic shifts not reflected in the market consensus. Second, as it is often not absolute changes in interest rates, but changes in interest rates relative to other markets that determine the margin of performance in international fixed income investing, an independent economic outlook does not require accurate growth forecasts for each individual market, but only economic growth differentials to be able to add value. Whether the portfolio will invest in U.S. bonds or not, the large influence of the U.S. dollar and the Treasury market on foreign markets underlines the importance of an independent outlook on the U.S. economy.

Thus, the economic outlook forms the foundation for bonds and currencies strategic allocation. An economic outlook for each country should be constructed to assist in ranking the relative attractiveness of markets. However, even though economic fundamentals in a particular country may be extremely bond supportive, bond prices may be too high to make it an attractive investment. Likewise, bonds are sometimes excessively cheap in countries with poor economic fundamentals, yet may still provide an attractive investment opportunity. Thus, the economic outlook must be compared with either consensus economic forecasts, or some market value measure to identify attractive investment opportunities.

The strategic allocation decision regarding which markets to overweight or underweight relative to the benchmark is thus a complex interaction of expected returns derived from assessing economic trends, and technical and value factors. Each set of variables is defined and explored below, beginning with the fundamental factors used to create the economic outlook.

Nominal bond yields deflated by current inflation, although not a precise measure of the market’s real interest rate premium, are easily measurable and can still provide some useful insight into bond valuation. Real yields can be compared across markets or against their long-run averages, such as 5 or 10 years, in each market. The usefulness of real yields as a measure of relative value has diminished as global inflation rates have converged to very low levels.

Historic trends, as well as the overall levels, should be taken into account when assessing market sentiment. For example, an indication that managers are underweighting Japanese bonds might lead some to conclude that Japanese bonds are due for a rally even though international fixed income managers have consistently underweighted the Japanese market, in part due to its low nominal yields. Sentiment surveys, however, may not capture all market participants such as retail investors, who can also move markets.

We will let “local currency” be the currency of the country where the manager has invested and use the subscript “L” to denote the local currency. So, to a U.S. portfolio manager, yen would be the local currency for bonds purchased in the Japanese bond market and denominated in yen, while for a Japanese portfolio manager, U.S. dollars would be the local currency for bonds purchased in the U.S. and denominated in U.S. dollars.

The expected total return of an unhedged international bond portfolio in terms of the home currency depends on three factors:

Mathematically, the expected total return of an unhedged bond portfolio in terms of the home currency can be expressed as follows: ³³⁹ total expected portfolio return in manager’s home currency where

The expected portfolio return as given by equation (1) is changed to the extent the manager alters exposure to each country’s exchange rate. A common instrument used to alter exposure to exchange rates is a currency forward contract. So, let’s look at these contracts and how they are priced. This will lead us to an important relationship that we will use in the balance of this chapter, called interest rate parity.

Most currency forward contracts have a maturity of less than one year. For longer-dated forward contracts, the bid-ask spread increases; that is, the size of the bid-ask spread for a given contract increases with the length of the time to contract settlement. Consequently, currency forward contracts become less attractive for hedging long-dated foreign exchange exposure. Other instruments, such as currency swaps, ³⁴⁰ can be used for hedging.

A manager can use currency forward contracts to lock in an exchange rate at the future delivery date. In exchange for locking in a foreign exchange rate, the manager forgoes the opportunity to benefit from any advantageous foreign exchange rate movement but eliminates downside risk.

Earlier, the relationship between spot prices and forward prices was demonstrated. Arbitrage arguments can also be used to derive the relationship for currency forward contracts. Consider a U.S. manager with a 1-year investment horizon who has two choices:

Which is the best alternative? It will be the alternative that produces the largest number of U.S. dollars one year from now. Ignoring U.S. and country i’s taxes on interest income or any other taxes, we need to know two things in order to determine the best alternative:

The number of U.S. dollars that the LC 155,395 can be exchanged for depends on the exchange rate one year from now. Let F denote the exchange rate between these two currencies one year from now. Specifically, F will denote the number of U.S. dollars that can be exchanged for one unit of the local currency one year from now and is called the forward exchange rate. Thus, the number of U.S. dollars at the end of one year from the second alternative is:

The investor will be indifferent between the two alternatives if the number of U.S. dollars is $106,000, equal to the dollars resulting from alternative 1. That is,

Thus, if one year from now the spot exchange rate is $0.6821 per one local currency unit, then the two alternatives will produce the same number of U.S. dollars.³⁴¹ If the local currency has appreciated by more than 0.95%, i.e., one local currency unit can be exchanged for more than $0.6821, then there will be more than $106,000 at the end of one year. An exchange rate of $0.6910 per one local currency unit, for example, would produce $107,378 (LC 155,395 times $0.6910). The opposite is also true if one local currency unit can be exchanged for less than $0.6821. For example, if the future exchange rate is $0.6790, there will be $105,513 (LC 155,395 times $0.6790).

Now suppose that a dealer quotes a 1-year forward exchange rate between the two currencies. The 1-year forward exchange rate fixes today the exchange rate one year from now. Thus, if the 1-year forward exchange rate quoted is $0.6821 per one local currency unit, investing in the bank in country i will provide no arbitrage opportunity for the U.S. investor. If the 1-year forward rate quoted is more than $0.6821 per one local currency unit, the U.S. manager can earn an arbitrage profit by selling the local currency forward (and buying U.S. dollars forward for the local currency). In this example, assume the borrowing and lending rates within each country are equal.

To understand this arbitrage opportunity, consider how a portfolio manager could take advantage of a mispricing in the market.³⁴² Under the conditions in the above example, assume that the bid for a 1-year forward contract in local currency is quoted $0.6910 per local currency unit. The portfolio manager could generate an arbitrage profit by using the following strategy:

Let’s look at the outcome of this strategy at the end of one year:

Now consider the case where the 1-year forward exchange rate quoted is less than $0.6821 and see how a portfolio manager can exploit the situation by buying the local currency forward (or, equivalently, selling U.S. dollars forward). Suppose that the 1-year forward exchange rate is $0.6790 and assume the borrowing and lending rates within each country are equal. The strategy implemented by the portfolio manager is:

Let’s look at the outcome of this strategy at the end of one year:

The conclusion is the 1-year forward exchange rate must be $0.6821 because any other forward exchange rate would result in an arbitrage opportunity.

It can be demonstrated that the forward exchange rate between an investor’s home currency, denoted “H ” and the currency of country i, is equal to where c_H and c_i are called the cash rate. The cash rate is generally the eurodeposit rate (i.e., offshore deposit rate) for funds deposited in that currency which matches the maturity of the forward contract. The London Interbank Offered Rate, LIBOR, is the most quoted offshore (eurodeposit) rate. LIBOR deposit rates are available for U.S. dollars and most other major currencies, including EURIBOR for euro-denominated deposits.

In our earlier illustration involving the U.S. dollar and the exchange rate of country i, we know that

By rearranging the above terms, the forward exchange rate discount or premium (or the percentage change of the forward rate from the spot exchange rate), denoted by f_H,i, approximately equals the differential between the short-term interest rates of the two countries. That is, ³⁴⁴

The forward rate can also be expressed in “points” or the difference between the forward and spot rate, F_H,i - S_H,i. When interest rates are lower in the foreign country (i.e., the forward points are positive), the forward foreign exchange rate trades at a premium.

Now, what will determine whether or not the manager will hedge the exposure to a given country’s exchange rate using a currency forward contract? The decision is based on the expected return from holding the foreign currency relative to the forward premium or discount. That is, if the manager expects that the percentage return from exposure to a currency is greater than the forward discount or premium, then the manager will not use a forward contract to hedge the exposure to that currency. Conversely, if the manager expects the currency return to be less than the forward discount or premium, the manager will use a forward contract to hedge the exposure to a currency.

In the case where the manager expects that the percentage return from exposure to a currency is greater than the forward discount or premium, the unhedged return for country i can be expressed as:

In the case where the manager expects the currency return to be less than the forward discount or premium, we can express the hedged return for a country in terms of the forward exchange rate between the home and local currencies using the interest rate parity relationship. As equation (3) showed, the forward premium or discount is effectively equal to the short-term interest rate differential; thus,

Why would a manager want to undertake a cross hedge? A manager would do so if she expects her home currency to weaken, so she does not want to hedge the currency exposure to country i, but at the same time she expects that country j’s currency will perform better than country i’s currency.

When there is a cross hedge, the hedged return for country i, HR_{H ,i} , in equation (6) can be rewritten as follows: where f_j,i is the forward discount or premium between country j and country i. The above expression says that the cross hedged return for country i depends on (1) the expected bond return for country i, (2) the currency return locked in by the cross hedge between country j and country i, and (3) the currency return between the home currency and country j.

We can rewrite the above equation in terms of short-term interest rates as given by interest rate parity. That is, for f_j,i we substitute c_j - c_i. Doing so and rearranging terms gives:

Equation (7) says that the cross hedged expected return for country i depends on (1) the differential between country i’s bond return and country i’s short-term interest rate plus (2) the short-term interest rate in country j, and (3) the currency return between the home currency and currency j.

When there is a proxy hedge, the hedged return for country i, HR_H,i , in equation (6) can be rewritten as follows: where f_{H ,j} is the forward discount or premium between the home country and country j.

Notice that in the above equation, there is still the exposure to the exchange rate between the home currency and currency i. The proxy hedge comes into play by the shorting of the currency return between the home currency and currency j.

Based on interest rate parity we can replace f_{H ,j} with the difference in short-term interest rates, c_H - c_j , to get

Equation (8) states the expected return for country i using proxy hedging depends on

These equations show how integral the short-term interest rate differential is to the currency hedge decision. This means that (1) the short-term interest rate differential should relate to the currency decision and (2) bond market returns should be an excess return, calculated less the local short-term interest rate. This can be made explicit by adding and subtracting the home currency short-term interest rate to the four return relationships—unhedged, hedged, cross hedged, and proxy hedged. (The derivations are provided in the appendix to this chapter.) By doing so, this allows the forward premium (f_H,i = c_H - c_i ) to be inserted into the currency term giving: cross hedged expected return for country i, proxy hedged expected return for country i,

It is important to note that only the hedged position eliminates all currency risk. The cross hedge substitutes one currency exposure for another, but maintains foreign currency exposure. The proxy hedge leaves the portfolio exposed to “basis” risk if the proxy hedge currency appreciates relative to the investment currency.

Exhibit 3 illustrates an example comparing the explicit return forecasts for government bonds with a duration of 5 in both countries. Total returns are the sum of the excess bond market return plus the excess return due to currency, consistent with the approach explained in equations (9) through (12). These equations are restated below using US$ for the home currency, H , using currency j for the cross hedge and proxy hedge, and remembering f_US$,i ≈ C_US$ - C_i :

As mentioned earlier, the first two components of the above equations, the U.S. cash rate and the expected excess bond return in country i, are identical in all four equations, and equal to the expected hedged bond return. Thus, we can begin with the hedged bond return and compare the excess currency returns (the third component of the equations) of the unhedged, cross hedged, and proxy hedged strategies. The hedged bond return is

Let’s look at this component for the unhedged strategy. From the first equation: or equivalently, since from interest rate parity f_US$,i = c_US$ - c_i , we can rewrite the expression as

Turning to our illustration, the expected return on currency i of 2.3% is less than the short-term interest rate differential of 2.5% over the 1-year horizon (5.5% in the U.S. versus 3.0% in country i). Stated another way, the expected excess currency return component to a U.S. dollar-based investor from an unhedged bond holding in currency i is -0.2%. Consequently, the position would offer a higher return when hedged back into U.S. dollars.

Now consider a cross hedging strategy. Cross hedging allows the portfolio manager to create a currency exposure that can vary substantially from the underlying bond market exposure. A cross hedge replaces one foreign currency exposure with another that usually has a higher expected return. The excess currency component from the cross hedge strategy is: or equivalently, since from interest rate parity f_US$,j ≈ c_US$ - c_j , we can rewrite the expression as

In the illustration, the short-term interest rate differential of 2.6% between the U.S. and country j (c_US$ - c_j ) is greater than the 2.0% expected appreciation of the currency of country j versus the U.S. (e_US$,j ). In this case, the expected excess currency return for the cross hedge strategy for country i using country j (i.e., e_US$,j - (c_US$ - c_j )) is -0.6%. The expected return from cross hedging is 5.4%, so a cross hedge with country j will not be used because the expected return is less than the unhedged position and a straight hedge of currency i.

Finally, let’s look at the proxy hedging strategy. From the return of the proxy hedged strategy we know that

In our illustration, both currency i and currency j are expected to appreciate relative to the U.S. dollar. The relative currency appreciation between currency i and currency j is what is important according to the equation. If the appreciation for currency i—which the investor is long—is greater than the appreciation for currency j—which the investor is short—an investor will benefit from a proxy hedge. In our illustration, country i’s expected appreciation is 2.3% while country j’s is only 2.0%. Thus, there will be an expected currency return from this proxy hedging strategy of 30 basis points. This is what the first bracketed term in the excess currency return equation above says.

Just looking at the expected currency return from a proxy hedging strategy, however, is not sufficient. The above equation shows the expected currency return for the proxy hedging strategy must be adjusted to determine the excess currency return for the proxy hedging strategy. The adjustment is obtained by subtracting the short-term interest rate differential in countries j and i from the expected currency return from proxy hedging. If that differential is less than the expected currency return from proxy hedging, then proxy hedging is attractive. If it is greater than the expected currency return from proxy hedging, then proxy hedging is unattractive.

In our illustration, the proxy hedging strategy is attractive because the short-term interest rate differential between country j and country i is -10 basis points, which is less than the 30 basis point currency return for the proxy hedging strategy. The excess return from the proxy hedging strategy is then 30 basis points minus the -10 basis point short-term interest rate differential. So, the excess return from the proxy hedging strategy in our illustration is 40 basis points. The proxy hedged expected return is 6.4%, which is greater than the three other alternatives—unhedged, hedge with currency i, and cross hedge with currency j.

In Exhibit 4 we have changed the example in Exhibit 3 by altering one number. In this illustration, the expected appreciation for currency j is now 3.2% rather than 2.0%. Thus, the expected appreciation for currency j is greater than for currency i. The expected currency return for the proxy hedging strategy is then -90 basis points (2.3% - 3.2%). After adjusting for the short-term interest differential of -10 basis points, the excess currency return using country j in a proxy hedge is -80 basis points. Consequently, the proxy hedge return of 5.2% is unattractive, as it is less than the three other alternatives analyzed. In this illustration, the cross hedge presents the best choice based on the expected returns.

In European markets (except for the United Kingdom) and Japan, coupon payments are made annually rather than semiannually. Thus, the yield is simply the interest rate that makes the present value of the cash flows equal to the price plus accrued interest. No annualizing is necessary.

The yield quoted in terms of the home market’s convention for payments is called the conventional yield. For example, Exhibit 5 displays data from the J.P. Morgan Europe (MEUR) page from Reuters’ market information service. The column “CNV. YLD” is the conventional yield. So, the U.S. and U.K. yields of 4.20% and 4.68%, respectively, shown in Exhibit 5 are based on the bond-equivalent yield convention of doubling a semiannual yield since coupon payments are made semiannually. In countries where coupon payments are made annually, in Germany and Japan, for example, the conventional yield is simply the annual yield.

Despite the limitations of yield measures discussed earlier, managers compare yields within markets of a country and between countries. (We will give one example in the next section.) Holding aside the problem of potential changes in exchange rates, yield comparisons begin by adjusting conventional yield (i.e ., the yield as quoted in the home market) to be consistent with the way the yield is computed for another country. For example, a French government bond pays interest annually while a U.S. government bond pays interest semiannually. If the U.S. government bond yield is being compared to a French government bond yield either (1) the U.S. government bond yield must be adjusted to the yield on an annual-pay basis or (2) the French government bond yield must be adjusted to a yield on a bond-equivalent yield basis.

The adjustment is done as follows. Given the yield on an annual-pay basis, its bond-equivalent yield (i.e ., a yield computed for a semiannual-pay bond) is computed as follows:

To adjust the bond-equivalent yield of a semiannual-pay bond to that of an annual-pay basis so that it can be compared to the yield on an annual-pay bond, the following formula can be used:

For example, the conventional yield of a U.S. government bond as shown in Exhibit 5 is 4.20%. The yield on an annual-pay basis is:

Yield spreads are typically computed between a country’s yield and that of a benchmark. As explained, the U.S. government bond market and the German government bond market are the two most common benchmarks used. The next-to-the-last column in Exhibit 5, labeled “O/US T,” shows the spread between a country’s yield and the U.S. Treasury yield. Notice that for the French government bond, the spread is shown as +30 basis points. This spread is obtained by subtracting the French government bond of 4.54% (the conventional yield reported in Exhibit 5) from the adjusted U.S. government bond yield of 4.24% (as computed above).

The last column in Exhibit 5, labeled “O/GER,” shows the spread between a country’s yield and the German government bond yield. For example, when the spread of the French government bond yield over the German government bond yield is computed, since both markets pay coupon interest annually, the spread is simply the difference in their conventional yields. Since the yield on the French government bond is 4.55% and the yield on a German government bond is 4.47%, the spread is 8 basis points. (Exhibit 5 shows a 7 basis point spread. The difference is due to rounding.)

Bond and currency breakeven rates, the rate which make two investments produce identical total returns, are usually calculated versus a benchmark market return over a specific time horizon. A large yield spread between two markets implies a larger “cushion” (the required spread widening to equate total returns in both markets, or the breakeven rate) over the investment time horizon.

Comparing of forward interest rates can be instrumental in identifying where differences between the strategic outlook and market prices may present investment opportunities. As explained previously, forward interest rates use the shape of the yield curve to calculate implied forward bond rates and allow a quick comparison of what is required, in terms of yield shifts in each market, to provide a return equal to the short-term risk-free rate (a zero excess return). This would correspond to a bond excess return of zero in equations (9) through (12), or (r_i - c_i ) = 0. Forward interest rates represent a breakeven rate, not across markets, but within markets. The strategic bond allocation can then be derived by increasing exposure to markets where the expected bond return over the short-term interest rate is most positive—that is, where the expected bond yield is furthest below the forward yield. Forward rate calculators are also available on systems such as Bloomberg as illustrated in Exhibit 6.

The forward foreign exchange rate represents a breakeven rate between hedged and unhedged currency returns as previously shown in the components of return analysis. In terms of equations (9), (11), and (12), currency excess return is zero when the percentage change in the currency equals the forward premium or discount. As forward foreign exchange rates are determined by short-term interest rate differentials, they can be estimated from the interest rates on deposits, specifically, Eurodeposit rates as in equations (2) and (3), which can be easily obtained from market data services such as Bloomberg and Reuters.

Breakeven analysis provides another tool for estimating relative value between markets. Because the prices of benchmark bonds are influenced by coupon effects and changes in the benchmark, many international fixed income traders and portfolio managers find it easier to keep pace with changes in yield relationships than price changes in each market. A constant spread between markets when yield levels are shifting, however, may result in a variation in returns as differing benchmark bond maturities and coupons result in a wide spread of interest rate sensitivity across markets. For example, of the benchmark 10-year bonds listed in Exhibit 5, durations range from a low of 7.2 for Greece to 9.4 for Japan where yields equal one third of the next lowest yielding market. (The duration for the U.S. bond was 8.1.) Thus, market duration must be taken into account when determining breakeven spread movements.

Since European Monetary Union, yield differentials within Europe have remained extremely tight. Holding Italian versus German bonds provides a yield advantage of only 22 basis points per year. Obviously, this small amount of additional yield can be easily offset by an adverse price movement between the two markets. In the mid 1990s before European Monetary Union, Italian bonds would have yielded several hundred basis points more than German bonds as the additional currency risk involved in holding Italian bonds had a substantial impact on nominal yield spreads. Even a fairly wide yield cushion, however, can also quickly evaporate.

To illustrate this and show how breakeven analysis is used, look at the yield spread between the 10-year U.S. and Japanese government bonds on December 3, 2002 as shown in Exhibit 5. The spread is 322 basis points, providing Japanese investors who purchased the U.S. benchmark Treasury with additional yield income of 80 basis points per quarter. This additional yield advantage can be eliminated by the spread widening substantially less than the 80 basis points. The widening can occur in one of the following two ways:

It is important to note this breakeven analysis is not a total return analysis; it applies only to bond returns in local currency and ignores currency movements. This breakeven analysis is effective in comparing bond markets that share a common currency, as within the euro zone; however, currency must be taken into account when applying breakeven analysis to markets with different currencies. The additional yield advantage in the example above is erased if the U.S. dollar depreciates by more than 0.80% during the quarter. Below, we illustrate how a hedged breakeven analysis can be calculated using hedged returns, or simply the forward foreign exchange premium or discount between the two currencies.

We know that the duration of the Japanese bond is 9.4.³⁴⁶ This means that for a 100 basis point change in yield the approximate percentage price change for the Japanese bond will be 9.4%. For a 50 basis point change in yield, the percentage price change for the Japanese bond will change by approximately 4.7%. We can generalize this as follows:

We refer to this yield spread change as the breakeven spread movement. Note that the breakeven spread movement must (1) be related to an investment horizon and (2) utilize the higher of the two countries’ modified durations. Using the highest modified duration provides the minimum spread movement that would offset the additional yield from investing in a higher yielding market. So, in our example, the 3-month breakeven spread movement due to Japanese yields is 8.5 basis points, meaning that it is the spread movement due to a drop in Japanese rates by 8.5 basis points that would eliminate the 3-month additional yield from investing in U.S. Treasury bonds. The breakeven spread movement using the 8.1 duration in the U.S. would be 9.9 basis points (0.8/8.1 = 9.9); a difference of only 1.4 basis points.

The breakeven spread movement described above completely ignores the affect of currency movements on returns. It also ignores the implied appreciation or depreciation of the currency reflected in the forward premium or discount. If we subscribe to the methodology discussed earlier in the chapter of attributing cash returns to the currency decision, and measuring bond market returns as the local return minus the cash rate, the results of the breakeven spread movement analysis on a hedged basis may be quite different. We can easily calculate the hedged breakeven spread movement by adding in the forward foreign exchange discount or premium. At the time of this breakeven analysis, 3-month interest rates were 0.0675% in Japan and 1.425% in the United States. With this information we can obtain the embedded forward rate using equation (3); that is,

Alternatively, we could use equation (10) to calculate the expected hedged return to a yen-based investor over a 3-month period and compare it to the return on a Japanese 10-year bond over the same period. In order to do so, it is first necessary to adjust the U.S. government bond yield (which is quoted on a bond-equivalent yield basis) to an annual-pay yield basis because the Japanese yield is based on an annual basis. Earlier we showed that the conventional yield of 4.20% for the U.S. government bond as reported in Exhibit 5 is 4.24% on an annual-pay basis. Assuming no change in rates, the expected hedged return is: and the expected Japanese bond return is (1.02%/4, or 0.26%). Thus, the expected return on a hedged basis is 0.44%, which is close to the 0.46% in the first answer that we calculated.

Taxation issues also need to be taken into account when selecting individual bonds for purchase. For example, several markets have tax systems that encourage investors to hold lower coupon bonds, hence certain bonds will tend to trade rich or cheap to the curve depending on their coupon. In markets that impose withholding taxes on coupon payments, international fixed income portfolio managers often minimize their tax liability by replacing a bond that is near its coupon date with another bond of similar maturity. Market anomalies can also arise from differing tax treatment within markets. For example, Italian Eurobonds issued before 1988 are exempt of withholding tax for Italian investors, hence they tend to trade at a lower yield than similar maturity bonds issued after 1988.

Unhedged expected return:

Hedged expected return:

The hedged expected bond return for country i, equation (6), is derived by adding a currency hedge (-e_H,i + c_H - c_i) to the unhedged return, equation (5). By doing so we get: the two currency terms drop out yielding equation (6)

Cross hedged expected return:

To get the cross hedged expected return given by equation (11) we begin with equation (5) and enter into a currency forward that creates a short position in currency i and long position in currency j(f_j,i - e_i,j). The currency position e_i,j combined with the original long exposure to currency i, e_H,i, leaves a net long position in currency j versus the home currency, e_H,j. Thus,

Proxy hedged expected return:

To derive the proxy hedged expected return given by equation (12), we begin with the unhedged return, equation (5), and add a short currency position in currency j(f_H,j - e_H,j) to obtain the rewritten proxy hedged expected return equation given in the chapter:

The fact that equations (9), (10), (11), and (12) differ only by their last term emphasizes that the bond market decision is unrelated to the currency hedging decision.