Investing Across Borders
Investing across borders is a strategy employed by portfolio managers to diversify their portfolio and maximize returns. This involves managing currency risk, either actively or passively. For instance, a US-based portfolio manager might invest in Japanese bonds to take advantage of higher yields, while managing the risk of the yen depreciating against the dollar. The focus here is on extending the analysis of yield curve strategies from a single yield curve to multiple yield curves across different currencies.
Investors measure return in functional currency terms, which means considering domestic currency returns on foreign currency assets. This is represented in the following:
Single Asset:$$R_{DC} = (1 + R_{FC}) (1 + R_{FX}) – 1$$
Portfolio:$$R_{DC} = \sum_{i=1}^{n} \omega_i ( 1 + R_{FC,i} ) ( 1 + R_{FX,i} ) – 1$$
Where:
\(R and R_{FC}\) are the domestic currency returns expressed as a percentage.
\(R_{FC}\) is the foreign currency return expressed as a percentage.
\(R_{FX}\) is the percentage change of the domestic versus foreign currency.
\(\omega_i\) is the respective portfolio weight of each foreign currency asset (in domestic currency terms) with the sum of \(\omega\) equal to 1.
Macroeconomic Factors and Bond Returns
Macroeconomic factors such as inflation, economic growth, and monetary policy play a pivotal role in shaping the bond term premium and required returns. These factors vary across countries and are often mirrored in the relative term structure of interest rates and exchange rates.
Consider the economic expansion that followed the 2008 global financial crisis. The US Federal Reserve’s early reversal of quantitative easing, compared to the European Central Bank through 2019, resulted in significantly higher short-term government yields-to-maturity in the United States versus Europe.
The COVID-19 pandemic in early 2020 triggered a flight to quality, leading to a sharp decline in US Treasury yields-to-maturity.
Hedged and Unhedged Returns
When an investor fully hedges their investment, such as a 2-year US Treasury zero-coupon bond, the expected annualized return in EUR terms over two years is -0.60%. This is equivalent to the 2-year annualized yield-to-maturity of a German government zero-coupon bond at inception.
Covered Interest Rate Parity
The principle of covered interest rate parity establishes a no-arbitrage relationship between spot and forward rates for individual cash flows in T periods.
$$F\left(\frac{DC}{FC}, T\right) = S_0\left(\frac{DC}{FC}\right)\left(\frac{1 + r_{DC}}{1 + r_{FC}}\right)^T$$
where \( F \) is the forward rate, \( S_0 \) is the spot rate, and \( r_{DC} \) and \( r_{FC} \) reflect the respective domestic and foreign currency risk-free rates.
Uncovered Interest Rate Parity
Uncovered interest rate parity suggests that over time, the returns on unhedged foreign currency exposure will be the same as on a domestic currency investment. However, investors sometimes exploit a persistent divergence from interest rate parity conditions (known as the forward rate bias) by investing in higher-yielding currencies and borrowing in lower-yielding currencies.
Active fixed-income strategies across currencies must consider views on currency appreciation versus depreciation as well as yield curve changes across countries. For instance, an investor’s USD versus EUR interest rate view combined with an implicit view that USD/EUR would remain relatively stable led to the highest return in the unhedged case with a 1-year investment horizon.
Carry Trade
The European fixed-income manager might use leverage instead of cash by borrowing in euros when buying the 2-year US Treasury zero. This carry trade across currencies is a potential source of additional income subject to short-term availability if the positive interest rate differential persists for the life of the transaction.
Investing in a foreign currency fixed-income coupon bond is akin to replicating a risk-free domestic currency return. This process involves several steps:
- The investor sells their domestic currency, say USD, and purchases the foreign currency, say EUR, at the current spot rate to buy the bond.
- At the end of each semi-annual interest period, the investor receives a foreign currency coupon, which must be converted at the future USD/EUR spot rate.
- At maturity, the investor receives the final semi-annual coupon and principal, which must be converted to the USD using the future USD/EUR spot rate.
Exposure to FX Forward Exposures
The fixed-rate foreign currency bond exposes the investor to a series of FX forward exposures. These can be hedged upon purchase with a cross-currency swap. For instance, by foregoing the pay foreign currency fixed swap, the investor takes a foreign currency rate view by earning the foreign currency fixed coupon and paying foreign currency floating while fully hedging the currency exposure via the cross-currency basis swap.
An active strategy often involves going long (or overweight) on assets expected to appreciate and going short (or underweight) on assets expected to decline in value or appreciate less. The overweight and underweight bond positions may be denominated in different currencies, with the active strategy often using an underweight position in one currency to fund an overweight position in another.
Potential Risks
The yield curve strategy faces three potential risks:
- Yield curve movements—level, slope, or curvature—in the overweight currency.
- Yield curve changes in the underweight currency.
- Exchange rate changes.
Practice Questions
Question 1: A portfolio manager is analyzing the yield curve strategies across different currencies. The manager is considering the impact of the investor’s view of the benchmark yield and the investor’s view of currency value changes on the domestic currency return. In this context, which of the following equations correctly represents the domestic currency return on a single foreign asset, considering both the foreign currency return and the change in the value of the foreign currency?
- $$R_{DC} = \sum_{i=1}^{n} \omega_i ( 1 + R_{FC,i} ) ( 1 + R_{FX,i} ) – 1$$
- $$R = (1 + R_{DC}) (1 + R_{FX}) – 1$$
- $$R = (1 + R_{FC}) (1 + R_{FX}) – 1$$
Answer: Choice A is correct.
The equation \(R_{DC} = \sum_{i=1}^{n} \omega_i ( 1 + R_{FC,i} ) ( 1 + R_{FX,i} ) – 1\) correctly represents the domestic currency return on a single foreign asset, considering both the foreign currency return and the change in the value of the foreign currency. In this equation, \(R_{DC}\) is the domestic currency return, \(\omega_i\) is the weight of the ith asset in the portfolio, \(R_{FC,i}\) is the foreign currency return on the ith asset, and \(R_{FX,i}\) is the change in the value of the foreign currency relative to the domestic currency. The equation takes into account both the return on the foreign asset in its own currency and the impact of changes in the exchange rate on the return when converted back into the domestic currency. This is a key consideration for portfolio managers when investing in foreign assets, as changes in exchange rates can significantly affect the domestic currency return.
Choice B is incorrect. The equation \(R = (1 + R_{DC}) (1 + R_{FX}) – 1\) is incorrect because it implies that the domestic currency return is a factor in calculating the total return, which is not the case. The domestic currency return is the result of the foreign currency return and the change in the value of the foreign currency, not a factor in calculating it.
Choice C is incorrect. The equation \(R = (1 + R_{FC}) (1 + R_{FX}) – 1\) is incorrect because it does not take into account the weight of the asset in the portfolio. In a portfolio with multiple assets, each asset’s return and the change in the value of its currency must be weighted by its proportion in the portfolio to calculate the overall domestic currency return.
Question 2: A German fixed-income manager decides to invest in short-term US Treasuries to take advantage of higher yields-to-maturity. She purchases a USD Treasury zero-coupon bond maturing on 31 March 2021 at a price of 95.656, with an approximate yield-to-maturity of 2.25%. The USD/EUR spot rate at the time of purchase is 1.1218. One year later, the bond trades at a price of 100.028 and the USD/EUR spot rate is 1.1031. Which of the following statements is correct about the potential benefits for the German manager from this investment?
- The manager will benefit from bond price appreciation if the US Treasury yield-to-maturity falls during the holding period and if the USD she receives upon sale of the bond or at maturity buy fewer EUR per USD in the future.
- The manager will benefit from bond price appreciation if the US Treasury yield-to-maturity rises during the holding period and if the USD she receives upon sale of the bond or at maturity buy more EUR per USD in the future.
- The manager will benefit from bond price appreciation if the US Treasury yield-to-maturity falls during the holding period and if the USD she receives upon sale of the bond or at maturity buy more EUR per USD in the future.
Answer: Choice C is correct.
The German manager will benefit from bond price appreciation if the US Treasury yield-to-maturity falls during the holding period and if the USD she receives upon sale of the bond or at maturity buy more EUR per USD in the future. The yield-to-maturity (YTM) and bond prices have an inverse relationship. When YTM falls, bond prices rise. Therefore, if the YTM of the US Treasury falls during the holding period, the price of the bond will appreciate, resulting in a capital gain for the manager. Furthermore, if the USD/EUR exchange rate increases, the USD she receives upon sale of the bond or at maturity will buy more EUR. This means that the manager will receive more EUR for each USD she has, increasing her return on investment. This scenario is beneficial for the manager as it results in both a capital gain from the bond price appreciation and a gain from the favorable exchange rate movement.
Choice A is incorrect. The manager will not benefit if the USD she receives upon sale of the bond or at maturity buy fewer EUR per USD in the future. This would mean that the exchange rate has moved against her, reducing the amount of EUR she receives for each USD, and thus reducing her return on investment.
Choice B is incorrect. The manager will not benefit from bond price appreciation if the US Treasury yield-to-maturity rises during the holding period. As mentioned earlier, the YTM and bond prices have an inverse relationship. Therefore, if the YTM rises, the price of the bond will fall, resulting in a capital loss for the manager.
Glossary
- Functional Currency: The primary currency in which an entity conducts its operations.
- Yield Curve: A line that plots the interest rates, at a set point in time, of bonds having equal credit quality but differing maturity dates.
- Macroeconomic Factors: Factors that affect the economy as a whole, such as inflation, economic growth, and monetary policy.
- Bond Term Premium: The additional return that an investor requires to hold a long-term bond instead of a series of short-term bonds.
- Yield-to-Maturity: The total return anticipated on a bond if it is held until maturity.
- Carry Trade: A strategy in which an investor borrows money at a low interest rate in order to invest in an asset that is likely to provide a higher return.
- Forward Rate: The agreed upon price of an asset in a forward contract.
- Spot Rate: The current market price of an asset.
- Overweight: An investment position that is larger than the benchmark weight.
- Underweight: An investment position that is smaller than the benchmark weight.
Portfolio Management Pathway Volume 2: Learning Module 5: Yield Curve Strategies;
LOS 5(f): Discuss yield curve strategies across currencies.