Can anyone advise on a quicker/more efficient way of arriving at the answer? I’m afraid I wont have time to do all the below calculations on the exam day…
Susan Winslow manages bond funds denominated in US Dollars, Euros, and British Pounds. Each fund invests in sovereign bonds and related derivatives. Each fund can invest a portion of its assets outside its base currency market with or without hedging the currency exposure, but to date Winslow has not utilized this capacity. She believes she can also hedge bonds into currencies other than a portfolio’s base currency when she expects doing so will add value. However, the legal department has not yet confirmed this interpretation. If the lawyers disagree, Winslow will be limited to either unhedged positions or hedging into each portfolio’s base currency.
Given the historically low rates available in the US, Euro, and UK markets, Winslow has decided to look for inter-market opportunities. With that in mind, she gathered observations about such trades from various sources. Winslow’s notes with respect to carry trades include these statements:
- Carry trades may or may not involve a maturity mismatch.
- Carry trades require two yield curves with substantially different slopes.
- Inter-market carry trades just break even if both yield curves move to the forward rates.
Regarding inter-market trades in general her notes indicate:
- Inter-market trades should be assessed based on currency-hedged returns.
- Anticipated changes in yield spreads are the primary driver of inter-market trades.
- Whether a bond offers a relatively attractive return depends on both the portfolio’s base currency and the currency in which the bond is denominated.
Winslow thinks the Mexican and Greek markets may offer attractive opportunities to enhance returns. Yields in these markets are given in Exhibit 1, along with those for the base currencies of her portfolios. The Greek rates are for euro-denominated government bonds priced at par. In the other markets, the yields apply to par sovereign bonds as well as to the fixed side of swaps versus six-month Libor (i.e., swap spreads are zero in each market). The six-month Libor rates also represent the rates at which investors can borrow or lend in each currency. Winslow observes that the five-year Treasury-note and the five-year German government note are the cheapest to deliver against their respective futures contracts expiring in six months.
Exhibit 1
Sovereign Yields in Five Markets
Floating Fixed Rate with Semi-annual Payments
6 Mo Libor 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr
Mexico 7.10% 7.15% 7.20% 7.25% 7.25% 7.25%
Greece — 3.30% 5.20% 5.65% 5.70% 5.70%
Euro 0.15% 0.25% 0.30% 0.40% 0.50% 0.60%
UK 0.50% 0.70% 0.80% 0.95% 1.00% 1.10%
US 1.40% 1.55% 1.70% 1.80% 1.90% 1.95%
Winslow expects yields in the US, Euro, UK, and Greek markets to remain stable over the next six months. She expects Mexican yields to decline to 7.0% at all maturities. Meanwhile, she projects that the Mexican Peso will depreciate by 2% against the Euro, the US Dollar will depreciate by 1% against the Euro, and the British Pound will remain stable versus the Euro. Winslow believes bonds of the same maturity may be viewed as having the same duration for purposes of identifying the most attractive positions.
Based on these views, Winslow is considering three types of trades. First, she is looking at carry trades, with or without taking currency exposure, among her three base currency markets. Each such trade will involve extending duration (e.g., lend long/borrow short) in no more than one market. Second, assuming the legal department confirms her interpretation of permissible currency hedging, she wants to identify the most attractive five-year bond and currency exposure for each of her three portfolios from among the five markets shown in Exhibit 1. Third, she wants to identify the most attractive five-year bond and hedging decision for each portfolio if she is only allowed to hedge into the portfolio’s base currency.
Q. If Winslow is limited to unhedged positions or hedging into each portfolio’s base currency, she can obtain the highest expected returns by
- buying the Mexican 5-year in each of the portfolios and hedging it into the base currency of the portfolio.
- buying the Greek 5-year in each of the portfolios, hedging the currency in the GBP-based portfolio, and leaving the currency unhedged in the dollar-based portfolio.
- buying the Greek 5-year in the Euro-denominated portfolio, buying the Mexican 5-year in the GBP and USD-denominated portfolios, and leaving the currency unhedged in each case.
Solution
B is correct. Winston should buy the Greek 5-year bond for each portfolio. In the US dollar portfolio, she should leave the currency unhedged, accepting the exposure to the Euro, which is projected to appreciate by 1% against the USD. In the UK portfolio, she should hedge the bond’s EUR exposure into GBP. In the Euro-based portfolio there is no hedging decision to be made because the Greek bond is denominated in EUR.
Because yields are projected to remain unchanged in the US, UK, Euro, and Greek markets, the 5-year bonds will still be priced at par in six months when they have 4.5 years to maturity. Hence, the local market return for each of these bonds will equal half of the coupon: 0.975%, 0.55%, 0.30%, and 2.85%, respectively. The Mexican 5-year will be priced to yield 7.0% at the end of the period. Its price will be∑t=197.25/2(1+0.072)t+100(1+0.072)9=100.9501
Its local market return is therefore 4.576% = (100.9501 + 7.25/2)/100. By covered interest parity, the cost of hedging a bond into a particular currency is the short-term (six months here) rate for the currency into which the bond is hedged minus the short-term rate for the currency in which the bond is denominated. For hedging US, UK, and Mexican bonds into Euros for six months the calculation is:USD into EUR: (0.15% – 1.40%)/2 = –0.625%GBP into EUR: (0.15% –0.50%)/2 = –0.175%MXN into EUR: (0.15% – 7.10%)/2 = –3.475%
(Note that a negative number is a cost while a positive number would be a benefit.)
Combining these hedging costs with each bond’s local market return, the returns hedged into EUR, which can now be validly compared, are:US: 0.975% + (–0.625%) = 0.350%UK: 0.550% + (–0.175%) = 0.375%MX: 4.576% + (–3.475%) = 1.101%GR: 2.850% + 0 = 2.850%EU: 0.300% + 0 = 0.300%
The Greek bond is by far the most attractive investment. This would still be true if returns were hedged into USD or GBP. So, the Greek 5-year should be purchased for each portfolio. Whether or not to actually hedge the currency exposure depends on if the cost/benefit of hedging is greater than the projected change in the spot exchange rate. For the dollar-denominated portfolio, hedging the Greek bond into USD would “pick up” 0.625% (the opposite of hedging USD into EUR). But EUR is expected to appreciate by 1.0% against the dollar, so it is better to leave the bond unhedged in the USD-denominated portfolio. Hedging EUR into GBP picks up 0.175% of return. Since EUR is projected to remain unchanged against GBP, it is better (from an expected return perspective) to hedge the Greek bond into GBP.