Question

A Euro-Zone bond portfolio manager is looking to invest € 1,000,000. She has a choice between either a Euro-denominated bond with a 4% annualized return, and a 6-month (180 days) maturity, or a New Zealand dollar (NZD)- denominated bond with a 7% annualized return and also a 6-month maturity. Both bonds are AA rated. If the portfolio manager is not allowed to take any FX risk (meaning she must hedge all FX risks), which of the two bonds should she choose in order to maximize her return?

Market data:

NZD/EUR Spot rate: 1.8550 / 1.8600

NZD/EUR 6-month forward rate: 1.8900 / 1.8950

Assume a 360-day year.

Answer 1

Interest rate differential = 7% - 4% = 3%

Spot rate to convert Euro 1,000,000 into NZD = 1.8550

Forward rate to convert NZD to Euro after 6 month = 1.8950

Forward Premium on Euro = [(1.8950 - 1.8550)/18550] x 360/180 x 100

= 4.31%

Since Interest rate differential is less than forward premium, there is arbitrage opportunity to invest in the country where interest rate is lower.

So, She should choose to invest in the Euro denominated bond with 4 % annualized return.

If she invest in Euro denominated bond

After 6 months investment of Euro 1,000,000 will become 1,000,000 + 1,000,000 x 4% x 180/360 = Euro 1,020,000.

If she invest in NZD denominated bond.

convert Euro 1,000,000 into NZD @ NZD 1.8550 per Euro = NZD 1,855,000

Invest in NZD denominated bond for 6 months, it will become 1,855,000 + 1,855,000 x 7% x 180/360 = NZD 1,919,925.

Convert NZD 1,919,925 into Euro at forward rate i.e. NZD 1.8950 per Euro = 1,919,925/1.8950 = Euro 1,013,153.03

Hence the gain in investing in NZD denominated bond is Euro 13,153.03, where gain in investing in Euro denominated bond is Euro 20,000. So we should invest in Euro denominated bond.

If interest rate differential would have been greater than the forward premium, there would have been arbitrage opportunity to invest in the country where interest rate is higher.