Question

5. Covered Interest Arbitrage. The one-year interest rate in New Zealand is 6 percent. The one-year U.S. interest rate is 10 percent. The spot rate of the New Zealand dollar (NZ$) is $.50. The one-year forward rate of the New Zealand dollar is $.54.

a) Is covered interest arbitrage feasible for U.S. investors?

b) Is it feasible for New Zealand investors? In each case, explain why covered interest arbitrage is or is not feasible.

Answer 1

a) To determine whether covered interest rate arbitrage in possible or not for US investors

Current Spot rate = $0.50 / NZ$

We assume, US investor start with $100 or borrow $100 at US interest rate of 10% per annum

First we convert today $100 into NZ$ at current spot rate, we get $100 = 100 / 0.50 =NZ$ 200

Invest NZ$ 200 at 6% New Zealand interest rate for 1 year

Amount of NZ$ after 1 year = 200(1+6%) = NZ$ 212

Forward rate = $0.54 / NZ$

Converting NZ$ back to US$ at forward rate after 1 year, we NZ$ 212 = 212 x 0.54 = $114.48

Hence Amount of US$ after 1 year with US investor = 114.48

Yield for US investor = (Amount after 1 year in $ / Initial amount) - 1 = (114.48 / 100) - 1 = 1.1448 - 1 = 0.1448 = 14.48%

Since Yield for US investor is greater than US interest rate(cost of borrowing for US investor), Hence Covered interest arbitrage is possible for US investor.

b)

To determine whether covered interest rate arbitrage in possible or not for New Zealand investors

Current Spot rate = $0.50 / NZ$

We assume, New Zealand investor start with NZ$100 or borrow NZ$100 at New Zealand interest rate of 6% per annum

First we convert today NZ$100 into US$ at current spot rate, we get NZ$100 = 100 x 0.50 =$50

Invest US$ 50 at 10% US interest rate for 1 year

Amount of US$ after 1 year = 50(1+10%) = US$ 55

Forward rate = $0.54 / NZ$

Converting US$ back to NZ$ at forward rate after 1 year, we US$55 = 55 / 0.54 = NZ$101.8518

Hence Amount of NZ$$ after 1 year with New Zealand investor = NZ$101.8518

Yield for New Zealand investor = (Amount after 1 year in $ / Initial amount) - 1 = (101.8518 / 100) - 1 = 1.018518 - 1 = 0.018518 = 1.8518%

Since Yield for New Zealand investor is less than New Zealand interest rate(cost of borrowing for New Zealand investor), Hence Covered interest arbitrage is not possible for New Zealand investor.