Question

4. Suppose that you are an investor based in New Zealand, and you expect the U.S. dollar to depreciate by 1.25% over the next year. The interest rate on one-year risk-free bonds is 2.25% in the United States and 3.75% in New Zealand. The current exchange rate is NZD 1.38 per USD.

(a) Calculate the foreign currency risk premium from the New Zealand investor’s viewpoint. (3 marks)

(b) If the CIP condition holds, is the NZD dollar selling at a premium or discount compared to USD? By how much? (4 marks)

(c) What is the domestic currency return (from the New Zealand investor’s viewpoint) on the U.S. bond, assuming that the New Zealand investor’s expectations are met? (4 marks)

Answer 1

S_NZD/USD =1.38 / US$

As per the concept of Interest rate parity ,Forward exchange rate

$F_{x/y}=S_{x/y}*\frac{1+i_x}{1+i_y}$

F_NZD/USD = 1.38 *(1+3.75%/1+2.25%) = 1.40 NZD/USD.

The U.S. dollar to depreciate by 1.25% over the next year , So , Forward rate E(S) = 1.38 * (1-1.25%) = 1.363

Answer a) foreign currency risk premium = (E(S) - F)/S₀ = (1.363-1.40)/1.38= -0.0268 i.e. -2.68%

for New Zealand investor’s viewpoint , the investors are in premium of 2.68%

Answer b) the NZD dollar selling at a premium ,

As per CIP Forward rate should be 1.40 NZD/USD , but actual selling at  1.363 NZD/USD

1.40 -1.363 / 1.363 = 2.71%

Answer c) Domestic currency return for NZD view point = Return in USD bond + Depreciation in USD against NZD = 2.25%+1.25% = 3.5%