Answer:
No, a currency carry trade with positive profit can not be conducted.
Explanation:
The currency carry trade is the trading strategy where investor funding from lower-yield currency to invest in higher-yield currency with expectation to earn positive profit from the yield differences between the two currencies.
However, this strategy only works when the difference is big enough to compensate for the depreciation ( if any) of the higher-yield currency against the lower-yield currency.
With the given information, the strategy will not work because the depreciation of NZ$ against US$ after one-year is too big to be compensated for the yield difference.
For specific example, suppose the strategy is conducted, in 2008, an investor will borrow, for example, US$1 at 4.2%, exchange it to NZ$1.71. Then, invest NZ$1.71 at 9.1%.
In 2019, an investor will get NZ$1.86561 (1.71 x 1.091). The, he/she exchanges at the 2019 exchange rate, for US$1.36176 (1.86561 / 1.37). While at the same time, he will have to pay back 1 x 1.042 = US$1.042 => The loss making in US$ is US$0.32.
