Question

The New Zealand dollar to U.S. dollar exchange rate is 1.38, and the British pound to U.S. dollar exchange rate is 0.65. If you find that the British pound to New Zealand dollar is trading at 0.5, what would be the riskless profit per U.S. dollar invested?

Short answer

The riskless profit per U.S. dollar invested is$1.0748$.

Step-by-step solution

Concept Introduction 

The exchange rate is the rate at which domestic currency is exchanged with foreign currency. The exchange rate provides the relative price of fine in terms of domestic and foreign currency. rate is extremely volatile and it affects the economy's foreign trade. rate may be calculated as:

$\text{Exchange Rate}\left(e^t\right)=\frac{\text{Foreign pricelevel}\left({\mathrm{P}}_t\right)}{\text{DomesticPricelevel}\left({\mathrm{P}}_{\mathrm{d}}\right)}$

Explanation of solution

The exchange rate of the New Zealand dollar and US dollar is 1.36.

The exchange rate of the British pound and New Zealand dollars is 0.49.

Calculation of value of New Zealand dollars in British pound:

$$\begin{gathered} \text{Value of New Zealand dollars in British pound}=0.49\times \frac{1.36}{1}=0.6664 \\ CalculationofvalueofUSdollarsinBritishpound: \\ \text{Value of US dollar in British pound}=0.6664\times \frac{1}{0.62}=1.0748 \end{gathered}$$

Investment in US dollar assets is useful to earn riskless profits. To earn riskless profit an investor has to arbitrage. Firstly, exchange $1 into 1.36 New Zealand dollars, then exchange 1.36 New Zealand dollars into 0.6664 British pounds. Lastly, exchange 0.6664 British pounds into 1.0748 US dollars.