Assume the following information for a bank quoting on spot exchange rates:
$$\begin{array} { l l r }
\text { Exchange rate of Singapore dollar in U.S. } \$ & = & \$ .32 \
\text { Exchange rate of pound in U.S. } \$ & = & \$ 1.50 \
\text { Exchange rate of pound in Singapore dollars } & = & \text { S } \$ 4.50
\end{array}$$
Based on the information given, as you and others perform triangular arbitrage, what should logically happen to the spot exchange rates?
A) The Singapore dollar value in U.S. dollars should appreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should depreciate.
B) The Singapore dollar value in U.S. dollars should depreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should depreciate.
C) The Singapore dollar value in U.S. dollars should depreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should appreciate.
D) The Singapore dollar value in U.S. dollars should appreciate, the pound value in U.S. dollars should depreciate, and the pound value in Singapore dollars should appreciate.

Question

Assume the following information for a bank quoting on spot exchange rates:
$$\begin{array} { l l r } 
\text { Exchange rate of Singapore dollar in U.S. } \$ & = & \$ .32 \
\text { Exchange rate of pound in U.S. } \$ & = & \$ 1.50 \
\text { Exchange rate of pound in Singapore dollars } & = & \text { S } \$ 4.50
\end{array}$$
Based on the information given, as you and others perform triangular arbitrage, what should logically happen to the spot exchange rates?
A) The Singapore dollar value in U.S. dollars should appreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should depreciate.
B) The Singapore dollar value in U.S. dollars should depreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should depreciate.
C) The Singapore dollar value in U.S. dollars should depreciate, the pound value in U.S. dollars should appreciate, and the pound value in Singapore dollars should appreciate.
D) The Singapore dollar value in U.S. dollars should appreciate, the pound value in U.S. dollars should depreciate, and the pound value in Singapore dollars should appreciate.

Quizplus · Accepted Answer

According to the information given, doing a triangular arbitrage would involve buying pound with USD, selling the pound for Singapore dollars, and then selling the Singapore dollars for USD. Starting with $1, we would get:

1. Buy pound with USD: $1 / $1.50 = £0.67
2. Sell pound for Singapore dollars: £0.67 * \$4.50 = S\$3.02
3. Sell Singapore dollars for USD: S\$3.02 * $0.32 = $0.97

Since we started with $1 and ended up with $0.97 after performing the arbitrage, it means that the USD has depreciated relative to the other two currencies involved. Therefore, the Singapore dollar value in U.S. dollars should appreciate (since it took fewer USD to buy 1 SGD in step 3 than it did before), the pound value in U.S. dollars should depreciate (since we sold pounds for fewer USD in step 1 than it took to buy them initially), and the pound value in Singapore dollars should appreciate (since we had to pay more SGD for 1 GBP in step 2 than we were initially quoted). Therefore, choice D is the correct answer.

Assume the Following Information for a Bank Quoting on Spot