In: Finance
You can currently borrow or invest in the US at 2% and you can borrow or invest in Japan at 3%. The current exchange rate is $0.01/Yen. Inflation rate in the US is expected to be 5% and expected to be 1% in Japan. If the exchange rates will have adjusted to differences in inflation by the end of one year, show how these numbers will allow you to make profit. Be Specific. Show the profit you would make at the end of the year if you started by borrowing EITHER (choose one) $1 million or 1 million Yen today. Please show all work and do not use excel or a finance calculator.
$ | Yen | |
Borrowing/Deposit Rate | 2% | 3% |
Inflation Rate | 5% | 1% |
Amount available | $ 1 Million |
Spot Rate | $0.01/Yen |
1 Year Forward Rate | $0.0104/Yen |
As per Purchasing Power Parity Theorem, |
Forward Exchange Rate$ = Spot$ ( 1 + I$) / ( 1 + IYen) |
Forward Exchange Rate$ = 0.01 ( 1 + 0.05) / ( 1 + 0.01) |
Forward Exchange Rate$ = 0.0104 |
As per the Interst rates prevailing: |
Fair Forward Exchange Rate$ = 0.01 ( 1 + 0.02) / ( 1 + 0.03) |
Fair Forward Exchange Rate$ = 0.0099 |
a | Borrow $ 1 Million |
b | Convert to Yen, We receive $ 1 Million / $ 0.01 = Yen 100,000,000 |
c | Deposit Yen received for 1 Year |
Amount Recieved in Yen after 1 year = $ 100,000,000 (1+0.03) | |
Amount Recieved in Yen after 1 year = $ 103,000,000 | |
d | Reconvert the Amount received in Yen to $ |
We will receive, $ 103,000,000 / $ 0.0104 = 1,071,200 | |
e | Amunt required for repayment of Amount Borrowed = $ 1,000,000 (1+0.02) |
Amunt required for repayment of Amount Borrowed = $ 1,020,000 | |
f | Arbitrage Profit = d - e |
Arbitrage Profit = $ 1,071,200 - $ $1,020,000 | |
Arbitrage Profit = $ 51,200 |