The one-year CD rates for financial institutions with AA ratings are 5 percent in the U.S. and 8 percent in France. An AA-rated U.S. financial institution can borrow by issuing CDs or lend by purchasing CDs at these rates in either market. The current spot rate is $0.20/Euro.
-What should be the one-year forward rate in order to prevent any arbitrage?

Question

Quizplus · Accepted Answer

To prevent arbitrage, we need to compare the return from investing in the US and France. Let us assume an investment of $1,000. 
In the US: 
- Invest $1,000 in CDs at 5% for 1 year = $1,050
- Convert $1,050 to Euros at the current spot rate: $1,050/0.20 = €5,250 
In France:
- Invest $1,000 in CDs at 8% for 1 year = $1,080 
- Convert $1,080 to Euros at the current spot rate: $1,080/0.20 = €5,400 
If the 1-year forward rate is F, then the return from investing in the US and converting to Euros should be the same as the return from investing in France and converting to Euros: 
$1,000*(1+0.05)*(1+F) = $1,000*(1+0.08)*(1/0.20) 
1.05*(1+F) = 1.08/0.20 
1.05*(1+F) = 5.40 
1+F = 5.40/1.05 
F = 5.14/5 = $0.1944/€
Therefore, the one-year forward rate should be $0.1944/€ to prevent arbitrage.

The One-Year CD Rates for Financial Institutions with AA Ratings