Question

You have $1,000,000 to start with. Here are the facts:

Yen Spot Rate = 106 Yen/$ Yen

Fwd Rate = 103.5 Yen/$ 6 months

Interest Rates in Japan are 4% per annum (2% for 6 months).

Interest Rates in the USA are 8% per annum (4% for 6 months) for securities of similar risk and maturity.

What should you do?

Answer 1

First we need to calculate is there is any arbitrage possible or not.

According to the law of one price difference of interest rates in two countries should be same of difference of exchange rates between two countries.

Forward rate (Yen/$) / Spot rate (Yen / $) = ( 1 + Interest rate of Japan) / ( 1 + Interest rate of USA)

103.5 / 106 = 2% / 4%

They are not equal Hence there is arbitrage possible.

We have two options

Option 1:- We invest in USA

Option 2. We invest in Japan

We see in future yen is increases as compare to dollar and their interest difference is lower than their exchange difference.

Since we have $1000,000 we will do the following steps

Step 1. = Convert Dollar into yen with spot rate

Step 2. = Invest money in Japan and earn interest

Step 3. Convert Yen into Dollar at maturity.

Yen = $1000,000 * 106 = Yen 106,000,000

After investment in japan total amount receive = Yen 106,000,000 * 2% = Yen 108,120,000

Convert Yen into dollars with forward rate = Yen 108,120,000 / 103.5 = $1044638

Total profit = ( $1000000 - $1044638) = $44638

If we invest the amount in USA = $1000000 +4% = 1040000

Total Profit = $40000

We should invest in japan.