Covered Interest Arbitrage Assume that the interest rates for both the U.S. and
ID: 2640945 • Letter: C
Question
Covered Interest Arbitrage
Assume that the interest rates for both the U.S. and German banks are 2%. You borrow $1M dollars from a U.S. bank for 6 months, convert it to Euros and invest it in a German bank for 6 months. The spot rate is 1.3664 USD per EUR.
The forward rate is currently 1.3749 USD per EUR.
a) If interest rate parity holds, what should the German interest rate be?
b) Do you have an opportunity for covered interest arbitrage? Explain why or why not.
c) What is your profit in USD after 6 months on your $1M if you engage in covered interest arbitrage using a forward contract at the rate stated?
Explanation / Answer
Solution :
a) The interest rate parity is as follows:
F/So = 1+rh / 1+rf
F = forward rate ; So = spot exchange rate ; rh = domestic interest rate ; rf = foreign interest rate
1.3749 / 1.3664 = 1+0.02 / 1+rf
1.0062 X (1+rf ) = 1+0.02
rf = 1.37%
The german interest rate = 1.37%.
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b) There are 2 investment options available :
Option1: Suppose the investor borrows $ 1 million from a US bank and invest $ 1 million in another US bank which pays 2% semi annual .
The amount at the end of 6 months = $ 1,000,000 ( 1+0.02/2)2 x1
The amount at the end of 6 months if invested in US bank = $ 1,020,100
option 2 : The investor can convert $ 1 million into EUROS at the current spot rate of 1.3664 USD per EUR
and invest this money in German bank.
The equivalent amount in EUROS = 731,850.12 euros
If this money is invested in German bank paying 2% semi annual interest
The amount at end of 6 months = 731,850.12 euros ( 1+0.02/2)2x1
The amount at end of 6 months = 746,560.31 euros
At a forward rate of 1.3749 USD per EUR.
Equivalent US dollars at end of 6 months = $ 1,026,445.77
There is an opportunity for covered interest arbitrage because the value of dollar depreciates in 6 months , therefore money invested in German bank will earn interest compared to money invested in US bank .
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The profit in USD after 6 months on $1M if engaged in covered interest arbitrage using a forward contract at the rate stated = $ 1,026,445.77 - $ 1,020,100
Answer = $ 6,345.76