Question

Derek Jones, a foreign exchange trader at Charles Schwab, can invest $1 million, or the foreign currency equivalent of the bank’s short-term funds, in a covered interest arbitrage with Japan. Using the following quotes, can Derek make a covered interest arbitrage profit? If so, show the steps and calculate the amount of profit in USD.

Arbitrage funds available	$1,000,000
Spot exchange rate (¥/$)	¥106.00/$
6-month forward rate (¥/$)	¥103.50/$
US dollar 6-month interest rate	4%
Japanese yen 6-month interest rate	2%

Answer 1

	This a problem on Interest Rate parity -
	It says that -		F/S =	(1+ia)/(1+ib)
	F = Forward Rate
	S = Spot Rate
	ia =	Interest rate of A
	ib =	Interest rate on B
	If this equation holds good then the exchange rate across the globe will be the same.
Yen	ia =	2%
Dollor	ib =	4%
	s =	Yen/$	106
	F =	Yen/$	103.5
	Calculate the F as per IRP =
	F/106 =	1.02^(1/2)/1.04^(1/2)			(Assuming compounded annually)
	F =	1.0198	x 106
	F =	108.0992
	Here the Should be Fwd rate is not equal to the actual fwd rate, there is a opportunity for arbitrage.
	Stepts in Arbitrage -
	Step 1 =	Borrow $ 1000000 today for 6 months at 4%
		$ payable at the end of 6 months =	1000000 x (1.04^(1/2)) =	$        10,19,803.90
	Step 2 =	Convert $ to Yen using exchange rate 106 today.
		1000000 x 106 =		¥ 10,60,00,000.00
	Step 3 =	Invest these Yen for 6 months at 2% rate.
		Yen Inflow on maturity =		106000000 x 1.02^(1/2)
				€ 10,70,54,752.35
	Step 4 =	Cover this amount using forward rate-
		Sell Yen 6 months forward at 103.5
		$ receivable at the end of 6 months =
		107054752.35/103.5 =		$        10,34,345.43
	Profit =	$ Receivable		$        10,34,345.43
		- $ payable		$        10,19,803.90
		Profit -		$              14,541.53