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Make sure you show all your work so I can give you partial credit.
Covered Interest Parity (CIP)
Suppose that the annual interest rate on Japanese yen is 7% and the annual interest rate on U.S. dollar is 9%, respectively. The spot rate is ¥$ 142 and the 90-day forward rate is ¥$ 139.
Does covered interest parity (CIP) hold? Why?
Assume you want to invest $1,000,000. Can you make arbitrage profit? Describe your strategy (where you would borrow and where you would invest) and quantify the arbitrage profit.
Using Covered Interest rate Parity,
Forward rate = Spot Rate x [1 + rf x (n/360)] / [1 + rd x (n/360)]
The forward rate should be = 142 x [1 + 0.07 x (90/360)] / [1 + 0.09 x (90/360)] = 142 x 0.99511 = 142.3056
Since the forward rate calculated is different from the actual forward rate, there is an arbitrage opportunity.
Step 1:
Borrow $1,000,000 at 9% for 90 days, and enter into the forward contract for the rate of ¥$ 139.
Amount owed after 90 days = 1,000,000 x (1 + 0.09 x 90/360) = $1,022,500
Step 2:
Convert the borrowed amount to Yen using the spot rate
After converting, amount in Yen = 1,000,000 x 142 = ¥142,000,000
Step 3:
Invest the converted amount at the Japanese rate for 90 days
Amount at the end of 90 days = 142,000,000 x (1 + 0.07 x 90/360) = ¥144,485,000
Step 4:
Convert the amount back to dollars usinng the forward rate.
Amount after conversion = 144,485,000 / 139 = $1,039,460.43
Step 5:
Pay off the borrowed amount
Profit in 90 days = 1,039,460.43 - 1,022,500 = $16,960.43
Profit today = 16,960.43 / (1 + 0.09 x 90/360) = $16,587.22
For immediate profit, $16,587.22 can be borrowed today at 9% and repaid with the profit in 90 days.