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Finance Jan 22, 2021

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.

Expert Solution

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.

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