Question

1. Suppose that the annual interest rate is 2.5 percent in Korea and 4.2 percent in Germany, and that the spot exchange rate is Won1933.2/€ and the forward exchange rate, with one-year maturity, is W1915.5/€. Assume that a trader can borrow up to €2,000,000 or Won3,866,400,000.

1. Does the interest rate parity hold? Show your work.
2. Is there an arbitrage opportunity? (covered interest arbitrage)
3. If there is an arbitrage opportunity, what steps should we take in order to make an arbitrage profit?
4. What will be our maximum profit?

Answer 1

Covered interest rate parity:

Forward rate, F = 1933.20 * [ 1.025/1.042]

F = 1933.20 * 0.9837 = 1901.67

No-arbitrage forward price is 1 euro = Won1901.67

b.

• No-arbitrage forward rate is 1901.67
• However, forward rate quoted in the market is 1915.50
• So there exists arbitrage opportunity.

c.

Steps:

At T = 0,

1. Borrow Won3,866,400,000 at 2.5%
2. Convert to euro at spot rate, 1 euro = Won1933.20 and euro 2,000,000
3. Invest euro in German market for 1 year at 4.5%
4. Enter into Currency Forward contract to Sell 1 euro at Won1915.50 after 1 year.

At T=1;

1. Receive the investment proceeds from the German market and get 2,084,000 [i.e; euro 2,000,000 * (1 + 0.042) ]
2. Oblige the forward contract and Sell each euro at Won1915.50 and get Won 3,991,902,000 [i.e;  2,084,000 * 1915.50 ]
3. Repay loan borrowed last year at 2.5%. Borrowed = Won 3,866,400,000 and interest at 2.5% * 3,866,400,000 = Won 96,660,000.  Total amount = Won 3,866,400,000 + Won 96,660,000 = Won 3,963,060,000
4. Arbitrage Profit =  3,991,902,000 - 3,963,060,000 = 28,842,000