A foreign exchange trader faces the following quotes: Spot rate (¥/€) 148.0 3-mo

Question

A foreign exchange trader faces the following quotes:

Spot rate (¥/€) 148.0

3-month forward rate (¥/€) 145.0

3-month Japanese yen interest rate (annualized) 1.0%

3-month European euro interest rate (annualized) 2.0%

The trader has a credit line to borrow up to €30,000 (or its yen equivalent). If instead, this trader wants to implement an uncovered interest arbitrage (UIA) strategy, what steps would he or she take? Would this trade be profitable if the realized spot rates in 3 months would be ¥147.0/€?

Explanation / Answer

Spot rate (€/¥) = 1/148 = 0.006757

3-month forward rate (€/¥) 1/145. = 0.006897

Forward premuim = (0.006897 - 0.006757 / 0.006757) * 12 / 3 * 100 = 8.26%

3-month European euro interest rate (annualized) = 2.0%

as uncovered interest arbitrage (UIA) strategy,

Firm should borrow €30,000 (equivalent yen) in YEN (i.e 202.70 yen) and buy €30,000

1. Invest €30,000 @ 2% p.a. for 3 months and receive = 30000 * 1.005 = 30150

2. convert €30150 by applying 3 months forward rate and receive = ¥ 207.93

3. repay principal amount borrowed alongh with interest thereon

= 202.70 yen * 1.0025 = 203.21

Arbitrage gain = ¥ 207.93 - ¥ 203.21 = ¥4.72 or ¥4.72 * 145 = €684.4

Yes it would be profitable if the realized spot rates in 3 months would be ¥147.0/€

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