Question

Toshi Numata, FX analyst at Credit Suisse (Tokyo), observes that the ¥/$ spot rate has been holding steady, and both U.S. dollar and yen interest rates have remained relatively fixed over the past few weeks. Toshi wonders if he should try an interest arbitrage strategy. Toshi's research associates — and their prediction models — are predicting the spot rate to move to ¥100.00/$ 90 days from today. Assume each year has 360 days and the interest rate for short loans is priced using the simple interest rate method.

Table 2. – Use for Questions a) to c)

Assumptions Value

Arbitrage funds available (¥) YEN 80,000,000

Equivalent arbitrage funds available ($) USD 1,000,000

Spot rate (¥/$) 80.00

90-day forward rate (¥/$) 90.00

180-day forward rate (¥/$) 95.00

U.S. dollar LIBOR rate p.a. for the next 180 days 2.000%

  Japanese yen LIBOR rate p.a. for the next 180 days 0.000%

a) Calculate the expected gain in $ from an Uncovered Interest Arbitrage (UIA) strategy using the expected spot rate in 90 days predicted by Toshi’s research associates.

b) The actual spot rate 90 days from today turned out to be72.00 (¥/$) instead of 100 (¥/$) as predicted. Discuss how Toshi’s interest arbitrage strategy in question a) is affected.

c) Discuss how a Covered Interest Arbitrage strategy is different from an Uncovered Interest Arbitrage strategy.

Answer 1

Part (a)

Arbitrage funds available (¥), F_Yen = YEN 80,000,000

Equivalent arbitrage funds available ($), F_$ = USD 1,000,000

Current Spot rate (¥/$), S₀ = 80.00

Expected spot rate after 90 days (¥/$), S₁ = 100.00

We invest F_$ at $ interest rate, i_$ = 2.000% for 90 days to get the maturity proceed = F_{$, maturity}= F_$ x (1 + i_$ x n / 360) = 1,000,000 x (1 + 2% x n / 360) = 1,000,000 x (1 + 2% x 90 / 360) = $  1,005,000

If F_Yen is invested at Yen interest rate, i_Yen = 0.000% for 90 days to get the maturity proceed = F_{Yen, maturity} = F_Yen x (1 + i_Yen x 90 / 360) = YEN 80,000,000 x (1 + 0% x 90 / 360) = YEN 80,000,000

$ equivalent of this amount = F_{Yen, maturity} / S₁ = 80,000,000 / 100 = $  800,000

Hence, the expected gain in $ from an Uncovered Interest Arbitrage (UIA) strategy using the expected spot rate in 90 days predicted by Toshi’s research associates = F_{$, maturity}- 800,000 = $ 1,005,000 - 800,000 = $  205,000

Part (b)

S₁ = 72

$ equivalent of the maturity amount = F_{Yen, maturity} / S₁ = 80,000,000 / 72 = $ 1,111,111

Hence, the expected gain in $ from an Uncovered Interest Arbitrage (UIA) strategy using the expected spot rate in 90 days predicted by Toshi’s research associates = F_{$, maturity}- 1,111,111 = $ 1,005,000 - 1,111,111 = - $ 106,111

Toshi’s interest arbitrage strategy in question a) is adversely affected. The profitable position has turned to a loss making position.

Part (c)

In a covered interest arbitrage, the trader takes a forward contract to hedge against the exchange rate in future. The forward rate is locked in today itself.

• If the interest rate differential between the two currency is higher than the forward premium (discount) or expected change in spot rate then, the trader makes an arbitrage by  invest in the higher interest yielding currency. The forward rate premium does not negate the profit completely.
• If the interest rate differential is less than the forward premium (or expected change in the spot rate), the trader makes the arbitrage by investing in the lower yielding currency.

So, the main differences between uncovered interest and covered interest arbitrage are as follows:

Sl. No.	Situation	Uncovered Interest arbitrage	Covered interest arbitrage
1.	Exchange rate risk	Uncovered, fully exposed to exchange rate fluctuation.	Covered, exchange rate risk is mitigated through forward position,
2.	Gains and Losses	Losses and gains both can be infinite.	losses / gains are regulated