Question

Suppose you are given the following information:

Ft($/¥)(3 month; 90 days) = $0.0098 St($/¥) = $0.0095 it =0.04 (the annualized 3 month T-bill rate in the U.S.) it*=0.03 (the annualized 3 month T-bill rate in Japan)

Is there a covered interest arbitrage opportunity? Explain.

Check: (1+i ̃)

Compare: (1+i ̃^*)F/S

Answer 1

As per Covered Interest parity

F/S= (1+interest rate in US)^t/(1+interest rate in Japan)^t

The Theoretical Forward rate F is given by

F = S*(1+interest rate in US)^t/(1+interest rate in Japan)^t

=0.0095 * 1.04^(3/12)/1.03^(3/12)

= 0.009523

As the actual forward rate of $0.0098/Yen is higher than the theoretical forward rate, there is an arbitrage opportunity

Steps of Arbitrage

1.Today, Borrow $1 in spot market at interest rate of 0.04 or 4% for 3 months. Convert this to Yen at the spot rate of $0.0095/Yen to get 1/0.0095 = 105.2632 Yen. Invest the Yen in Japan at 3% for 3 months to a maturity value of 105.2632*1.03^(3/12) = 106.0439 Yen .

Simultaneously , Sell 106.0439 Yen in forward market at a rate of $0.0098/Yen.

2. After one year, get 106.0439 Yen and sell it using forward to get 106.0439 *0.0098 = $1.03923

Pay the $ loan of $1*1.04^(3/12) = $1.009853 and pocket the remaining $0.0292377 as arbitrage profit.