Question

Interest Rate Parity (invest here, or invest there) China investment rate for 1 year = 7% Japan investment rate for 1 year = 1% Spot quote = 16.10 -11 CNYJPY (6 character coding, NOT fraction) 1 year forward quote = 15.40 02 CNYJPY Use the data above to determine if covered interest arbitrage is possible. Basically, you’ll do 4 math problems. Should China invest at home, or convert and invest in Japan? Should Japan invest at home, or convert and invest in China.

2. Japan invests 100 Yen in China and brings it back to Japan?

Answer 1

Spot, S = 16.10 CNY / JPY

i_China = 7%

i_Japan= 1%

For no arbitrage, Forward rate, F_{no arbitrage} = S x (1 + i_Japan) / (1 + i_China) = 16.10 x (1 + 1%) / (1 + 7%) = 15.20

F_actual = 15.40 02

Since the F_actual is not equal to F_{no arbitrage}, the covered interest arbitrage is possible.

Let's assume there is 100 CNY

• If we invest this in China for 1 year, amount = 100 x (1 + i_China) = 100 x (1 + 7%) = CNF107
• We can convert this into 100 x 16.10 = 1,610 JPY. Invest in Japan, the maturity amount will be = JPY 1,610 x (1 + i_Japan) = 1,610 x (1 + 1%) = 1,626.10. Convert it back to CNY using the forward rate = CNY 1,626.10 / 15.40 = CNY 105.59

Let's assume we JPY 100

• If we invest this in Japan for 1 year, amount = 100 x (1 + i_Japan) = 100 x (1 + 1%) =JPY 101
• We can convert this into CNY 100 / 16.10 = CNY 6.21. Invest in China, the maturity amount will be = CNY 16.21 x (1 + i_China) = 6.21 x (1 + 7%) = CNY 6.65. Convert it back to JPY using the forward rate = JPY 6.65 x 15.40 = JPY 102.35

Thus the covered interest rate arbitrage can be executed like this:

• Borrow JPY 100 in Japan; Liability after 1 year = 100 x (1 + 1%) = JPY 101
• Convert this in CNY and invest in China= CNY 100 / 16.10 x (1 + 7%) =CNY 6.65
• Convert the maturity amount back to JPY using the covered forward posiiton = JPY 6.65 x 15.40 = JOY 102.35
• Payoff the liability from step 1 = 102.35 - 101 = JPY 1.35

Thus initial investment = 0

Payoff after 1 year = JPY 1.35.

Thus we got a reward or return without any initial investment. This is the possible arbitrage we are talking about.