Question

11. Assume the interest rate on 6-month risk free debt denominated in US dollars is 1.57%, the interest rate on 6-month risk free debt denominated in Chinese yuan is 4.35%. If the spot market exchange rate for the Chinese yuan (USD/CNY) is 6.7165, what must the 6-month forward rate on the Chinese yuan be if interest rate parity holds?

12a . If the 6-month forward exchange rate for the Chinese yuan 6.7925 and the spot market exchange rate and interest rates are as indicated in question 11, what trades should you make to take advantage of the arbitrage opportunity? Be specific about both current and future transactions (i.e., be sure to specify what currency/currencies are involved and how, and the amount of each – you can make any assumption you like about the amount of currency to start).

b. How profitable is the trade? (State the profitability, either in dollars or yuan, or as a percent of initial amount borrowed.)

Answer 1

(11) Current Exchange Rate = 6.7165 CNY per $, US Interest Rate = 1.57 % and Chinese Interest Rate = 4.35 %

If Interest Rate Parity holds, then 6-month forward rate = [1+ Chinese Interest Rate / 1 + US Interest Rate] x Current Exchange Rate = [1+(0.0435/2) / 1+(0.0157/2)] x 6.7165 = CNY 6.8091 / $

(12) If the actual 6-month forward rate is 6.7925 CNY / $, instead of the interest rate parity predicted 6.8091 CNY / $ an opportunity for an arbitrage arises. The same can be executed as desrcibed below:

- Borrow $ 1 at the risk-free US interest rate of 1.57 % for 6-months. This creates a $ payable of 1 x [1+(0.0157/2)] = $ 1.00785 6-months later

- Convert the borrowed $ 1 into CNY at the current rate of 6.7165 CNY / $ to yield = (1 x 6.7165) = 6.7165 CNY

- Lend this converted CNY amount for 6-months at the Chinese Interest Rate of 4.35 % for 6-months.

- The lending yields 6.7165 x [1+(0.0435 / 2)] = CNY 6.8626

- Convert this lending yield into $ at the actual (and not predicted) forward rate to yield (6.8626 / 6.7925) ~ $ 1.01032

- The difference between the lending yield and the repayment liability is the arbitrage profit

- Arbitrage Profit = (1.01032 - 1.00785) ~ $ 0.00247

Hence, the arbitrage profit is $ 0.00247 per $ borrowed.