Question

Given that i=0.09; i*=0.0025; F(HC/FC )= 7.80; S(HC/FC) = 7.30, discuss if there is an arbitrage opportunity. What would you do if you are an arbitrageur?

Considering the actions that arbitrageurs are likely to take, explain in detail what you expect to happen (movements) for IRP condition to hold again?

(Note: interest rates are annual and forward rate is for a 12-month contract).

Answer 1

The Interest Rate Parity (IRP) condition is as under:

F_HC/FC = Forward Rate between Home and Foreign Currency = 7.80

S_HC/FC = Spot Rate between Home and Foreign Currency = 7.30

i_HC = Interest rate for home currency = 0.09

i_FC = Interest rate for foreign currency = 0.0025

Solving the RHS of the above equation we get:

7.93 ≠ 7.80

Thus the IRP condition does not hold and there is opportunity for arbitrage.

If I were an arbitrageur, then I would undertake the following steps:

1. Borrow in foreign currency at 0.25% and convert this amount into home currency at the spot rate of 7.30.

2. Invest in the home country at 0.9% for one year and simulatenously enter into a one-year forward contract to exchange the home currency for foreign currency at the existing forward rate of 7.80.

3. After one year, redeem the investment in home country, execute the forward contract, repay the loan taken in foreign currency along with interest and earn the arbitrage profit.

The following movements are likely to occur to for IRP tp hold again:

1. As arbitraegurs keep on exchanging domestic currency for foreign currency, the spot rate is likely to go up.

2. As arbitraegurs keep on entering into the one-year forward contract to buy foreign currency at the end of the period, the one year forward rate is likely to go down.