Step 1: Determine whether an arbitrage opportunity exists.
We can arrange the formula for covered interest rate parity to look like:
(1 + rdomestic) − [((1 + rforeign) × ForwardDC/FC) / SpotDC/FC] = 0
If this condition holds with the financial data above, there are no arbitrage opportunities.
(1 + 0.01500) − [((1 + 0.04000) × 112.99000) / 116.35000] = 1.01500 − 1.00997 = 0.00503
Since the no arbitrage condition does not hold, we move on to:
Step 2: Borrow Domestic or Foreign?
The sign on the result of step 1 is positive, so borrow foreign.
| (rd − rf) |
| (Forward − Spot) / Spot |
| (0.01500 − 0.04000) |
| (112.99000 − 116.35000) / 116.35000 |
| -0.02500 |
> |
-0.02888 |
Step 3: Arbitrage Process
|
| Description |
Rate |
Calculation |
Result |
|
| Calculate foreign equivalent & borrow this amount. |
Spot |
JPY 58,175,000 / 116.35000JPY/USD |
USD 500,000 |
|
| Invest Domestic at Domestic interest rate* |
|
JPY 58,175,000 × (1 + 0.01500) |
JPY 59,047,625 |
|
* This is the amount you will have available to repay the loan. |
|
|
|
|
|
|
|
|
|
| Calculate loan payoff (foreign currency) |
|
500,000USD × (1 + 0.04000) |
USD (520,000) |
|
| Calculate payoff in Domestic currency** |
Fwd |
520,000USD × 112.99000JPY/USD |
JPY (58,754,800) |
|
**This is the amount you need to repay. |
|
|
|
|
| Calculate Arbitrage Profit |
|
JPY 59,047,625 − JPY 58,754,800 |
JPY 292,825 |
