jacksparrow

The profit is AFTER paying the interest cost. You are double counting if you compare your profit to your loan. Step 1 we are paying 1.02^(90/360) = loan +interest.
So the profit above is net the interest cost.

The other point. Remember, we didn't put up 1000 yen (see first rule of arbs in prev post). So we earned 4.8562 on 0 equity capital. That's the fundamental of arbitrage. You have zero equity to start and end up with profit. We borrowed, so in essence our return is infinite or limited by our ability to borrow.

19831985

First rule of arbitrage - always, always always, use someone else's money. So borrow and pay interest, invest in something that is risklesss, and pay back loan and you still have a profit.

Here is how I would approach this:

First, since no bid-ask. Go one way around and see where you end up. If you lose try the other way.

Borrow yen enter forward rate in future. To make the math easier borrow 1,000 Yen. You then owe 1.02^(90/360)*1000 = 1004.9629 Yen in 90 days.
Convert to US @ spot 0.00812 =8.12
earn US interest rate = 8.12*1.045^(90/360) = 8.2098
Now convert to Yen using your forward rate agreement = 8.2098 / .00813= 1009.8155
Pay off loan plus interest and whats left is profit = 1009.8155 -1004.9629 =4.8526 profit

If you get a loss then go the opposite direction.

The key concept is to realize that you are calculating what the interest rate parity says things should be in the future. If you didn't have the forward, it would not be riskless arbitrage but since you can enter the forward you are locking-in your conversion back so you can make a riskless arbitrage profit.

Make sense?



Edited 1 time(s). Last edit at Saturday, May 7, 2011 at 06:11PM by stingreye.

wilslm

> Pay off loan plus interest and whats left is profit = 1009.8155 -1004.9629 =4.8526 profit

That's how I did it (which similar to how the book did it), but it is not profitable if you look at the last step. You earned 4.8562 yens, out of 1000 yens, that's a profit of 0.485% in 90 days, or about 1.94% annually, which is less than 2% the Japanese rate!