An investor examines the following rate quotes for the Brazilian real (BRL) and the Australian dollar (AUD) and shorts BRL500,000.
The risk-free arbitrage profit that is available is closest to:
We should read BRL/AUD = 1 AUD = 2.1388 BRL
I used excel so rounding may be different.
Short 500,000 BRL @ 2.1128 and buy AUD 236,653
At same time go long the BRL in the FWD market @2.1388 (see below for the size of this trade)
Have to borrow in BRL an so in 1 year have to repay 500,000 x 1.041 = 520,500
You invest 236,653 AUD @ 3.1% to get AUD 243,989
Convert this AUD 243,989 to BRL at 2.1388 = 521,843
You have more than you need to pay off you loan 521,843 - 520,500 = 1,343
The idea is that the forwrard is mispriced.
Arb free Fwd = 2.1128 x 1.041 / 1.031 = 2.13329
But Fwd quote 2.1388
I think I shouuld only be able to buy BRL at 2.13329 but in Fwd I can buy at 2.1388
So I willgo long BRL and short AUD in FWD mkt.
To balance the risk I must then short BRL in spot.
A currency trader observes the following rates:
| Spot exchange rate (Sf /d) | 1.7550 |
|---|---|
| 12-month forward rate (Ff /d) | 1.7900 |
| Domestic 12-month risk-free rate | 3.00% |
| Foreign 12-month risk-free rate | 4.50% |
A riskless arbitrage profit exists that is closest to:
Calc arb free fwd rate
1.755 x 1.045 / 1.03 = 1.780058
So arb free says in fwd mkt I can sell 1 DOM and but 1 FOR
But fwd quoted at 1 DOM = 1.79 FOR
So Buy FOR with quoted fwd,
This means sell FOR in spot
Now it depends on how much you are going to sell. 1 FOR or 1.755 FOR
Assume 1 FOR
Borrow 1 FOR at 4.5% have to pay back 1.045
Buy 0.5698 DOM deposit at 1.03 = 0.5669 covnert back to FOR @ FWd rate 1.799 = 1.0558
More than you need to pay off the load. 1.0558 - 1.045 = 0.10823
Buy you need to know how much FOR you are selling in the spot market to get an answer.