Mary Joe has a credit line of $1,000,000 (or equivalent in major currencies) for
ID: 2474122 • Letter: M
Question
Mary Joe has a credit line of $1,000,000 (or equivalent in major currencies) for arbitrage. She had access to the following rates, and she managed to generate CIA profits. Replicate her arbitrage and calculate her profits based on the following rates:
Assumptions
Value
SFr. Equivalent
Arbitrage funds available
$1,000,000
SFr. 1,281,000
Spot exchange rate (SFr./$)
1.2810
3-month forward rate (SFr./$)
1.2740
U.S. dollar 3-month interest rate
4.800%
pa
Swiss franc3-month interest rate
3.200%
pa
Note that interest rates are expressed in annualized terms!
Assumptions
Value
SFr. Equivalent
Arbitrage funds available
$1,000,000
SFr. 1,281,000
Spot exchange rate (SFr./$)
1.2810
3-month forward rate (SFr./$)
1.2740
U.S. dollar 3-month interest rate
4.800%
pa
Swiss franc3-month interest rate
3.200%
pa
Explanation / Answer
We are dealing with 3 month forward rate The interest rate parity condition Forward Rate / Spot Rate = (1+ Swiss interest rate x 3/12) / (1+ US interest rate x 3/12)
We calculate theoretical Forward rate using Interest rate parity condition
or Forward Rate = Spot Rate x (1+ Swiss interest rate x 3/12)/(1+ US interest rate x 3/12)
or Forward Rate = 1.2810 SFr/ $ x (1+ 3.2% x 3/12) / (1+ 4.8% x 3/12)= 1.2759 SFr/$
But actual 3 month Forward rate is 1.2740 SFr/$
Thus, there is a breakdown in interest rate parity
"Covered interest arbitrage (CIA) involves taking advantage of a breakdown in interest rate parity to earn an arbitrage (risk-free profit) without committing one’s own capital.
"Forward $ @1.2740 SFr/$ is cheaper than the theoretical Forward rate of 1.2759 SFr/$
For Arbitrage, sell dollars in spot market and buy dollars in the forward market
Now (t=0)
Borrow $1,000,000 @ 4.80% for 3 months
Amount to be repaid after 3 months= $1,012,000 =$1,000,000. x (1+4.8% x 3/12)
Convert $1,000,000 into SFr at the current spot rate of 1.2810 SFr/$
Amount in SFr received= 1,281,000 =$1,000,000. x 1.281
Invest 1,281,000 SFr @ 3.20% for 3 months
Amount to be received after 3 months=SFr 1,291,248 =1,281,000. x (1+3.2% x 3/12)
Enter into a forward contract to sell dollars @ 1.2740 SFr/$ after 3 months
After 3 months (t=3 months)
Receive SFr 1,291,248
Convert to dollars using the forward contract
Dollars received= $1,013,538.46 =1,291,248. / 1.274
Repay principal and interest on borrowing= $1,012,000
Arbitrage profit= $1,538.46 =$1,013,538.46 - $1,012,000.