Mary Joe has a credit line of $1,000,000 (or equivalent in major currencies) for

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.

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