Question

Rose Lever is a foreign exchange trader for a bank in New York. She observes the following​ rates: Spot exchange​ rate: ​ SF0.9872/$ ​3-month forward​ rate: SF0.9907/$ ​3-month U.S. interest​ rate: 2% per annum ​3-month Swiss interest​ rate: 4% per annum a. Can you help Ms. Lever identify whether there is an arbitrage opportunity or not by calculating the theoretical forward​ rate? b. Can you help Ms. Lever form a covered interest arbitrage strategy to generate​ profit? Please describe each step of the covered interest arbitrage and show the arbitrage profit. If she has to borrow any​ currency, please borrow​ 1,000,000. c. Please calculate the SF forward discount. Is it higher or lower than the current interest rate​ difference? Which​ action(s) in part b. would help bring the forward discount to be in line with the interest rate​ difference?

Answer 1

a) Theoretical Forward Rate = Spot rate * (1+Swiss interest rate)^n/(1+US interest rate)^n

where n is the time in years

=0.9872*(1.04/1.02)^(3/12) = SF 0.992004/$

As the actual forward rate is different than the theoretical forward rate, there is an arbitrage opportunity

b) As the actual forward rate is lesser, one has to sell the SF at the forward rate to get the benefit of arbitrage

Steps

1. Today , Borrow 1,000,000 USD for 3 months at 2%. Amount at maturity will be 1000000*1.02^(3/12) = USD 1004962.93

2. Today, Convert the amount  to SF at the spot rate of SF0.9872/$ to get 1000000* 0.9872 = SF 987200

3. Today, invest the proceeds in SF at 4% for 3 months to amount to 987200*1.04^(3/12) =SF 996927.28

4. Today, Sell the forward contract to sell SF 996927.28 and buy $ at the rate of SF0.9907/$

5. After 3 months, Get SF 996927.28 and sell them using forward to get $996927.28/0.9907 =$1006285.74

6. Repay the dollar loan of $1004962.93 and take the remaining amount of $1322.81 as arbitrage profit.

c) Spot $/SF exchange rate = 1/0.9872 = 1.012966

Forward $/SF exchange rate = 1/0.9907 = 1.009387

The forward discount of SF = (1.009387-1.012966)/1.012966 = -0.003532856

Annualised forward discount of SF = -0.003532856*4 = -0.01413 or -1.413%

It is lower than the current interest difference of 2%

As more and more people start taking arbitrage advantage, there will be many short positions on SF Futures which will correct the Forward rate , bringing it closer to theoretical forward rate of SF 0.9920/$ and forward discount to be in line with the interest rate difference