Question

Q6) In early 2012, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404 ($ per franc). Interest rates in the U.S. and Switzerland were 0.25% and 0% per annum, respectively, with continuous compounding. The three-month forward exchange rate was 1.0300 ($ per franc).

What arbitrage strategy was possible?

Answer 1

Interest rate parity theory(IRPT) is atheory which states that ''the size of the forward premium(or discount) should be equal to the interest rate differential between two countries''. If IRPT holds then the price will be in equilibrium and there will be no arbitrage profit.

Under Interest rate parity theory(IRPT),

F A/B = Forward rate (Currency A per Currency B)

S A/B = Spot rate  (Currency A per Currency B)

iA = Interest in Curreny A

i B = interest in currentcy B

t = time to expiry

Spot rate = $1.0404/Sfr

US interest rate =0.25% per annum

Switzerland interest rate = 0 % per annum

3-month No arbitrage Forward rate as per IRPT= $1.0404*[(1+0.0025*3/12) / (1+0*3/12)] = $1.0411/Sfr

But actual traded 3-Month Forwrad rate = $1.0300 /Sfr

As there is Mismatch in Forward pricing hence Arbitrage opportunity is Possible.

Conduct the Following steps to earn arbitrage gain through Covered interest arbitrage-

Step-1: Borrow 1Sfr @0% interest for 3 months and buy $1.0404 at current spot rate

Step-2: Invest $1.0404 for 3 [email protected]% interest per year

Step-3: Enter into forward contract to buy 1Sfr @$1.0300 /Sfr

Step-4: After 3 month  $ to be received from the $deposit made at Step-2 =$1.0404* (e^0.0025*3/12)=$1.0411

Step-5: Sfr payment to be made for the borrowing at step-1

=>1Sfr* (e^0*3/12) = 1Sfr [ because interest is 0%]

spep-6: Buy 1Sfr as per forward contract@$1.0300 /Sfr and repay the Sfr borrowing

$ to be paid to buy 1Sfr = 1Sfr * $1.0300 /Sfr= $1.0300

step-7:Arbitrage gain after 3 month-

Receive $1.0411- paid $1.0300 = $0.0111