Question

Using the yen per dollar exchange rate of 120yen/€1 and the 6 months $libor is 4% per annum and the 6 month Yen libor is 7% per annum

You must calculate a 6-month forward rate.

Show how CIP represents an arbitrage concept.

Answer 1

yen per dollar

120

6 month $ Libor

4%

per annum

6 month Yen libor

7%

per annum

Forward rate can be computed using CIP =

F = S *(1+if)/(1+id)

F= forward rate

S = Spot rate

120

If= interest rate prevailing at foreign country for 6 month

2.0%

id= interest rate prevailing at domestic country for 6 month

3.5%

Forward rate

121.76

CIP represents an arbitrage concept

Covered interest parity sayd that no arbitrage opportunity exit in equilibrium market. Forward rate will take into account interest rate differences between two countries in a manner that profit earned due to interest rate difference will offset by losses in forward contract.

Lets take this example

Interest rate difference in two country = 7%-4%

3.0%

per annum

borrow in US currency and invest in Yen .

Borrow say $1million in US currency for 6 month @4% per annum

Use this sale proceed in cash market to convert in Yen =$1mill*120

120,000,000

Yen

Invest or lend Yen @ 7% PA for 6 month

Enter into forward rate agreement to convert Yen for USD after 6 month = yen121.76/USD

Money received after 6 month in Yen = 120million*7%/2 +120million

124,200,000

yen

Convert Yen to USD using Forward rate = Yen 124.2million/121.76

$         1,020,000

Money payable in USD after 6 month = 1million+1million*4%/2

$         1,020,000

Hence, we are seeing money received and money to be paid in USD is exactly same and no arbitrage opportunity exists in equilibrium market

Had there been no CIP and forward rate were different we could have made money using arbitrage opportunity