Question

Key rates:

U.S.: 1.50% return on $-denominated bond.

Japan: 0.20% return on ¥-denominated bond.

Forward: ¥106.952/$.

What is the equilibrium spot exchange rate between $ and ¥?

If the spot exchange rate is ¥108.734/$, show the transactions to conduct the CIA.

Draw a graph of international interest rate parity as those shown in the lecture notes to illustrate and explain your calculations in details.

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 prodit.

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

Here $ Return or interest = 1.50%

Yen return or interest = 0.20%

as the time is not gven , hence lets assume t = 1 year.

Forward rate = ¥106.952/$.

Hence

¥106.952/$. = Spot rate * (1.0020)/ (1.0150)

=>Spot rate = ¥108.340/$

hence the No arbitrage or equilibrium Spot rate = ¥108.340/$

But the actual traded spot exchange rate is ¥108.734/$

If actual spot rate is ¥108.734/$, then the IRPT forward rate = 108.734*(1.0020)/ (1.0150)

=>IRPT forward rate = ¥107.341/$

But the actual Forward rate = ¥106.952/$.

transactions to conduct the CIA(Covered interest Arbitrage)-

Step-1: Borrow $1 @01.50% interesst and buy ¥108.734

Step-2: Invest ¥108.734for 1 [email protected]% interest paer year

Step-3: Enter into forward contract to buy $ @¥106.952/$.

Step-4: After 1 year ¥ to be received from the ¥ deposit made at Step-2 =¥108.734*(1.002)= ¥108.951

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

=>$1* (1.015) = $1.015

spep-6: Buy $1.015 as per forward contract@¥106.952/$ and repay the $ borrowing

Yen to be paid to buy $1.015 = $1.015*¥106.952/$= ¥108.556

step-7:Arbitrage gain after 1 year-

Receive ¥108.951- paid ¥108.556 = ¥0.395

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