Question

# 11. Suppose that on January 1, the cost of borrowing Japanese yen for the year is...

11. Suppose that on January 1, the cost of borrowing Japanese yen for the year is 4%. Market expectation for the inflation is 3% in the U.S. and 2% in Japanese. At the same time, the spot rate is ¥111.2/\$ on January 1 while the 12 month forward rate is ¥108.5/\$.

a. What is the interest rate expected in U.S. if the interest rate parity holds?

What is the real interest rate in Japan and what is the real interest rate in the U.S. according to the Fisher Effect?

Solution :-

If the interest rate Parity holds =

FR Rate x/y / Spot Rate x/y = ( 1 + Intt Rate X ) / ( 1 + Intt Rate Y )

108.50 / 112.20 = ( 1 + 0.04 ) / ( 1 + Y )

( 1 + Y ) = 1.04 / 0.967

( 1 + Y ) = 1.0755

Y = 0.0755 = 7.55%

Therefore Expected Interest Rate in US = 7.55%

Now As per Fisher Effect =

( 1 + NIR ) = ( 1 + RIR ) * ( 1 + Inflation )

( 1 + RIR ) = ( 1 + NIR ) / ( 1 + Inflation )

Now RIR = [ ( 1 + NIR ) / ( 1 + Inflation ) ] - 1

Where NIR = Nominal Interest Rate

RIR = Real Interest Rate

In case of Japan

RIR = [ ( 1 + 0.04 ) / ( 1 + 0.02 ) ] - 1 = 0.0196 = 1.96%

In case of US

RIR = [ ( 1 + 0.0755 ) / ( 1 + 0.03 ) ] - 1 = 0.0442 = 4.42%

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