Question

You are given the following data:

1-year nominal risk free rate in dollar area(I_USD )=5.053%   

1-year nominal risk free rate in JPY area(I_{JPY )=}8.158%

Real risk free rate = 3.5%

Current spot exchange rate: =JPY115.60/USD   

(1) How much are the inflation rate in the Dollar area and JPY area respectively according to Fisher Effect?

(2) What is the Inflation rate differential between the two countries?

(3) What is the interest rate differential between the two countries?

(4) How much is the 1-year forward exchange rate according to Interest Rate Parity?

(5) What is the forward premium/discount on JPY?

(6) How much is the expected spot exchange rate in 1-year according to Purchasing Power Parity?

(7) What is the forecast percentage change in the spot rate of JPY?

Answer 1

Answers:

(1) Fisher effect -

The fisher effect describes relation between real rate and nominal rate. Where real rate mean a rate of interest without considering inflation and a nominal rate is risk free rate after considering inflation.

Formula : Nominal rate = real rate of interest * Inflation rate

(1+i) = (1+r)*(1+π)

Where,

i = the nominal interest rate

r = the real interest rate

π = the inflation rate

(a) Inflation rate in dollar area -

1.05053 = (1.035)*(1+π)

  (1+π) = 1.05053/1.035

(1+π) = 1.01500

Therefore π = 1.5%

(b) Inflation rate in JPY area -

1.08158 = (1.035)*(1+π)

(1+π) = 1.08158/1.035

(1+π) = 1.04500

Therefore π = 4.5%

(2) Inflation rate differential between two countries -

As per the concept of Purchasing Power Parity (PPP), the currency that has the higher inflation rate will depreciate relative to the currency with the lower inflation rate. When a currency's exchange rate behaves exactly as described here, economists state that the currency's real effective exchange rate in shorter terms, its real exchange rate was constant. The inflation rate differential is the difference between the inflation rate in one country and the inflation rate in another.

Hence,

(1+π usd) = (1+π jpy)* (1+e)

Where -

πusd = inflation rate of USD country

πjpy = inflation rate of JPY country

and e = inflation rate differential in both the countries

Therefore,

1.01500 = (1.04500)* (1+e)

e = [(1.045/1.015) - 1]*100

e = 2.956%

(3) interest rate differential between the two countries -

As per Interest Rate Differential (IRD), interest rate differential =

8.158% - 5.053% = 3.105% (approx).

(4) 1-year forward exchange rate according to Interest Rate Parity -

• The basic premise of IRP is that hedged returns from investing in different currencies should be the same, regardless of their interest rates.
• A currency with lower interest rates will trade at a forward premium in relation to a currency with a higher interest rate.

For formula please refer attached image below -

Therefore,

F0 = 115.60 * (1.08158) / (1.05053)

F0 = JPY118.40/USD

(5) forward premium/discount on JPY -

Currency JPY is trading at discount against currency USD. As a currency with lower interest rates will trade at a forward premium in relation to a currency with a higher interest rate. In given case, since interest rate of country JPY is higher than that of country USD, currency JPY shall trade at discount against currency USD.

For formula, please refer attached image below -

F¥ = Discount/premium

In our case, since direct quotation is not available, we shall use the second formula.

Hence,

Discount = (115.60 - 118.40)/118.40 *360/360*100

= -2.36% (approx)

(6) expected spot exchange rate in 1-year according to Purchasing Power Parity -

S1 = S0 * (1+ Inflation JPY)/(1+ Inflation USD)

(Where,S1 = expected spot rate in 1 year)

S1 = 115.60 * (1.04500)/(1.01500)

S1 = JPY119.02/USD (approx)

(7) forecast percentage change in the spot rate of JPY -

% change = (S1- S0)/ S0 *100

= (119.02 - 115.60) / 115.60 *100

= 2.96% (approx).