MBA (Finance specialisation)
&
MBA – Banking and Finance
(Trimester)
Term VI
Module : – International Financial Management
Unit II: Foreign Exchange Markets
Lesson 2.3
(Theories of Exchange rate – Interest rate parity theory and International fisher effect )
Interest Rate Parity relationship
This relationship links interest rates of two countries
with spot and future exchange rates. It was made
popular in 1920s by economists such as John M.
Keynes. The theory underlying this relationship says
that premium or discount of one currency against
another should reflect interest rate differential
between the two countries. In perfect market
conditions, where there are no restrictions on the
flow of money and there are no transaction costs, it
should be possible to gain the same real value of
one's monetary assets irrespective of the country (or
currency) in which they are invested.
Interest Rate Parity relationship
For example, an investor has one unit of pound sterling. He
can invest it in the UK money market and earn an interest of
it on it. The resulting value after one year will be:
£1 (1 +i£)
Alternatively, he can buy So dollars (the current exchange
rate being So dollars = 1 pound sterling) and invest this
dollar amount in US money market. The end value after
one year will be:
$So (1 + i$)
The equilibrium condition demands that these two sums be
equal. If the two sums were not equal, then the investor
would invest in that currency where the end value of
their monetary assets is going to be more.
Interest Rate Parity relationship
But once this action is generalized by the similar expectations of
all investors, equilibrium is going to be reestablished. Thus, in
equilibrium situation,
$S0 (1 + i$) = £1(1 + i£)
$S0 [ (1 + i$)/(1 + i£) ] = £1
This expression on the left side of the above equation is future
exchange rate. We can write
S1 = S0 [ (1 + i$)/(1 + i£) ]
This expression can be written for any two currencies, A (home
currency) and B (foreign currency), by replacing dollar and
pound sterling. Thus,
S1 = S0 [ (1 + iA)/(1 + iB)].
The above equation is known as Interest rate parity relationship.
Interest Rate Parity relationship
S1 = S0 [ (1 + iA)/(1 + iB)].
For simplicity, we can re write the above equation as
F = S [ (1 + ihome)/(1 + iforeign)]
Or
F/S = [ (1 + ihome)/(1 + iforeign)]
Subtracting ‘1’ from both the sides , we have
(F – S)/S = [(ihome – iforeign )/ (1 + iforeign)]
As a limiting case, if we assume that foreign interest rates are small as
compared to unity then the denominator (1 + iforeign) in the limit tends to
‘1’ and the above relation would be given as
(ihome – iforeign ) = Premium/Discount for a unit period
i.e. the forward premium and discount rate are to be equal to interest
rate differential between the domestic and foreign interest rates for no
interest arbitrage situations.
Interest Rate Parity relationship
S1 = S0 [ (1 + iA)/(1 + iB)].
For simplicity, we can re write the above equation as
F = S [ (1 + ihome)/(1 + iforeign)]
Or
F/S = [ (1 + ihome)/(1 + iforeign)]
Subtracting ‘1’ from both the sides , we have
(F – S)/S = [(ihome – iforeign )/ (1 + iforeign)]
As a limiting case, if we assume that foreign interest rates are small as
compared to unity then the denominator (1 + iforeign) in the limit tends to
‘1’ and the above relation would be given as
(ihome – iforeign ) = Premium/Discount for a unit period
i.e. the forward premium and discount rate are to be equal to interest
rate differential between the domestic and foreign interest rates for no
interest arbitrage situations.
Interest Rate Parity relationship
The arbitrage process due to difference in forward
premium/discount and interest rate differential would
become clear from the following examples:
Rule 1: If (F-S)/S X 12/N x 100 is less than ( R(Home) – R(foreign)
Borrow money from foreign country
 Convert into home currency using spot rate
Invest in home country at R(home)
Reconvert the money into foreign currency using forward
rate.
The money available after reconversion will be more than
(money borrowed in foreign currency + interest on money
borrowed in foreign currency).
Interest Rate Parity relationship
Consider example given below
Given ( Home Country : India , Foreign Country : U.S.)
Spot Rate (Rs/$) = 62
6 mths Forward rate = 62.5
Interest rate in India = 12%
Interest rate in U.S. = 8%
Step 1: Calculate forward premium/discount using the formula
(F-S)/S X 12/N x 100
Forward premium/discount = [(62.5 – 62)/62 ] x (12/6) x 100 =
1.612
Dollar is at premium
Step 2: Given interest rate differential ( Rindia – Rus ) = 4%
Step3: Since interest rate differential is greater than forward
premium, borrow from the country where interest is lower and
invest in the country where interest rate is higher.
Interest Rate Parity relationship
Step 4: Borrow $ 10000 at the rate of 8% p.a.
Dollars to be refunded after six months = 10000 +
Interest for six months @ 8% (400) = $ 10,400
Step 5 Convert dollars into rupees using spot rate
10000 x 62 = Rs 62000
Step 6 Invest rupees at the rate of 12% p.a. for six
months: 62000 ( 1.06) = 657200
Step7: Covert Rs 657200 into dollars using
forward rate : 657200/62.5 = $ 10515.2
Step 8: Gain = $ (10515.2 – 10400) = $ 115.2
Interest Rate Parity relationship
Rule 2: If (F-S)/S X 12/N x 100 is more than ( R(Home) – R(foreign)
 Borrow money from home country .
 Convert into foreign currency using spot rate.
Invest in foreign country at R(foreign) .
Reconvert the money into home currency using forward rate.
The money available after reconversion will be more than
(money borrowed in home currency + interest on money borrowed
in home currency).
Interest Rate Parity relationship
Consider example given below
Given Home Country : India , Foreign Country : U.S.
Spot Rate (Rs/$) = 62
6 mths Forward rate = 63
Interest rate in India = 12%
Interest rate in U.S. = 10%
Step 1: Calculate forward premium/discount using the formula
(F-S)/S X 12/N x 100
Forward premium/discount = [(63 – 62)/62 ] x (12/6) x 100 = 3.225806
Dollar is at premium
Step 2: Given interest rate differential ( RIndia – R u.s.) = 2%
Step3: Since interest rate differential is smaller than forward premium, borrow
from the country where interest is higher and invest in the country where
interest rate is lower.
Interest Rate Parity relationship
Step 4: Borrow Rs 10000 at the rate of 12% p.a.
Rupees to be refunded after six months = 10000 + Interest for six
months @ 12% (600) = $ 10,600
Step 5 Convert rupees into dollars using spot rate
10000 / 62 = 161.29
Step 6 Invest dollars at the rate of 10% p.a. for six months
161.29 ( 1.05) = 169.35
Step7: Convert $ 169.35 into rupees using forward rate
169.35 x 63 = 10669.35484
Step 8: Gain = Rs (10669.35 – 10600) = Rs 69.35
International Fisher effect
According to relative form of purchasing parity theory
Forward /premium discount = difference in inflation rate of two countries
According to interest rate parity theory
Forward /premium discount = difference in interest rate of two countries.
Combining the two , we have ,
Difference in inflation rate = Difference in interest rate , or
(rhome – rforeign ) = (ihome – iforeign )
(rhome – ihome ) = (rhome – iforeign )
The above equation implies that , in the absence of
restrictions on trade flows and capital flows the expected
real rate of return on capital tends to equalise. The above
equation is referred as Fisher Open Condition or
International fisher effect.