International Parity Conditions Explained

International Parity
Condition
Kanchan kandel
1kanchan.kandel399@gmail.com

International Parity Conditions
Law of one price
Absolute form of Purchasing Power Parity
Relative form of Purchasing Power Parity
Reasons for departure from PPP
Covered Interest Parity Condition
Reasons for violation of interest parity condition
Uncovered/open Interest Parity Condition
Combined PPP and Interest Parity

Law of One Price
When there is a difference of price of a product in two places,
there is possibility of arbitrage. Arbitrage is thus an act of buying
a product cheaper in one place and of selling the same product in
higher price in another place. The parties involved in arbitrage
are referred as arbitragers.
According to “Law of one price”, in the absence of
transportation and other cost (such as monopolist, tax)
completive market will equalize the price of an identical tradable
goods in two countries when price are express in same currency.
Thus, if Pi is the per kg price of rice in Nepal, P*i is the per kg
price of rice in USA and S(Rs/$) is the exchange rate of NPR
against USD, then as per the law of one price,
Pi = S($/£) x P*i ----- Equation (I)
Pi=E x Pi*

Law of One Price (contd..)
In case the law of one price is not valid, the buying decision helps in
bringing the condition as stated by the law of one price
Example: Suppose Pi= NPR 90 per kg, P*i= USD 1.5 per kg and
S($/£) is 65, then the Rupee equivalent price of rice in USA is NPR
65/USD x USD1.5/kg = NPR 97.5/kg. Having the price of rice
per kg in Nepal as NPR 90 only, there will be buying of rice from
Nepal only and not from USA, thus resulting in higher Nepal price
and falling USA price until they satisfy the law of one price.

Purchasing Power Parity (PPP) Principle
The equation (I) is:
Pi = S(Rs/$) x Pi*
thus, S(Rs/$) = Pi/ Pi* ------ Equation (II)
or E= Pi/Pi*
Thus, the equation (II) is the Purchasing power parity (PPP)
principle which postulates that exchange rates must move to
compensate for price of same product differentials.

Absolute form of Purchasing Power Parity (PPP)
Principle
In the absence of international trade barrier, price of same basket of
product in two countries should be equal , when measuring in a
common currency.
Absolute PPP principle is based on law of one price(LOP) but it takes
basket of goods not individual i.e.
∑P = Ex ∑P*……….III
Here, ∑P and ∑P* are the costs (price) of the basket of goods and
services in Nepal in Rupees and in USA in Dollars respectively.
Thus, this form of PPP gives a simple explanation of changes in
exchange rates.
It is difficult to test the validity of absolute form of PPP principle
because different baskets of goods are used in different countries for
computing price indexes. Different baskets are used because tastes and
needs differ from country to country.

Cont…
Weight given to different goods in basket will also make difficulty
to measure validity of PPP.
It is not appropriate in non tradable goods i.e. service, because you
will not go for dental service in china because of low cost of dental
service as compare to Nepal.

Relative form of Purchasing Power Parity (PPP)
Principle
Relative form of PPP principle is nothing but the same expression as in
Absolute form of PPP principle, but made in terms of percentage
change over a period of time.
suppose price of product of domestic country is currently P and one
year expected inflation for the country is I then after one year country
price of product will be P(1+I)
Again price of foreign product is P* and expected inflation for next
year is I* then after one year foreign country price of product will be
P* (1+I*)
And current exchange rate is S and the change in exchange rate for next
year is e* then expected exchange rate (S*) for next year will be E
(1+E*).
Now replacing this values on equation 1 (P=E P*)
P (1+I)=E(1+e*) p*(1+I*) ….IV {here we just replace P =EP* by
new or after one year price of domestic and foreign goods and
exchange rate.}

Cont….
by rearranging equation I and IV we get
P* E (1+ I) =E(1+ e*)P* (1+ I*) { replacing P by P*E
because we have P=EP*)
Or
e*={(1+I)/1+I*)}-1……….V (for exact calculation)
e*= I-I* ……. VI for approximate calculation

Relative form of PPP Principle (Contd..)
In above equation (V), the PPP principle is on relative form which
explains about the relationship between the change in inflation and the
change in exchange rate.
Example of Relative form of PPP principle:
If inflation of US= 5%, Inflation of UK is = 10%, then the value of
GBP against USD should fall as follows:
e*(USD/GBP) = {(1+I)/(1+i*)}-1
=(1+.05)/(1+.10)}-1
=.95454-1=0.04545
If change in price (i.e., inflation) in USA is higher than in UK, then the
value of GBP against USD should appreciate.
• From aprox formula we can get change in exchange rate (e*) is (I-
I*)=10%-5%= 5% i.e. near 4.545% which is calculate from exact
formula.

Cont…
If I>I* and the exchange rate between two countries does not
change, then consumer purchasing power is greater on foreign
than on home goods( arbitrage opportunity), and vice versa in
this case PPP does not exist.
So PPP theory suggests that the exchange rate will not remain
constant, but will adjust to maintain the parity in purchasing
power.
If I<I*(foreign country inflation exceeds the domestic country
inflation), e* will be negative, i.e. foreign currency will
depreciate.
If I>I*( domestic country inflation exceeds the foreign country
inflation), e* will be positive, i.e. foreign currency will
appreciate

Reasons for departure from Purchasing Power Parity
(PPP) Principle
Restrictions on movements of goods/services
- Transportation
- Import Tariffs
- Non-Tariff restrictions
Price indexes with commodities which are not traded inter-country
Statistical reasons i.e., measurement of inflation differentials

Reasons for departure from Purchasing Power Parity
(PPP) Principle (Contd..)
Despite of aforementioned, when the relationship between the
inflation differential is made with the change in exchange rates of
two countries for a long period of time, usually it is seen that there
is correlation between the inflation differentials and the change in
exchange rates. This suggests that to some extent, PPP does hold
itself useful for the analytical purpose.

Covered interest arbitrage
It is the process of capitalizing on the interest rate different between
two countries (interest arbitrage) while covering your exchange rate
(hedging exchange rate ) with forward contract.
Covered interest arbitrage tends to force a relationship between
forward rate premiums and interest rate differentials
Example1: Following information is available:
 You have $500,000 to invest
 The current spot rate (S) of the Moroccan dirham is $.110.
 The 60-day forward rate (F) of the Moroccan dirham is $.108.
 The 60-day interest rate in the U.S. is 1 percent (i.e. 6% pa)
 The 60-day interest rate in Morocco is 2 percent (i.e. 12% pa)

Cont…
Covered interest arbitrage (for US based investor)
would involve the following steps:
Convert dollars to Moroccan dirham: $500,000/$.11 =
MD4,545,454.55
Deposit the dirham in a Moroccan bank for 60 days. You will have
MD4, 545,454.55 × (1.02) = MD4, 636,363.64 in 60 days.
Take short position in 60 days forward contract , i.e. you will sell
your dirham investment at 60 days forward rate.
In 60 days, convert the dirham back to dollars at the forward rate
and receive MD4,636,363.64 × $.108 = $500,727.27
Your arbitrage profit will be $727.27 ($500,727.27-$500,000)

7.7
Example 2 of Covered Interest Arbitrage
kanchan.kandel399@gmail.com
16

Interest Rate Parity (IRP)
If gain from different interest rate differential is offset by sufficient
amount of forward rate differ from a spot rate then it is known as
interest rate parity.
Then, covered interest arbitrage is no longer feasible, and the
equilibrium state achieved is referred to as interest rate parity (IRP).
(1+rd)=F/S (1+rf)……………VII
where, rd= domestic interest rate
rf= foreign interest rate.
F= forward exchange rate
S= spot exchange rate.
• If this equation satisfy then there will be no arbitrage opportunity.

Cont…
(1+rd)>F/S (1+rf) if this condition satisfy then borrow loan from
foreign market at foreign interest rate and invest that amount in
domestic market at domestic interest rate.
(1+rd)<F/S (1+rf) if this condition satisfy then borrow loan from
domestic market at domestic interest rate and invest that amount in
foreign market at foreign interest rate.

Interpretation of IRP
When IRP exists, it does not mean that both local and foreign
investors will earn the same returns.
What it means is that investors cannot use covered interest arbitrage
to achieve higher returns than those achievable in their respective
home countries.
19

Does IRP Hold?
Various empirical studies indicate that IRP generally holds.
While there are deviations from IRP, they are often not large
enough to make covered interest arbitrage worthwhile.
This is due to the characteristics of foreign investments, including
transaction costs, political risk, and differential tax laws.
20

Reason for violation of IRP
Political Risk
A crisis in the foreign country could cause its government to restrict
any exchange of the local currency for other currencies.
Investors may also perceive a higher default risk on foreign
investments.
Differential Tax Laws
If tax laws vary, after-tax returns should be considered instead of
before-tax returns.
21

Uncovered interest rate parity
If foreign investment is not hedge (forward contract is not
taken) , is known as uncovered interest rate.
Here not taking any forward contact means you are taking
exchange rate risk by converting your domestic investment in
expected exchange rate (S*).
Lets consider this example:
Suppose interest rate in Nepal(rd) is 4% and in USA(rf) is 6%.
Investable fund is NPR 85000 (i.e. dollar 1000, assuming spot
exchange rate is Rs.85/$)
And expected future exchange rate (S*) are Rs.88/$, 83.40/$
and Rs.88/$ 22kanchan.kandel399@gmail.com

Cont….
If you invest in Nepal, after one your worth will be Rs.88400
(Rs.85000*1.04).
If you invest in USA, after one year your worth will be $1060
($1000*1.06)
After one year expected exchange rate become Rs. 88/$ then
your worth in NPR will 93280 ($1060*Rs.88/$) ,which is
Rs.4880 more than domestic investment.
If exchange rate become Rs. 83.40/$ the net worth in NPR will
88404 ≈ 88400 ( Rs.83.40*$1060/$), equal to domestic
investment
If exchange rate become Rs.80/$ the net worth in NPR will be
Rs. 84800 ( Rs.80/$*$1060), which is Rs.3600 less than
domestic investment. 23kanchan.kandel399@gmail.com

Considering above example if we replace expected exchange rate
(S*) in IRP equation {(1+rd)=F/S(1+rf)} then new equation
will be (1+rd)=S*/S(1+rf)…….IX, which is known as
uncovered interest rate parity.
Remember that S* = S(1+e*).
So equation IX can be rewrite as (1+rd)=S(1+e*)/S(1+rf),
where S and S will be cancel and new equation will be:
(1+rd)=(1+e*) (1+rf)………….X
(1+rd)>S*/S(1+rf), borrow at foreign interest rate and invest at
domestic interest rate.
(1+rd)<S*/S(1+rf), borrow at domestic interest rate and invest
at foreign interest rate. 24kanchan.kandel399@gmail.com

International Parity Conditions Explained

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International Parity Conditions Explained