1. PARITY RELATIONSHIPS
Purchasing Power Parity
Interest Rate Parity
Fisher Effect
International Fisher Effect

2. ARBITRAGE
Arbitrage is profit derived without taking any risks. (due
to different rates in different places)
Bid
Ask
Trader A in Sydney (per $)
A$
5.4500 – 5.5012
Trader B in NY (per A $)
US $ 0.1785 – 0.1817
Convert one of them to indirect quote
 For Trader B (per $)
A$
5.5035 – 5.6022
 A customer buys US $ 10,000 from Trader A in Sydney
by paying A $ 55012.
 These US $ 10,000 are sold at A $ 5.5035 per $ to get
A $ 55035 from Trader B in New York
 Earns a profit of A $ 23 without any risk.

Rajiv Srivastava
International Financial Management
2

3. ARBITRAGE - CONDITION
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Banks/Dealer operate on the basis of BUY LOW &
SELL HIGH
Clients and arbitrageurs also operate on the same
principle for profit. This implies that the Ask Rate
at one place/dealer must be lower than the Bid
Rate at another place/dealer. For arbitrage to
exist Bid of one must exceed Ask of another.
Bid 1
Ask 1
Bid 2
Ask2
Bid 2
Ask 1
Ask2
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ARBITRAGE
Bid 1
NO ARBITRAGE
Rajiv Srivastava

4. 3 POINT ARBITRAGE
Bid
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Ask
A dealer in London offers
 Japanese Yen (JY)/$
110.25
111.10
 Singapore $ (S$)/$
1.6520
1.6530
A dealer in Tokyo offers
 Japanese Yen (JY/SG)
68.30
68.50
Sell 1,000,000 Yen to buy $ in London:
 Get US $ 9,000.90 (1,000,000/111.10)
Sell US $ 9,000.90 to get Singapore $:
 Get Singapore $ 14,869.50 (9,000.90x1.6520)
Sell these Singapore $ in Tokyo:
 Get Japanese Yen 1,015,587 (14,869.50 x 68.30)
PROFIT = 15,587 Yen
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International Financial Management
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5. CROSS RATE – CHAIN RULE

Cross multiply the rates of Japanese Yen
to $ and Singapore $ to US $ to obtain
Yen to Singapore $ rate
Bid (Yen/S$) =
Bid (Yen/$)/Ask (S$/$)= 66.6969 Y/S$
Ask (Yen/S$) =
Ask (Yen/$)/Bid (S$/$)= 67.2518 Y/S$

The cross rates in London and the rates in
Tokyo offer arbitrage opportunities as Bid
in Tokyo is higher than Ask in London.
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International Financial Management
5

6. LAW OF ONE PRICE

In competitive markets characterised by
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numerous buyers and sellers
With free access to information
no barriers to trade
nominal or zero transaction cost, and
rationale behaviour.
Only one price must prevail. If not so, the
arbitrageurs will force different markets to
converge through buying in cheaper
market at a lower price and selling in
expensive market at a higher price.
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International Financial Management
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7. PURCHASING POWER PARITY
(PPP)
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Attributed to Swedish Economist Gustav Cassel;
The cost of a common basket of goods must cost
same in different countries and therefore they will
determine the exchange rate of two currencies.
If a basket of goods in India costs Rs 4,000 and
the same basket of goods costs $ 100, then the
exchange rate should be Rs 40 per $.
If the basket of goods in India can be purchased
at a price of less than Rs 40 (say Rs 38) then
arbitrageurs will buy goods in India, sell in USA
for $ 1, convert to Rs 40 making a profit of Rs 2.
Hence the law of one price forms the basis of PPP.
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International Financial Management
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8. ASSUMPTIONS - PPP
SPOT Exchange Rate = Ratio of absolute price of
common basket of goods

Each country has price index, and the ratio of the price
indices can be used to determine the spot exchange rate.
ASSUMPTIONS
 Based on the concept that demand for a country’s
currency is determined by the demand and supply
factors related to the goods produced by that country.
 Exchange rates will adjust to keep the purchasing power
constant.
 Arbitrage of goods and commodities will force the prices
to be equal across international borders.
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International Financial Management
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9. LIMITATIONS
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Definition of basket of goods, weights in indices
Relative utility of goods in different countries
Difference in styling
Quality differences
Transportation cost
Trade restrictions
Tariff barriers
Exchange controls
Non tradable goods (land, construction, services
like transportation, consultancy etc)
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International Financial Management
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10. EMPIRICAL EVIDENCE

With the switch over from Fixed (Gold Standard & Bretton
Woods) to Flexible Exchange Rate System, it was expected
that changes in exchange rate will follow inflation rates, as
per PPP. However it did not happen. Some of the reasons
are
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Prices changes are slow and trading based on prices is still slower.
The changes in exchange rates have been very frequent, large
and persistent, which is not the pattern of inflation rates.
For developed nations about 50% of GNP comes from non-traded
goods. Hence commodity arbitrage applies only to half the trade.
Purchasing powers of currencies in different countries are different.
Exchange rates respond to factors other than goods arbitrage,
(Price levels in different countries), like interest rates and portfolio
considerations for return on investment.
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International Financial Management
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11. ABSOLUTE & RELATIVE PPP

Absolute form of PPP describes relationship
between the average price levels and the expected
equilibrium exchange rates.
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Nominal exchange rate at any point of time is ratio of
relative prices for a representative basket of goods.
Inflation rates derive the exchange rates; Differences in
exchange rates are governed by inflation rates.
Relative form of PPP deals with the percent
change in the spot rates over a period rather than
absolute spot rates at any given point of time.
•
Absolute PPP may not hold for several reasons; yet
Relative PPP may hold.
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International Financial Management
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12. RELATIVE PPP
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Let the actual exchange rate is not same as given by
PPP. Instead of Rs 40/$ the rate is Rs 45
If the rate of inflation in India is 15% the same
basket of goods in India will now cost Rs 4,600 i.e.
P2i = P1i * (1+Ri)
If the rate of inflation in USA is 5% the same basket
of goods in USA will now cost $ 105 i.e.
P2u = P1u * (1+Ru)
S2 = P2i/P2u = P1i * (1+Ri) / P1u * (1+Ru)
S2 = S1 * (1+Ri) / (1+Ru)
Relative Change in Exchange Rate =
(Ri-Ru)/(1+Ru)
This is Relative Purchasing Power Parity.
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International Financial Management
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13. RELATIVE PPP

Even though actual exchange rate may deviate
from Absolute PPP, the
 Changes in relative price levels will determine
the appreciation/depreciation of exchange rate.
 Country/currency with higher inflation will
witness depreciation by an amount almost equal
to the inflation rate differential.
 Relative PPP is based on tradable goods only.
 Non tradable goods and capital account
transactions are ignored. If price indices of only
internationally traded good are chosen then
only Relative PPP may hold very accurately.
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International Financial Management
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14. INTEREST RATE PARITY (IRP)
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Like changes in the exchange rate can be
explained by Relative Purchasing Power Parity,
interest rate differential of two countries can
explain the difference in SPOT and FORWARD
rates.
Let the current rate of exchange is Rs 44 per $,
and the interest rates prevalent in India and USA
are 15% and 5% respectively.
Depending upon the forward rate the
arbitrageurs will work the following way:
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International Financial Management
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15. INTEREST RATE PARITY (IRP)
If 6m forward rate is Rs 45/$
 Today:
 Borrow $1 at 5% for 6m (Return $1.025)
 Convert it into rupee at SPOT Rs 44/$
 Invest for 6 months in India
 Buy $ 6m forward ($1.025 at Rs 45.00/$)
 After 6 months;
 Get Rs 44*(1+0.15/2) = Rs 47.30
 Pay Rs 46.125 (1.025x45) to buy required $
 Pay Debt of $ 1.025
 Profit of Rs 1.175 (Rs 47.300 – Rs 46.125)
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International Financial Management
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16. INTEREST RATE PARITY (IRP)
If 6m forward rate is Rs 48/$, then
 Today:
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Borrow Rs 44 at 15% for 6 m (Return Rs 47.30)
Convert them into $1 at spot Rate of Rs 44/$
Invest the $ in USA market at 5%
Sell a 6m-forward contract for $1.025 maturity
value at Rs. 48
6 months later:
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Get $ 1.025
Convert in rupees and get Rs 49.20
Pay debt of Rs 47.30
Profit Rs 1.90 (49.20-47.30)
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International Financial Management
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17. COVERED INTEREST
PARITY THEOREM
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The gains made in the investment must exactly
offset the gains made by speculation in the
conversion of currency at different times.
In efficient markets investment in either currency
must result in same returns. The investment
climate in two countries must determine the
exchange rates over a period of time.
There will not be any arbitrage opportunity if
( 1 + Id ) = F
(1+ If ) S

Else it will provide arbitrage opportunity by
borrowing in one currency and investing in
another currency.
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International Financial Management
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18. FORWARD
PREMIUM/DISCOUNT

Approximate IRP can be rewritten as
(Id − If ) F − S
= Premium / Discount
=
S
(1+ If )
Assumed: No transaction costs i.e. no bid ask spread, and
No difference in lending and borrowing rates.
It implies that
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Premium/discount on a currency will be equal to the
differential on the interest rates in two countries.
If interest rates in domestic markets are higher, then
domestic currency will be at discount (F > S).
Interest rate differential can be used to forecast the
appreciation/depreciation of the currency in short term.
Forward rates are unbiased indicator of future spot
rates.
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International Financial Management
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19. FISHER EFFECT
Relationship between inflation and interest rates
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Nominal interest rates vary directly with inflation rate.
Nominal rates of interest express the rate of exchange between
current money and future money.
Investors value money in terms of purchasing power. Therefore
the returns on investment have to be valued in terms of how
rich one gets after providing for purchasing power of the time at
which the investment was made.
Fisher Effect:
(1 + r) = (1 + a) x (1 + i)
Real rates of return are same across borders.
Implies ad = af
Or rd – rf ≈ id – if
Nominal interest rate differential must equal
inflation differential
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International Financial Management
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20. INTERNATIONAL FISHER EFFECT
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Nominal interest rates reflect expected inflation rates.
Arbitrage through capital flows would ensure that
interest differential between two countries will be
compensated by future change in the spot rate.
Combining PPP and Fisher Effect: Expected return from
investing at home must equal that of investing abroad.
Interest rates provide relationship between spot rates
and future spot rates
S1
1 + rd
=
S0
1 + rf
rd − rf
S1 − S0
=
≅ rd − rf
S0
1 + rf
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International Financial Management
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21. Assumptions
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Financial assets in different countries are
perfect substitute. (No difference in quality of
financial assets of various nations).
No restriction on capital flows across nations
i.e. full capital account convertibility with no
end-use restrictions.
Uniform taxes and tax credits passed for
parent investors in their countries.
Rajiv Srivastava
International Financial Management
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22. PARITY RELATIONSHIPS
Changes in
Spot Rate
Forward Rates as unbiased
Predictor of Spot rates
Forward
Premium or
Discount
Interest
Rate Parity
Rajiv Srivastava
Relative Purchasing
Power Parity
International
Fisher Effect
Difference in
Nominal Interest
Rates
Difference in
Expected
Inflation Rates
Fisher
Effect
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