Intl parity cond.

PARITY RELATIONSHIPS

Purchasing Power ParityInterest Rate ParityFisher EffectInternational Fisher Effect

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 2International Financial Management

ARBITRAGE - CONDITION 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

ARBITRAGEBid 1 Bid 2 Ask 1 Ask2

NO ARBITRAGE


3 POINT ARBITRAGEBid 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


CROSS RATE – CHAIN RULE Cross multiply the rates of Japanese Yen

to $ and Singapore $ to US $ to obtain Yen to Singapore $ rateBid (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.


LAW OF ONE PRICE In competitive markets characterised by

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.


PURCHASING POWER PARITY (PPP)

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.


ASSUMPTIONS - PPPSPOT 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.


LIMITATIONS 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)


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 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.


ABSOLUTE & RELATIVE PPP Absolute form of PPP describes relationship

between the average price levels and the expected equilibrium exchange rates. 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.


RELATIVE PPP 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.


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.


INTEREST RATE PARITY (IRP) 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:


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)


INTEREST RATE PARITY (IRP)If 6m forward rate is Rs 48/$, then Today:

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:

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)


COVERED INTEREST PARITY THEOREM

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

Else it will provide arbitrage opportunity by borrowing in one currency and investing in another currency.

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FORWARD PREMIUM/DISCOUNT

Approximate IRP can be rewritten as

Assumed: No transaction costs i.e. no bid ask spread, and No difference in lending and borrowing rates.

It implies that 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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FISHER EFFECTRelationship between inflation and interest rates 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


INTERNATIONAL FISHER EFFECT 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

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Assumptions 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.


PARITY RELATIONSHIPS

Forward Rates as unbiased Relative PurchasingPredictor of Spot rates Power Parity

International Fisher Effect

Interest FisherRate Parity Effect

Changes in Spot Rate

Forward Premium or Discount

Difference in Nominal Interest Rates

Difference in Expected Inflation Rates


Intl parity cond.

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Transcript of Intl parity cond.