PARITY CONDITIONS IN INTERNATIONAL FINANCE

R. Srinivasan

Arbitrage Opportunity

• Arbitrage opportunity between domestic and international markets, exchange rates, interest rates and inflation rate, lead to the situation of law of one price.

• Five key economic relationship:– Purchasing Power Parity (PPP)– Fisher Effect (FE)– International Fisher Effect (IFE)– Interest Rate Parity (IRP)– Forward rates as unbiased predictors of future spots rates

(UFR)

FE

PPPIFE

IRP

UFR

Expected percentage change of spot rate of foreign currency

–3%

Expected inflation rate differential

+3%

Forward discount or premium on foreign

currency

–3%

Interest rate differential

+3%

In the above Exhibit, let us say If India’s inflation is expected to exceed that of US by 3%; then • Indian rupee is likely to depreciate by 3%• 1-year forward India rupee is likely to sell at 3% discount relative to US $; and• 1-year interest rates should by 3% higher than that of US

Inflation & International Arbitrage• Inflation plays an important role• Other rates and prices are adjusted to rate of inflation• It is a logical outcome of expansion of money supply in excess of real

output growth• Money is neutral; i.e., a 10% increase in money supply will cause the

prices to rise by 10%• International arbitrage enforces the law of one price, then the

exchange rate between the home currency and domestic goods must equal the exchange rate between the home currency and foreign goods

• Example – If Rs.10 can buy a loaf of bread in India; and the same is available for $ 1 in the

US, then the exchange rate between Rupee and dollar should be one $ = Rs.10 – Otherwise, arbitrage opportunity exists in the commodity and it will get

imported into the country where it is costlier from the country it is cheaper, thus making riskless profits

Purchasing Power Parity

• It was first propagated by Gustav Cassel in 1918 post World War I. It states that: – The price levels should be equal across all

countries, when expressed in a common currency; otherwise, arbitrage opportunity exists

– It rests on the underlying assumption that free-trade will equalize the prices across the countries

– But PPP ignores transportation costs, tariffs, quotas, product differentiation and other restrictions

Big Mac Index• It is calculated by comparing the prices of Big Macs worldwide (being

produced in more than 120 countries)– Suppose it is available for Rs. 95 in India and in the US it is sold for $ 3.00,

then the exchange rate in PPP terms would be:

– If the actual exchange rate is Rs. 46 per $ then

– The nominal PPP exchange rate can be expressed as:

• Where ‘t’ is the target time period (in years), e is the exchange rate; ih is inflation rate in home country; if is the rate of inflation in the foreign country

Exercise

• If US & Euro-zone are running annual inflation rates of 5% and 3%, respectively and the spot rate is one € = $0.75, then what should be the PPP rate of € in three year period

• ($0.7945)

• If inflation rates in India is 8% and that of the US is 2% then the Indian rupee should depreciate by about 6% to equalize to the $ price of the goods in the two counties. PPP is often represented in the following approximation:

• However the real exchange rate is the nominal exchange rate adjusted for changes in the relative purchasing power of each country. This can be expressed as:

• Where e’t is the rupee in terms of foreign currency e.g., $. It is the real exchange rate at time t.

Exercise

• Between 1980 and 1995, the ¥ / $ exchange rate moved from ¥226 / $ to ¥94/$. During the same 15-year period, the CPI in Japan rose from 91 to 119 points and that of US rose from 82 to 152. Calculate the nominal exchange rate in PPP terms and real exchange rates. Also calculated the rate of appreciation or depreciation in ¥.

(0.006241; 160.23) (0.007508; 133.33)

• 71%

Fisher Effect

• FE, tries to establish the relation between the current and the future purchasing power, as measured by the real interest rates. It means, irrespective of their location (same or different countries)– The lender is concerned with how many more goods can be

obtained in future by forgoing consumption today.– Alternatively the borrower thinks otherwise.

• In case of the existence of interest (real) rates differentials, it leads to arbitrage opportunities, in the domestic and foreign capital markets, in the form of capital flows, should occur.

Components of Nominal Interest Rates• All publicly available information (in the financial newspapers, internet and

other media) is nominal interest rates. However, it does not indicate our real monetary gain. To arrive at the real interest rates, it must be adjusted for inflation. The Fisher Effect states that nominal interest rate r is made up of two components

• Real required rate of return a• Inflation premium equal to the expected amount of inflation i.• It can be expressed as:

OR

E.g.,• If the required return is 3%, and the inflation is expected to be 10%; then

the nominal rate is likely to be 13% (approx.) or 13.3% (exact).

• Fisher effect asserts that real returns are equalized across countries through arbitrage; i.e., ah = af; where ah and af are domestic and foreign real interest rates. Any interest rate differential would enable capital flow from the country with lower interest to country with higher rates of interests. Hence the interest rate differential should be approximately equal to the anticipated inflation; i.e.,

• The exact relationship can thus be expressed as:

• In effect, currencies with high rates of inflation should bear higher interest rates, to eliminate any arbitrage opportunity.

International Fisher Effect• PPP implies that exchange rates will move to offset changes in inflation rate

differentials. Thus a rise in India’s inflation will lead to a fall in the exchange rate of rupee vis-à-vis dollar

• FE implies that any differential in the real interest rates in any two countries, would cause the capital outflows from the lower interest rate country to higher interest rate country

• IFE is the combined result of the two effects. It is denoted by:

• Where is the expected exchange rate in period t. The single-period analogue to eq.3 is:

•

Exercise

• Assume that the 1-year interest rate is 4% on US $ and 13% on rupees.– If the current exchange rate is $ 1 = Re 50, what is

the expected future exchange rate in one year?– If a change in expectations regarding future US

inflation causes the expected future spot rate t rise to Rs. 60, what should happen to the Indian interest rates?

Solution

• The changes in the inflation rates causes the expected future spot rate to rise to Rs. 60; then the nominal interest rates will be:

Forward Premium / Discount

• Foreign currency is said to be at Forward discount when the future exchange rate of rupee is at a discount; and vice-versa. It is computed as follows: