"Exchange Rate Determination"-International Finance -5

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Exchange Rate Determination

Purchasing Power Parity Principle

The Purchasing Power Parity principle (PPP) was enunciated by a Swedish economist, Gustav Cassel in 1918. According to this theory, the price levels (and the changes in these price levels) in different countries determine the exchange rates of these countries’ currencies. The basic tenet of this principle is that the exchange rates between various currencies reflect the purchasing power of these currencies. This tenet is based on the Law of One Price.

The Law of One Price

The assumptions of Law of One Priceare

· Movement of Goods: The Law of One Price assumes that there is no restriction on the movement of goods between countries, i.e. it is possible to buy goods in one market and sell them in another. This implies that there are no restrictions on international trade, either in the form of a ban on exports or imports, or in the form of quotas.

· No Transportation Costs: Strictly speaking, the Law of One Price would hold perfectly if there were no transportation costs involved, though there are some transactions (explained later) which bypass this assumption.

· No Transaction Costs: This law assumes that there are no transaction costs involved in the buying and selling of goods.

· No Tariffs: The existence of tariffs distorts the Law of One Price, which requires their absence to hold perfectly.

According to the law of one price, in equilibrium conditions, the price of a commodity has to be the same across the world. If it were not true, arbitrageurs would drive the price towards equality by buying in the cheaper market and selling in the dearer one, i.e. by two-way arbitrage. For e.g., if the cost of steel in Germany (in dollar terms) were $300/tonne and in the US it were $350/tonne, arbitrageurs would start buying steel in Germany to sell it in the US. This would increase the steel prices in Germany and reduce the US prices. This process will continue till steel becomes equally priced in both the countries.

The equalization of prices is possible only in perfect-market conditions, where there are no transportation costs and no restrictions on trade in the form of tariffs. In the presence of these two, the price of a commodity can differ in two markets by the quantum of transportation cost between the two countries and/or the amount of tariff imposed on the commodity. Continuing the earlier example, if the cost of transporting a tonne of steel from Germany to the US were $25, the arbitrage would continue to take place only till the difference between the price of steel in the two countries was reduced to $25. However, the process of the genuine buyers of a commodity buying from the cheaper market imposes stricter conditions on the prices in the commodity markets by driving the price to equality in the different markets. Hence, if the cost of transporting steel from the two markets to the buyer country is the same, the price of steel will have to be the same in both the markets. If there is some difference in the transportation costs, then the price may differ to the extent of such difference in the transportation costs. Since this difference in transportation costs is expected to be less than the cost of transporting the commodity from one market to the other (Germany and the US in our example), the genuine buyers’ preference brings the world prices of a commodity closer than is required by arbitrage. Even where arbitrage does not take place, the actions of genuine buyers make the world prices remain close.

We have seen that the price of any commodity has to be the same across countries, when they are expressed in the same currency everywhere (dollar price in our example). What about prices denominated in the local currencies? This is where the law of one price links exchange rates to commodity prices. According to this law, the domestic currency price of a commodity in various countries, when converted into a common currency at the ruling spot exchange rate, is the same throughout the world. So the price of a commodity in country A can be easily calculated by converting its price in country B’s currency at the ruling spot exchange rate between the two countries’ currencies.

There are three forms of PPP, which emerge from the law of one price – the absolute form, the relative form and the expectations form.

The Absolute Form of PPP

If the law of one price were to hold good for each and every commodity, then it will follow that:

P_A = S(A/B) x P_B (Eq. 5.1)

Where, P_A and P_B are the prices of the same basket of goods and services in countries A and B respectively.

Eq. 5.1 can be rewritten as:

S(A/B) = (Eq. 5.2)

According to this equation, the respective price levels in the two countries determine the exchange rate between two countries’ currencies. For e.g., if the cost of a particular basket of goods and services were Rs.2,125 in India and the same cost $50 in the US, then the exchange rate between the rupee and the dollar would be 2,125/50 = Rs.42.50/$.

Absolute PPP makes the same assumptions as the Law of One Price. It also makes a few additional assumptions:

· No transaction costs in the foreign currency markets: It assumes that there are no costs involved in buying or selling a currency.

· Basket of commodities: It also assumes that the same basket of commodities is consumed in different countries, with the components being used in the same proportion. This factor, along with the Law of One Price, makes the overall price levels in different countries equal.

Though the explanation provided by the absolute PPP is very simple and easy to understand, it is difficult to test the theory empirically. This is due to the fact that the indexes used in different countries to measure the price level may not be comparable due to:

· The indexes being composed of different baskets of commodities, due to different needs and tastes of the consumers

· The components of the indexes being weighted differently due to their comparative relevance.

· Different base years being used for the indexes.

Due to these reasons, these price indexes cannot be used to evaluate the validity of the theory.

The Relative Form of PPP

The absolute form of PPP describes the link between the spot exchange rate and price levels at a particular point of time. On the other hand, the relative form of PPP talks about the link between the changes in spot rates and in price levels over a period of time. According to this theory, changes in spot rates over a period of time reflect the changes in the price levels over the same period in the concerned economies.

Relative PPP relaxes a number of assumptions made by the Law of One Price and the absolute PPP. These are:

· Absence of transaction costs

· Absence of transportation costs

· Absence of tariffs

The relaxation of these assumptions implies that even when these factors are present, in certain conditions the relative PPP may still hold good. (These conditions are explained in a subsequent section). The relative form can be derived from the absolute form in the following manner:

Let S^~(A/B) denote the percentage change in spot rate (expressed in decimal terms) between currencies of countries A and B over a year, and and denote the percentage change in the price levels (expressed in decimal terms), i.e. the inflation rates in the two countries over the same period of time. If

P_A = S(A/B) x P_B (Eq. 5.1)

then, at the end of one year,

P_A(1 + ) = S(A/B) {1 + S^~(A/B)} x P_B (1 +) (Eq. 5.3)

Here, the left-hand side of the equation represents the price level in country A after one year, the first term on the right-hand side of the equation represents the spot exchange rate between the two currencies at the end of one year, and the last term gives the price level in country B after one year. These terms are arrived at by multiplying the figures at the beginning of the year by 1 plus the percentage change in the respective figures.

Dividing Eq. 5.3 by Eq. 5.1, we get

(1 + ) = {1 + S^~(A/B)} x (1 + ) (Eq. 5.4)

We can rewrite the equation as:

1 + S^~(A/B) =

or, S^~(A/B) = – 1 (Eq. 5.5)

or, S^~(A/B) = (Eq. 5.6)

Eq. 5.6 represents what is advocated by the relative form of the Purchasing-Power Parity Principle. According to the equation, the percentage change in the spot rate (A/B) equals the difference in the inflation rates divided by 1 plus the inflation rate in country B. For example, if the inflation rate in India were 10% and that in the US were 3%, the Rs/$ rate would change over a period of one year by (0.10 – 0.03)/1.03 = 0.068 i.e., 6.8%.

The effect of different inflation rates can be understood clearly from Eq. 5.6. Continuing the example of India and the US, a higher inflation rate in India than in the US makes the first term on the RHS of the equation greater than 1, and hence the RHS positive. A positive change in the Rs/$ spot rate implies that one year hence, a dollar would command a higher number of rupees, i.e. the dollar would appreciate. It follows that a country facing a higher inflation rate would see its currency depreciating.

The Expectations form of PPP

According to this form of PPP, the expected percentage change in the spot rate is equal to the difference in the expected inflation rates in the two countries. This theory assumes that speculators are risk-neutral and markets are perfect. Let the expected percentage change in the spot rate be denoted by S^*(A/B), the expected inflation rate in country A by , and the expected inflation rate in country B by . If a person buys the underlying basket of commodities in country A and holds it for one year, he can expect to earn a return equal to the expected inflation rate in country A, i.e. . On the other hand, if he decides to buy the same basket of commodities in country B, hold it for one year, and then convert his returns in currency B into currency A at the spot rate that is expected to rule at that time {i.e., S*(A/B)}, his expected returns will be equal to the expected inflation rate in country B, i.e. , plus the expected change in the spot rate. If the speculators are risk-neutral, as this theory assumes, then these two returns should be equal, i.e.

= + S*(A/B)

S*(A/B) = – (Eq. 5.7)

Eq. 5.7 is called the expectations form or the efficient markets form of PPP. If the Indian inflation rate is expected to be 8% over the next year, and the US inflation rate is expected to be 2%, the Rs/$ exchange rate can be expected to change by 6%.

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One of the features of perfect markets is that people are expected to behave rationally. Rational behavior implies that expectations would reflect the true behavior of variables over the long-term. This, in turn, means that the expected change in the exchange rate and the expected inflation rates would equal the actual average change in the exchange rates and the actual average inflation rates. Let us now see whether the purchasing-power parity principle is observed to hold in the real world. Empirical evidence Regarding PPP A multitude of studies have been conducted over a number of years to verify whether the law of one price and the various forms of PPP actually hold good. These studies were conducted using various sets of data and various methods of testing. According to the findings of a study conducted by J. David Richardson, the law of one price does not seem to hold good in the short-term, especially for goods having an inelastic demand (as these are the goods for which differential prices can be charged in different countries without the demand getting affected). In case of other goods, it does hold good, though only in the long-term. As for the relative PPP, the results of the various studies have been quite conflicting. Irving B.Kravis and Richard E. Lipsey conducted a study and arrived at the conclusion that PPP does not hold precisely. They found that there were substantial departures over long periods even for traded goods, while for non-traded goods PPP does not seem to hold even over short periods. According to a study conducted by Hans Genberg, PPP does not seem to hold good either with fixed exchange rate regimes, or with flexible exchange rate regimes. Niels Thygesenâ€™s study points out that a change in spot rates is not reflected in a change in prices for quite a long period of time. One of the studies conducted by J. Hodgson and P.Phelps arrives at the conclusion that a change in prices does affect the exchange rate, though with a long time lag. Yet another study by Rogalsi and Vinso found that a change in prices gets immediately reflected in the exchange rate movements, as the forex markets are perfect and reflect all the available information with immediate effect. Though highly conflicting results have been obtained by different studies, those based on the generally available data largely indicate that PPP does not hold good, i.e. the movements in exchange rates are not explained by movements in price levels, and vice versa. A major reason for this happening is that there are a number of other factors that also affect the movements in exchange rates, especially in the short-term, which may dominate the effect of inflation. This limits the effect of price movements on the exchange rates. There are three other major reasons for the PPP not holding good. Reasons for PPP not Holding Good Earlier sections mention the assumptions applicable to the Law of One Price and to the various forms of PPP. If any of these assumptions does not hold good, the PPP would also not hold. Besides, even if PPP were actually holding good, the results of an empirical study could get affected by the statistical methods employed. These factors give rise to the following reasons for PPP not holding good: â€¢ Constraints on movement of commodities â€¢ Price index construction â€¢ Effect of the statistical method employed. Constraints on Movement of Commodities As mentioned earlier, one of the constraints on movement of goods is transportation cost, either between the two countries producing the same commodity, or between the buyer country and the two producing countries. Another constraint is the presence of tariffs. These factors allow deviations in prices, and hence, a deviation from absolute PPP. At the same time, it was also shown earlier that if the quantum of deviation in prices on account of these factors is consistent over time, relative PPP might still hold. One factor, which affects both absolute as well as relative PPP, is the presence of quotas imposed on the amount of goods that may be exported from, or imported to a country. As this restricts the quantity of goods arbitrageurs can move from one place to another, it allows for deviations from prices which would reign, were PPP to hold good. Another such factor is the impossibility of moving some items from one place to another. These include perishable goods like milk and vegetables, immovable goods like land and buildings etc., and some kind of services such as those related to tourism. The immovability of such items allows their prices to deviate from one country to another. Product differentiation is another factor, which allows different prices to exist for goods produced in different countries. For example, the price of apples grown in the US may be different from those grown in India because of the difference in the quality. Price Index Construction Movement in prices is generally measured by price indexes. Price indexes used in different countries are based on different baskets of commodities, with the proportions of the commodities in accordance with the usage and taste of the residents of the particular country. When these indexes are used to measure the movement in price levels, the results do not conform to PPP. Many a times, the base year of these indexes is different. While this does not hinder the use of these indexes for verifying relative PPP, these indexes become inappropriate for verifying absolute PPP. Effect of the Statistical Method Employed There are two major ways in which the statistical method can affect the results of an empirical study. The first is through incorrect measurement of the difference in the inflation rates in the two economies. The second is through ignoring the fact that there is a two-way link between the spot exchange rate and inflation rates. Both the factors affect the other, i.e. while the inflation rates affect the exchange rates, the former also get affected by any change in the latter. Any statistical method that fails to recognize this two-way cause-effect flow is likely to produce erroneous results. The fact that PPP does not always hold good, gives rise to the concept of real exchange rate. The spot rate, adjusted for the change in price levels in the two countries during a specified period, gives the real exchange rate. Any change in the real exchange rate is called the real appreciation or depreciation of the currency. One of the ways to calculate the real exchange rate is: Sr(A/B) = S(A/B) x Where, S(A/B) is the spot rate at a point of time, IA and IB are the price indexes in the respective countries having the same base year, and Sr is the real exchange rate. For example, if the spot rate is Rs.42.50/$, and the price index in India and the US is at 110 and 103 respectively, the real exchange rate will be Sr = 42.50 = Rs.39.80/$ If the real exchange rate in the base period (i.e. at the beginning of the period over which the relevant inflation rates are applicable) was Rs.40/$, the rupee can be said to have appreciated in real terms. Interest Rate Parity The PPP gives the equilibrium conditions in the commodity market. Its equivalent in the financial markets is a theory called the Interest Rate Parity (IRP) or the covered interest parity condition. According to this theory, the cost of money (i.e., the cost of borrowing money or the rate of return on financial investments), when adjusted for the cost of covering foreign exchange risk, is equal across different currencies. This is so, because in the absence of any transaction costs, taxes and capital controls (i.e., restrictions on international investments and financing), investors and borrowers will tend to transact in those currencies which provide them the most attractive prices. Besides, the arbitrageurs will always be on the lookout for an opportunity to make riskless profits. The resultant effects on the demand and supply would drive the value of currencies towards equalization. This process is explained in detail in the following sections. Just like the price of commodities across different countries influence the buyersâ€™ and sellersâ€™ decision as to where they should transact, the ruling interest rate on financial assets denominated in different currencies affect investorsâ€™ and borrowersâ€™ decision regarding the market they would like to transact in. Let us start with the investors. Investors Decision Any individual or corporate is unlikely to have fully-matched income and expenditures in each and every period. While there are periods where the current expenditure is more than the current income giving rise to a requirement to borrow, there are also periods where the opposite holds true giving rise to a chance to invest. These periods of surplus or shortfall may range from a few days to a few years. Suppose a corporate has surplus funds for a period of one year. It could either invest them in securities denominated in the domestic currency, or in securities denominated in any other currency. The returns it will earn if it invests in securities

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denominated in a foreign currency will depend on two factors – the interest rate on those securities, and the change in the value of the relevant currency. Suppose the currency in which the company’s investments are denominated depreciates during the period of the investment. In that case, the gain by way of interest earned will stand eroded by the loss on conversion to the domestic currency. With the exchange rates being flexible, there is always the risk of exchange rates moving unfavorably. Since an investment in securities denominated in the domestic currency does not face any exchange risk, the same risk will have to be removed from other investments as well, in order to make their returns comparable. The investor can do this by entering into a forward contract for the relevant maturity. By taking the forward rate into consideration, the investor will be able to know the total returns that can be earned on securities denominated in different currencies, which will enable him to invest where his returns are maximized.

Let us assume the domestic currency to be A and the foreign currency to be B. An investor can earn a return of r_A on domestic deposits, and a return of r_B on the foreign currency denominated securities. For making an investment in the latter, the investor will have to first convert his holdings in currency A into currency B. Let the spot rate at which this conversion takes place be S(A/B). At the same time, let the relevant forward rate be F(A/B). For every unit of currency A, the investor will get 1/S(A/B) units of currency B. This, when invested, will at the end of one year give

1/S(A/B) x (1 + r_B) units of B

These, when converted at the forward rate, will give x (1 + r_B) units of A

At the same time, an investment in the domestic currency will, at the end of one year, give (1 + r_A) units of A.

Now suppose that (1 + r_A) > x (1 + r_B) (Eq. 5.8)

In such a case, investors will prefer to invest in securities denominated in currency A rather than in currency B, as it would fetch them a higher return. If the opposite were true, i.e.

(1 + r_A) < x (1 + r_B) (Eq. 5.9)

the investors will prefer to invest in securities denominated in currency B. The investors will be indifferent as to the choice of currency only if

(1 + r_A) = x (1 + r_B) (Eq. 5.10)

i.e. the returns on both the investments were equal.

Let us see an example. Let us assume that

Spot (Rs./$) = Rs.45/$

r_Rs = 14%

r_$ = 5%

1-yr F(Rs/$) = Rs.49.2/$

Investible funds = Rs.1,000.

If the investor invests in a rupee deposit, at the end of one year he would have

Rs.1,000 (1 + 0.14) = Rs.1,140

If instead, he wants to invest these funds in a dollar deposit, he would first need to convert his rupee holdings into dollars. The Rs.1,000 will fetch him

= $22.22

A dollar deposit of $22.22 would, after one year, fetch

$22.22 (1 + 0.05) = $23.33

Converted into rupees at the forward rate, this would give

Rs. (23.33 x 49.2) = Rs.1147.836.

Since the covered yield on the dollar deposit is higher than the rupee yield, the investor would like to invest money in the former.

Using Eq. 5.10, we can say that the forward rate at which the investor would be indifferent between the two deposits, would be where

F(Rs/$) = S(Rs/$) x

= 45 x = Rs.48.65/$

An easier interpretation of Eq. 5.10 is possible. Let us subtract (1 + r_B) from both sides of the equation. This gives us

(1 + r_A) – (1 + r_B) = – (1 + r_B)

Solving the equation, we get

r_A = r_B + x (1 + r_B) (Eq. 5.11)

The RHS of Eq.5.11 gives the covered yield on currency B. The second term on the RHS of the equation is nothing but the forward premium on currency B. Hence, investors will be indifferent between securities denominated in the two currencies when the domestic currency interest rate is equal to the foreign currency interest rate plus the forward premium on the foreign currency. If the former exceeds the latter, investors will prefer securities denominated in the domestic currency. In case the opposite is true, investors will prefer foreign-currency securities.

Borrowers’ Decision

When the need to borrow money arises, the borrower has the option to borrow in the domestic currency, or in foreign currency. Again, his decision will be based on the cost of domestic currency borrowing as compared to the covered cost of foreign borrowing.

For every unit of domestic currency borrowed, the borrower will have to pay at the end of the year

(1 + r_A) units of A.

Borrowing 1 unit of A is equivalent to borrowing 1/S(A/B) units of currency B. At the end of one year, the borrower will have to repay

units of B.

When converted at the forward rate, this gives

units of A.

Hence, the borrower will borrow in currency A if

(Eq. 5.12)

On the other hand, he will borrow in currency B if

(Eq. 5.13)

He will be indifferent to the choice of currencies if

(Eq. 5.14)

Again, Eq. 7.14 can be rewritten as

(Eq. 5.15)

As we see, Eq. 5.15 is the same as Eq. 5.11. Here, the RHS of the equation gives the covered cost of foreign currency borrowing.

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Let us again take an example. Let

S(Rs/$) = Rs.45.40/$

rRs = 10%

r$ = 4%

1 yr F(Rs/$) = Rs.48.37/$

If the borrower wants to borrow Rs.1,00,000 now, he may borrow either in rupees or in dollars. If he borrows in rupees, at the end of the year he would need to pay

Rs.1,00,000 (1.10) = Rs.1,10,000.

If instead, he borrows in dollars, he will need to borrow

At the end of the year, he would need to pay back

$2202.65 (1.04) = $2290.75

To repay these many dollars, he would need

Rs.(2290.75 x 48.37) = Rs.1,10,803.58

As the covered cost of borrowing in dollars is higher than the cost of borrowing in rupees, the borrower would prefer to borrow in rupees. Again, from Eq. 5.14 we can say that the borrower would be indifferent between the two currencies if

F(Rs/$) = S(Rs/$) x

= 42.50 x

= Rs.44.95/$.

Covered Interest Arbitrage

In addition to investors and borrowers, one more class of players benefit from cost of money varying from one currency to another – the arbitrageurs. If Eq. 5.10 does not hold good, the arbitrageur can make riskless profits by borrowing in the cheaper currency and investing in the costlier, using the forward market to lock-in his profits. For example, if Eq. 5.8 were to hold good, the arbitrageur would borrow in the foreign currency, convert the receipts to the domestic currency at the on-going spot rate, and invest in the domestic currency denominated securities, while covering the principal and interest from this investment at the forward rate. At maturity, he would convert the proceeds of the domestic investment at the prefixed forward rate and pay-off the foreign liability, with the difference between the receipts and payments serving as his profit. In case of Eq. 5.9 holding good, the arbitrageur would borrow in the domestic currency, convert it into foreign currency at the spot rate, invest the proceeds in foreign currency denominated securities, and cover the principal and interest from this investment at the forward rate, thus locking his domestic currency returns. This process of borrowing in one currency and simultaneously investing in another, with the exchange risk hedged in the forward market is referred to as covered interest arbitrage.

For example, if

S(Rs/$) = 45.40

Annualized return on a 6-month deposit in Rs. = 12%

Annualized return on a 6-month deposit in $ = 6%

6-m F(Rs/$) = 47.31

Then, the covered yield on the dollar deposit will be

= 0.1467 = 14.67%.

As the covered yield on the dollar deposit is higher than the cost of borrowing rupee funds, the arbitrageur would borrow funds in the rupee market and invest them in the dollar market. Suppose he borrows Rs.1,000. He can convert them at the spot rate into

$ = $22.02

Investing these, at the end of 6 months he will receive

If these dollars are converted in the forward market, the arbitrageur will receive

Rs. (22.68 x 47.31) = Rs.1,073

On the rupee borrowings, he will have to repay

The arbitrageur can use the proceeds from the dollar investments to pay-off this liability. At the end of the process, he would have made a profit of

Rs. (1,073 – 1,060) = Rs.13

It follows from the above discussion, that whenever Eq. 5.11 is not satisfied, it will result in

· Investors preferring investing in one currency over another;

· Borrowers preferring to borrow in one currency over another;

· Arbitrageurs borrowing in one currency and investing in another.

All these three activities result in the forex markets and money markets getting affected in a manner that makes the interest rates and exchange rates adjust, so that Eq. 5.11 becomes true. The above mentioned activities would result in

· Foreign currency interest rate going up as a result of increased borrowing in that currency;

· Domestic interest rate falling as a result of increased investments in the currency;

· The spot rate falling due to increased supply of foreign currency in the spot market. For a given level of forward rate, this results in an increase in the forward premium on the foreign currency;

· The forward rate increases due to increased demand for the foreign currency in the forward market. For a given level of spot rate, this will result in an increase in the forward premium on the foreign currency.

Relationship between PPP and Interest Rate Parity

Uncovered Interest Parity Condition

In the previous chapter it was observed that if risk were ignored, then the expected spot rate would be equal to the forward rate. It follows from Eq. 5.10 that

(Eq. 5.16)

where

(A/B) is the expected spot rate at the end of one year.

By definition, (A/B) = S(A/B) x {1 + S* (A/B)}

where

S^*(A/B) is the expected percentage change in the spot rate.

Hence, Eq. 5.16 can be written as

(1 + r_A) = {1 + S^*(A/B)} x (1 + r_B)

Solving, we get,

1 + r_A = 1 + S^*(A/B) + r_B + {S^*(A/B) x r_B}

Since the last term on the right-hand side is likely to be very small, we may ignore it and get the approximate equivalent equation:

r_A = S^*(A/B) + r_B

or,

r_A – r_B = S^*(A/B) (Eq. 5.17)

Eq. 5.17 is referred to as the uncovered interest parity condition or the International Fisher effect. According to it, the expected percentage change in the spot rate should be approximately equal to the interest differential.

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The Fisher Effect

The interest rate that we have been using till now is the nominal interest rate. The nominal interest rate does not represent the real increase in the investor’s wealth, as the increase is subject to the inflation rate. The real increase is reflected by the real interest rate, a concept made popular by Irving Fisher. According to Fisher, the nominal interest rate is a combination of the real interest rate and the expected rate of inflation. More explicitly, the Fisher effect or the Fisher equation states that

1 + r = (1 + i) x (1 + P^*)

where

r = nominal rate

i = real rate

P^* = expected inflation rate

Solved, it gives

r = i + P^* + (i x P^*)

Since the last term will be quite small, we can say that on an approximate basis,

r = i + P^*

i.e., the nominal rate is equal to the real rate plus the expected inflation rate.

The Relationship

According to the expectations form of the PPP,

S^*(A/B) =

According to the uncovered interest rate parity condition,

S^*(A/B) = r_A – r_B

It follows that

Rearranging, we get

(Eq. 5.18)

Eq. 5.18 is the Fisher open condition. It says that the nominal interest rates minus the expected inflation rates, i.e, the real interest rates are equal across different countries. Intuitively also, the real interest rates should be equal across countries, otherwise the resultant capital flows will bring them to equality.

It can be observed that any of the three equations can be derived from the other two. If we assume two of them to hold good, it will automatically follow that the third also holds good. So, if we assume that the Fisher open condition and the expectations form of PPP hold good, we will be implicitly assuming that uncovered interest parity also holds good. Similarly, if uncovered interest parity is assumed to be true and the real interest rates are expected to be equal across different countries, it is implied that expectations form of PPP is assumed to be true.

Reasons for Departure From Interest Rate Parity

While introducing the topic of interest rate parity, it was mentioned that this theory holds good in the absence of a few factors like taxes, capital control and transaction costs. In reality, the presence of these factors allows interest rates and forward premiums to deviate from the covered IRP. Covered IRP does not hold good perfectly because of the following reasons:

· Transaction costs

· Political risks

· Taxes

· Liquidity preference

· Capital controls.

Transaction Costs

The process, which brings interest rates and exchange rates into line, involves investing in one market and/or borrowing in another, and converting one currency into another. The transaction cost involved in money market operations is the difference between the investment and the borrowing rate. The bid-ask spread is the cost involved in conversion of currencies. The deviations from the IRP have to exceed these costs in order to make dealing in the foreign markets (both currency markets and money markets) profitable. Hence, the presence of these costs allows deviations up to the costs involved.

The arbitrage process discussed earlier, also referred to as the round-trip arbitrage, allows the maximum deviations from the parity. This is because the arbitrageur has to bear the bid-ask spread as well as the money market costs. The arbitrageur borrows in one market to invest in the other. While he has to pay the higher interest applicable to borrowings, he receives the lower interest rate applicable to investments. After borrowing one currency, he converts it into the other currency, and reconverts the currency on maturity. In the process, he receives the lower ‘bid’ rate while selling, and has to pay the higher ‘ask’ rate while buying a currency. These costs, together, allow a huge deviation from IRP.

In this way, transaction costs allow for departures from the interest rate parity.

Political Risks

Investment in a foreign currency denominated security can be made in two ways. One is, investing directly in securities issued in the country to which the currency belongs. For e.g., a US citizen may invest in T-bills issued by the Government of India. The other way is to invest in deposits denominated in the foreign currency held domestically, or in some third country. For e.g., a French citizen may hold a dollar deposit with a London bank. In the second case, the investor faces only the currency risk. In the first case, the investor faces the political risk as well. It is the risk of any change in the foreign country’s laws or policies that affect the returns on the investment. It may take the form of a change in the tax structure, or a restriction on repatriation of proceeds of the investment, or a sudden confiscation of all foreign assets, among other things. This additional risk makes the investors require a higher return on foreign investments than warranted by the interest parity. This factor allows deviations from the parity to take place.

While generally it is the foreign investment which has a higher political risk attached to it and hence requires a higher return, sometimes it is the other way round. Residents of a country which is politically very unstable may like to invest in a relatively stable country, even when there is an interest disadvantage. This would again allow deviations from the IRP, this time on the other side.

Despite the presence of additional political risk in foreign investments, the presence of third country investors may push the variables towards the parity. This would happen due to the fact that they may perceive the additional risk as equal between the two countries, and would have to take it on irrespective of which of the two countries they invest in. Hence, they may require an equal risk premium on either side of the parity, thus disallowing any variation from it.

The factor of political risk generally affects only the investment decisions, as no country is likely to change its laws or policies in a way which would make it difficult for the borrower to repay his obligations. Yet, it is a strong enough factor to allow deviations from the parity line.

Taxes

Taxes can affect the parity in two ways – through withholding taxes, and through differential tax rates on capital gains and interest income. The following section analyzes these factors.

Withholding Taxes

Generally, any resident making a payment to a foreign resident is required to withhold a part of that payment as taxes, and pass it on to the tax authority of his country. To that extent, foreign currency earnings of an investor stand reduced, permitting a deviation from the interest parity up to the extent of the tax withheld. Normally, this factor gets canceled out if the investor receives a tax credit from his government for the amount paid as withholding taxes. Hence, it affects the parity only if the tax credit is not given, or if it is less than the amount paid as withholding taxes.

Difference Tax Rate

Deviations from the interest parity are possible if the earnings on account of transactions in foreign currency are treated as capital gains, and hence are taxed at rates different from the rates applicable to interest income. Suppose an investor pays tax on capital gains at the tax rate t_c, and on normal income at t_y. Then, for that investor the interest parity line will be given by

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Hence, if

i.e., the capital gains tax rate is lower than the income tax rate, then there would be a premium attached to investing in those foreign currencies which are at a premium. Also, borrowers would like to borrow in a foreign currency, which is at a discount.

The differential tax structure normally changes the parity line for only there players who need to convert currencies occasionally. The major players in the forex markets, i.e. the banks, do not face this differential tax rate as they frequently deal in the market, and hence any earnings on account of a change in the exchange rates is taken as a normal business income for them and taxed accordingly. Hence, the IRP is not affected by this factor. As a result, the infrequent players get an arbitrage opportunity, which is not available to the major players. They get a chance to benefit by denominating their investments and borrowings in the currency that provides them the tax advantage.

Liquidity Preference

An asset’s liquidity is measured by the quickness with which it can be converted into cash, at the least possible cost. While the time that is taken to liquidate a foreign investment may be the same as that taken for liquidating a domestic investment, the costs involved are different. Suppose an investment is liquidated before maturity. There will be some costs involved in the process which are likely to be the same for both kinds of investments. But there is an additional cost involved in liquidating covered foreign investments before maturity. It is the cost of canceling the cover (i.e., canceling the forward contract), which was explained in the previous chapter.

The presence of this cost makes the investors require a premium over the interest parity for making foreign investments. The amount of this premium would depend on the liquidity needs of the investors. The higher the expectation that the investment may have to be liquidated before maturity, the higher will be the required premium. The possibility of raising short-term finance from alternate sources also has an effect on the required premium. If such alternate sources are available, it is likely to reduce the premium demanded by the investors.

Capital Controls

The factors mentioned above are likely to cause only small deviations from covered interest parity. The most important cause of large deviations from the parity is the presence of capital controls. Capital controls include restrictions on investing or borrowing abroad and on repatriation of investments made by foreign residents. It also includes restrictions on conversion of currencies. These controls restrict the market forces from bringing the interest rates and exchange rates in line with the parity. As a result of these controls, the interest rates in the euro-market (where these regulations do not apply) are more in line with the parity, than the domestic interest rates in different countries.

Exchange Rate Forecasting

A plethora of factors affect the levels of, and movements in exchange rates, often in a conflicting manner. A number of theories were propounded to explain these effects. Though a consistent prediction of the exact level of future exchange rates is impossible, these theories help in forecasting the possible direction of the movement. Such forecasting is very important for players in the international markets, as the exchange rates have a great impact on their profits.

Forward Rate

Forward rate is expected to be an unbiased predictor of the future exchange rate. There are two criteria for judging the effectiveness of a forecasting tool – its accuracy and its unbiased ness. A forecasting tool is said to be accurate if the forecast generated proves to be in accordance with the actual future values of the concerned variable, with minor forecasting errors. An unbiased estimate is, where the probability of an overestimate is the same as the probability of an underestimate. This makes the forecast accurate on an average.

Various empirical studies have concluded that forward rates are indeed unbiased predictors of future spot rates, where the markets are competitive. For the market to be competitive, the concerned currencies should be freely floating and heavily traded. The presence of central bank intervention reduces the efficiency of the market. There is no evidence to support that the forward rates are accurate predictors of future rates. One possible reason for the inaccuracy of the forward rates is, that at any point of time, the forward rate reflects expected developments in the variables affecting the exchange rates. On the other hand, the actual future spot rates are affected by all the expected and unexpected developments. As the unexpected developments cannot be factored in the forward rates, the estimates based on these are normally inaccurate. Due to this, the shorter the time gap, the more accurate the forecast based on forward rates is expected to be.

The Demand – Supply Approach

It has been mentioned in the previous chapters that a currency’s exchange rate is determined by the overall supply of and demand for that currency. According to this view, changes in exchange rates can be forecasted by analyzing the factors that affect the demand and supply of a currency. Since these factors are listed out in the balance of payments account, this approach is also referred to as the

Balance of Payments Approach

When the exchange rates are fixed, the effect of other factors is balanced by official demand or supply, which helps in preventing the movement of the exchange rate. In case of a flexible exchange rate regime, however, any change in other factors results in a movement in the exchange rate. Since it is the flow of payments into and out of a country caused by these factors which is recorded in the BoP account, a forecast of exchange rate movements based on this approach takes into account the flow of demand and supply of currencies. Let us now see how exchange rate movements can be forecasted in accordance with this approach.

The demand curve of a currency is mainly derived from the country’s supply curve of exports. The supply of a currency is derived mainly from the country’s imports. Other factors affecting the value of a currency are trade in services, income flows (i.e. flows on account of interest, dividends, rents and profits), transfer payments and foreign investments. While an exogenous increase in exports has the effect of appreciating the domestic currency, an exogenous increase in imports results in depreciating the local currency. A change in the level of trade in services has a similar effect.

As mentioned previously, income flows depend on past investments and the current rate of return that can be earned on these investments. Hence, an expected change in the rate of returns can be used to predict the direction of exchange rates. Any change resulting in a reduction of an inflow would depreciate a currency, while a reduction of an outflow would appreciate the domestic currency.

Similarly, an increase in net transfers out of the country result in a depreciation of the currency and vice versa. An increase in the net inflows on account of foreign investments has two effects. While the domestic currency appreciates at the time of the inflow, its supply increases in the future periods on account of the interest, dividends, profits or rent earned by that investment and repatriated. The two factors affect the forecast of the exchange rates in the relevant periods accordingly. Another important factor needed to be considered here is the expected change in earnings from foreign investments. Earnings from foreign investments have two components – the interest rate or the income out of the investment itself, and the expected income arising from a change in the value of the currency (which would be realized at the time of liquidation of the investment). The second component is affected by any expected change in the value of the currency. Hence, if a country’s currency is expected to appreciate in the future, it is likely to attract more foreign investment, thus resulting in the currency’s appreciation now. So a future expectation of a change in the currency’s value gets reflected in a current change in its value.

Let us now understand how other economic variables are expected to influence the exchange rate. One of the most important economic variables affecting exchange rates is the relative price levels in the respective countries. According to this approach, a relatively higher inflation affects the relative prices of that country’s exports and imports. This results in the exports coming down and the imports increasing, thus depreciating the currency. This approach, thus, supports the PPP. This approach also supports the IRP, as it says that an increase in domestic interest rates would attract more foreign investments, and thus result in an appreciation of the currency.

An important aspect of this theory is, that the mechanism employed to explain exchange rate changes implies that any change in the value of a currency is only an instrument to correct the temporary imbalance in the system. For example, if a currency depreciates due to the country experiencing a relatively higher inflation than its trading partners, the depreciation reduces the foreign currency price of the country’s exports and thereby restores the competitiveness of the exports. At the same time, the imported goods are made more expensive by the depreciation, thereby reducing imports. This improves the current account balance. But sometimes it is observed that this does not happen. Despite depreciation, the current account balance continues to worsen. This results in instability in the exchange markets as well. This phenomenon is called the J-curve effect. According to this, when both imports and exports are price inelastic in the short run but price elastic in the long run, volume of exports and imports do not immediately respond to the change in relative prices of exports and imports, caused by depreciation of home currency. This leads to deterioration in the Balance of Trade

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hence, BoP) for the home country. This makes the currency depreciate further. This happens because it takes people some time to adjust to the change in relative prices. Despite a higher price of imports, people change-over to import substitutes only after a time lag. Similarly, it takes time for the producers of exported goods to increase their production of these goods, and for the foreign consumers to start consuming more of these goods. Till such time that the exports go up and the imports come down, the trade balance continues to worsen and the domestic currency continues to depreciate. After this time lag, the current account balance improves and the exchange rate stabilizes.

Figure 5.1: The J curve after depreciation

Figure 5.2: The J curve after appreciation

When the import demand and the export supply curves behave in the manner as implied by these figures, the supply curve of the currency becomes downward sloping (instead of the upward sloping curve). This introduces instability in the exchange markets. Let us see how. Consider figure 5.3. The SRs and the DRs represent the supply and demand for rupee against the dollar, with the equilibrium exchange rate between the dollar and the rupee being represented by Se($/Rs). According to this figure, any small appreciation in the value of the rupee (i.e. an upward movement of the exchange rate from the equilibrium exchange rate) results in the demand for rupees exceeding the supply, and hence a further appreciation of rupee. Similarly, any small depreciation of rupee sees a higher supply of rupee than the demand, and hence a further depreciation. This makes the exchange markets extremely unstable. Now consider figure 5.4. Here, despite the supply curve being downward sloping, any movement of the exchange rate away from the equilibrium results in the market forces forcing it back to equilibrium point. An appreciation of the rupee sees a higher supply than demand, thus lowering the exchange rate. A depreciation faces a higher demand, forcing the exchange rate to move up. In this figure, the forex markets are stable despite a downward sloping supply curve of the currency. This is so because in figure 5.4, the demand curve is flatter, and hence more elastic than the supply curve. It is the opposite case in figure 5.3. It follows that for the exchange markets to be unstable, the demand curve for a currency has to be relatively less elastic than the supply curve, with the supply curve being downward sloping. This happens when the import demand curve is inelastic, with the export supply curve being even more inelastic. If the export supply curve is less inelastic than the import demand curve, the increase in the value of exports would more than compensate the short run increase in the value of imports (with the value of imports increasing due to the increase in price of imports more than offsetting the decrease in the quantity of imports due to the inelasticity). In the opposite case, the increase in the value of the exports would not be able to compensate the increase in the value of imports, thus giving rise to the J-curve and instability in the exchange markets. When represented in terms of elasticities of export supply and import demand curves, the conditions state that the two elasticities should together be greater than one to avoid exchange market instability. This is called the Marshall-Lerner condition.

Figure 5.3: Unstable Market

Figure 5.4: Stable Market

The Monetary Approach

The monetary approach assumes that PPP holds good, i.e. an increase in the price level results in the depreciation of a country’s currency and vice versa. Using this assumption, this theory arrives at a few results that are diametrically opposite to that given by the demand-supply approach.

Let us start with an increase in the real GNP (the real product) of a country. As the real product increases, so do the transactions and the demand for money needed to be held for making purchases. Hence, an increase in the real GNP results in an increase in the real money demand. Due to this, lesser money is left for purchase of goods, services and bonds. With no change in the money supply, this brings down the price levels. With a reduction in the demand for bonds, the bond prices also go down, resulting in an increase in the nominal interest rates. Since this approach assumes PPP to hold good, a reduction in the price levels brings about an appreciation of the currency. Hence, an increase in the real GNP brings about an appreciation of the currency. This is in contrast with the predictions of the demand-supply theory.

The theory also outlines the correction mechanism in the system. With a fall in the price level, the real money demand stands reduced. At the same time, an increase in the interest rates increases the opportunity cost of holding money, thus reducing the real demand for money. This leaves people with more money to spend on goods and services, thus increasing the price levels. This makes the currency appreciate.

There is another route through which a growth in real GNP affects the exchange rate. As we have seen, an increase in the real GNP increases the real demand for money. As much of this increased demand, as is not satisfied through an increase in the money supply, is satisfied through a current account surplus. This makes the currency appreciate.

Let us see the effect of an increase in money supply. Such an increase induces people to spend more on goods and bonds. This increases the price levels and reduces the nominal interest rates. The higher price level makes the currency depreciate.

The predictions of the monetary theory can be summarized as follows:

· An increase in the real GNP of a country causes its currency to appreciate. It follows that out of two countries, the country having a higher growth in the GNP will see its currency appreciating against the other country’s currency.

· An increase in real money demand makes the currency appreciate.

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Figure 5.3: Unstable Market

Figure 5.4: Stable Market

The Monetary Approach

The predictions of the monetary theory can be summarized as follows:

· An increase in real money demand makes the currency appreciate.

· An increase in nominal interest rates causes the currency to depreciate (as seen in the correction mechanism). This again goes against the predictions of the demand-supply approach.

· An increase in the money supply causes the currency to depreciate.

This theory also analyzes the effects of expected inflation. Expected inflation leads to higher nominal interest rates (since the nominal interest rate includes a premium for inflation). This causes a depreciation of the currency. The PPP says that inflation causes a currency to depreciate. According to the monetary approach, the effect on the exchange rates is immediate, rather than happening after the inflation takes place.

The Asset Approach

This approach is also referred to as the efficient market hypothesis approach. It does not talk about the effect of changes in the basic economic variables on the exchange rates. According to this approach, whatever changes are expected to occur in the value of a currency in future (whether based on the monetary theory or the demand-supply theory or any other approach), gets reflected in the exchange rates immediately. That is, any expected change gets absorbed immediately. Hence, the current exchange rate is the reflection of the expectations of the market as a whole.

This theory states that new information about the factors likely to affect exchange rates, comes to the market in a random manner. This news is quickly absorbed by the market. The efficient working of the market assumes that there are a large number of participants in the market whose aim is to maximize their profits. Through their profit-maximizing activities, the participants ensure that all available information is quickly absorbed by the market. There is one category of players in the currency markets, though, whose aim is not to maximize profits from currency movements. They are the central banks. The presence of central banks comes in the way of existing exchange rates reflecting the expected values of currencies truly.

This approach explains the implications of fiscal and monetary policy on exchange rates. Since a fiscal deficit is expected to increase the money supply levels sometime in the future, an increasing fiscal deficit is likely to trigger off an immediate depreciation of the currency, even without an immediate increase in the money supply. Similarly, an expected increase in the money supply through the monetary policy would cause the currency to depreciate immediately.

The Portfolio Balance Approach

The portfolio balance approach states that the value of a currency is determined by two factors – the relative demand and supply of money and the relative demand and supply of bonds. According to this approach, people can hold assets across different countries, denominated in different currencies (mainly in the form of currencies and bonds). Hence, any change in exchange rates changes the wealth of the holders of these assets, which becomes an instrument for maintaining equilibrium in money and bond markets.

According to this theory, interest rates and exchange rates are linked in the manner as shown by figure 5.5.

Figure 5.5: Portfolio Balance Model

A – Home currency; B – Foreign Currency

In figure 5.5, interest rates are shown on the y-axis, and the exchange rate on the x-axis, with a movement towards the right reflecting depreciation of the home currency. Curve bb represents the combinations of interest rates and exchange rates for which the bond market is in equilibrium, with curve mm representing those combinations for which the money markets are in equilibrium. As interest rates rise, the demand for bonds increases. With the supply of bonds not changing, this results in an excess demand. This demand can be reduced by reducing the wealth of the portfolio holders. A reduction in the wealth would induce portfolio holders to demand less of everything, including bonds. This is achieved through an appreciation of the domestic currency. The appreciation reduces the real wealth of the portfolio holders in domestic currency terms. Hence, appreciation of the domestic currency accompanies an increase in interest rates, in order to maintain the equilibrium in the bond market. This makes curve bb downward sloping. At the same time, an increase in interest rates means a lower demand for money. With money supply being constant, this results in an excess supply of money. To bring the money markets back to equilibrium, the demand for money needs to be increased. This can happen if the real wealth of portfolio holders increases through a depreciation of the domestic currency. The increase in the wealth induces higher demand for everything, including money. Hence, depreciation of the domestic currency accompanies an increase in the interest rates, to maintain the equilibrium in the money markets. This makes curve mm upward sloping.

The equilibrium level of interest rates and exchange rate are determined by the interplay of money market and bonds market, represented by the two curves in the figure. The theory goes on to assume that any change in money supply is effected via open-market operations by the government (or the central bank), thus changing the supply of bonds. Suppose there is a reduction in the money supply. This would be done by the government selling bonds in the market. The reduced money supply would shift the mm curve upwards to since the interest rate would increase for every level of exchange rate. The increase in the bonds’ supply would shift curve bb to the right to as at every level of exchange rate, portfolio holders would require increased interest rate. While this reduction in the money supply will definitely result in an increase in interest rates, the effect on exchange rates would depend upon the degree to which the two curves would shift, and hence could be in any direction.

If the money supply increases through a purchase of bonds by the government, the mm curve will shift downwards and the bb curve will shift to its left. This will be because the increased money supply and the reduced supply of bonds will reduce the interest rates at every level of exchange rates. If mm curve shifts more than bb curve, the currency will depreciate. In the other case, the currency will appreciate. In any case, the depreciation will be less than that predicted by the monetary approach.

This theory provides an explanation for a change in the value of a currency arising from a change in the real GNP. A higher real GNP results in a higher demand for both money and bonds. The higher demand for money increases interest rates and hence, shifts mm curve upwards. The higher demand for bonds reduces the interest rates and hence, shifts curve bb to the left. Both the shifts result in an appreciation of the currency, which is higher than that predicted by the monetary theory. But here, the effect on interest rates is ambiguous and depends on the quantum by which the two curves shift.

Role of News

The models discussed above show how expected changes are factored into exchange rate forecasts. Despite an understanding of these models, exchange rate forecasting is not very easy, often because of the conflicting interpretations provided by these approaches. One more factor that contributes to unpredictability of exchange rates is news. News, as per its definition, is something unexpected. Unexpected happenings keep on occurring, as we notice in our day-to-day lives. Since these events are unexpected, so is their effect on exchange rates. As many of the events can often not be forecasted, so are the associated changes in exchange rates.

News also explains why PPP does not always hold good. As an unexpected event occurs, the forex markets quickly absorb it and change accordingly. But the real markets are slow to absorb the news, and hence, there is a divergence from PPP till the real markets adjusts. In periods when a lot of unexpected events take place, this divergence becomes quite ambiguous.