1. Elaboración grupal

Exchange rate theories reason out the forex rate determination. They help the process of determining exchange rate between currencies. The exchange is governed by certain parameters. Depending on the parameters used, different exchange rate theories have been developed. There are Mint Parity, Purchasing Power Parity and Interest Rate Parity theories.

1.10.4.1 Mint Parity Theory

Under the Gold Standard or mint parity arrangement, rate of exchange is determined by reference to the gold contents of the two currencies, as each currency is expressed in terms of weight of gold. Gold standard prevailed upto 1931. Now it is not in practice. To understand the method, let us take an imaginary example. Let Re 1 = 0.001 gram of gold and US dollar (USD) 1 = 0.04 gram of gold. Then the rate of exchange between these two currencies under the Gold Standard will be : The rate of exchange is also known as the mint par of exchange, for at the Indian mint Re 1 will be = 0.001 gram of gold and at the US mint $ 1 = 0.04 gram of gold..

The actual exchange rate in the forex market will not be, however, USD 1 = 0.40, but slightly different due to bank commission. But bank commission cannot exceed certain limits as merchants can export or import gold to settle international payments incurring expenses of shipping and insurance when the commission charged is felt to be high. Suppose banks charge 10% commission and that to get USD 1, a merchant has to part with Rs. 40 plus 10% = Rs.44. Instead, the merchant can buy 0.040 gram of gold equivalent to one USD and export the same incurring say, Rs. 2 as forwarding and insurance cost of the 0.04 gram of gold to the American supplier of goods. The effective exchange rate comes to USD 1=Rs. 40 + Rs. 2 = Rs. 42. So banks cannot charge Rs 44 a dollar, but come down to Rs. 42. Similarly, it can be shown that a bank cannot offer less than Rs 38 a dollar (Rs 40 – Rs. 2) when the bank buys dollars. Thus the actual exchange rate is ± Rs.2 about the mint parity of USD 1

= Rs. 40.

1.8.4.2 Purchasing Power Parity Theory

There is another popular theory of exchange rate based on purchasing power parities of currencies. Under the purchasing power parity method, adopted when paper currencies are used, external value of a currency is determined on the basis of its internal value. As there is no gold convertibility option, a case with Gold standard, currencies have to be valued on the basis of their respective internal value either by reference to particular commodity or basket of commodities.

Say, a bale of cotton is sold for Rs. 20,000 in India while the same is USD 500 in USA. Then, Rs. 20000 = USD 500 or Rs. 40 = USD 1. If, the price of cotton rises in India, the value of Rupee falls against USD, if there is no sympathetic rise in price of cotton in USA. But basing currencies’ external value on the basis of price of a single commodity or basket of commodities internationally traded is not good, for only part purchasing power is considered. So, exchange rate computation and adjustment based on price index numbers [CPI, WPI, CLPI, etc]

is considered. Suppose in 2006 USD 1 = Rs. 44 and the price indices in both USA and India = 100. By 2007 the index number of Indian prices, say has become 105, while that of USA is 110. Then 2007 exchange rate will be:

USD 1 = 105/ 110 X Rs. 44 = Rs. 42 and Re. 1 = 150/280 x 1/44 = USD 1/42 or 0.0238.

Purchasing Power Parity (PPP) was first stated in a rigorous manner in 1918 by the Swedish economist Gustav Cassel, who used it as the basis for recommending a new set of official exchange rates at the end of World War I that would allow for the resumption of normal trade relations. Since then, PPP has been widely used by Central banks as a guide to establishing new par values for their currencies when the old ones were clearly in disequilibrium.

In its absolute version, purchasing power parity states that the equilibrium exchange

rate between domestic and foreign currencies equals the ratio between domestic and foreign price levels. Thus, if eo is the current equilibrium exchange rate (i.e. in equilibrium, one unit of foreign currency equals eo units of the home currency). Ph the home country price level, and P the foreign price level, then e = P / P or P e = P. In other words, a unit of homecurrency (HC) should have the same purchasing power around the world.

This theory is based on the law of one price; i.e. it rests on the assumption that free trade will equalize the price of any good in all countries - otherwise, arbitrage opportunities would exist. However, the theory ignores the effects of transportation costs, tariffs, quotas and other restrictions, and product differentiation.

The relative version is used more commonly now. Foreign price would indicate the necessary adjustment in the exchange rate between any pair of currencies. Formally, if Ph(t) and Pf(t) are the home and foreign price levels, respectively, and et is the HC value of one unit for foreign currencies all at time t, then: et / eo = (Ph,,t/P)/

(Pf,t/P), where, (Ph,o) (Pf,o) and eo are the base period equilibrium

h,,of,,o price levels and exchange rate, respectively and (P) (P,) and eare equilibrium price h,tftt levels and exchange rate, at period ‘t’.

This equation can be stated in terms of relative inflation rates using the following transformation. Let i and i be the (anticipated) price level increases (rates of inflation) h,tf,tbetween time 0 and time t for the home country and the foreign country, respectively; i.e. P/P= 1 + i and P/P= 1 + i. So, [ee][1 + i ]/ [1 + i.] Then, [(e - e)/h,th,o h,tf,tf,o f,tt / o = h,tf,t . to eo] is the relative (anticipated) exchange rate change between 0 and t, and this should equal: [ i - i] / [1+ i]which isthe relative price level change from time ‘0’ to time ‘t’. h,tf,t. f,t,

For example, if the current US price level is at 112 while the UK price level is at

107, relative to base price levels of 100 then, according to PPP, the dollar value of the Pound Sterling should have appreciated by approximately 4.67% [(0.12 - 0.07)/1.07 = 0.0467]. On the other hand, if the UK price level now equals 119, then the Pound Sterling should have depreciated by approximately 5.88% [(0.12 - 0.19)/1.19 = -0.0588] in the interim. A simplified [inexact] version of this formula is: (e - e )/e= [ i - i] / [1 + i].too h,tf,t. f,t. That is, the inflation differential between times ‘0’ and ‘t’ should equal the per cent change in exchange rate for that same time period.

Purchasing power parity bears an important message. Just as the price of goods in one year cannot be meaningfully compared to the price of goods in another year without adjusting for interim inflation, so exchange rate changes may indicate nothing more than the reality that countries have different inflation rates. In fact, according to purchasing power parity this should be case. If so, then exchange rate movements just cancel out change in the foreign price level relative to the domestic price level. These offsetting movements should have no effects on the relative competitive positions of domestic firms and their foreign competitors. Thus changes in nominal rates are off-setting nature of effects of inflation. If currency changes affect relative competitiveness, the focus must be not on nominal exchange rate changes but instead on changes in the real purchasing power of one currency relative to another. The real exchange rate is different from nominal exchange rate.

PPP graphic presentation

The relationship between the current spot and expected future spot rate and inflation rates can be shown graphically, as in Fig 2. Plot on the horizontal axis the inflation differential in favor of the home country, i.e. ïh – ïf , The vertical axis plots the percentage difference between future spot over current spot on the foreign currency relative to the home currency.

Fig 2 PPP Theory

• ïh -ïf = Inflation differential (in %) in favor of the home country.

• [S- S ] / S= Rate of change in expected future spot rate over current spot rate t+1 tt

The purchasing power parity line joins those points for which the future spot exchange rate is in equilibrium with the inflation differential. For example, if the inflation differential in favor of the home country is 2%, then the foreign currency must go at a future spot which is 2% more than current spot rate.

1.8.4.3 Interest Rate Parity Theory

Interest rate parity theory tries to bring out the relationship between spot and forward exchange rates. The currency of the country with a lower interest rate should be at a forward premium in terms of the currency of the higher interest rate country. More specifically, in an efficient market with no transactions costs, the interest differential should be (approximately) equal to the forward differential. Mathematics of the Theorem:

F/S = (1 + n.i(h))/(1 + n.i) where ,

‘n’(f) = `n’ period forward rate of a foreign currency given in direct quotation form

• S = spot rate given in direct quotation form

• ‘n’ = period in years

• i(h) = interest rate in home country per annum

• i(f) = interest rate in foreign country per annum

The one period, i.e., one year forward rate is given by : F/S = (1 + i)/(1 + i) Then, F-S/S = (1 + i - 1 - i)/(1 + i) = [ i - i ]/ [(1 + i] = [i - i] Approximately.

That is, rate of forward premium or discount, relative to current spot is approximately equals the difference in interest rates in the two countries.

Suppose US interest rate is 6% and in Indian Interest Rate is 8% p.a. If “S” = Rs. 40/$, 1 year forward $ rate is given by F/S = F/40 = (1 + (0.08))/(1 + (0.06) = (1 + 0.08)/(1 + 0.06) = [1.08/1.06] x 40 = Rs. 40.75/$

Six month forward rate is obtained as follows:

F/S = F/46.5 = (1 + (1/2)(0.08))/(1 + (1/2)(0.06)) = [1.06/1.03] x 40 = 40.39

Interest rate parity graphic presentation:

The relationship between the spot and forward rates and interest rates can be shown graphically, as in Fig 3.

Plot on the horizontal axis the interest differential in favor of the home country, i.e. ih-if. The vertical axis plots the percentage forward discount (negative) or premium (positive) on the foreign currency relative to the home currency. The interest parity line joins those points for which the forward exchange rate is in equilibrium with the interest differential. For example, if the interest differential in favor of the home country is 2%, then the foreign currency must go at a 2% premium over spot rate.

Fig 3: IRP presentation

• (ih – if) = Interest rate differential (in %) in favor of the home country.

• [F-S]/S = Rate of change in forward rate over current spot rate.