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Foreign Exchange – Reply to Pallavi’s Questions *February 13, 2012*

*Posted by Chetan Chitre in International Business Management.*

Tags: Cross Rates, foreign exchange, Interest Parity, Inverse Quotes, PPP

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Tags: Cross Rates, foreign exchange, Interest Parity, Inverse Quotes, PPP

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Hi Pallavi,

Thanks for writing in.

Most of your questions are pertaining to the basis for determination of exchange rates.

We all know that exchange rates are primarily determined using two methods – (1) Fixed Rates – which are decided by the government – quite often by the Central Bank of a country. (2) Flexible or Floating Rates – which are decided by the market forces.

However, if one is to question the “correctness” of these rates – how would one go about it. So for example if the USD is valued in India at Rs. 45 – should we say that it is over-valued or would it be under-valued? Is there some base rate towards which the exchange rates should gravitate to? If yes then what is the basis or logic of determination of such a rate? Further if that logic is known – can it be used for predicting future movements of the exchange rates?

These are some of the questions that are answered using one or a combination of the following approaches –

(1) Purchasing Power Parity

(2) Interest Rate Parity and the Fisher effect which is some modification of the Interest Parity approach.

(3) Asset Approach

Let us examine them –

**(1) Purchasing Power Parity** –

This has to do with the purchasing power of the two currencies in their respective countries. Thus if a Mc D Burger costs $ 1 in USA and if the same Mc D Burger costs Rs.30 in India – then the exchange rate between the two currencies should be USD 1 = INR 30. So one can take some representative basket of commodities – check its price in USA in terms of USD (say USD 200) and then check the price of the same basket in India in terms of INR (say INR 5000). Equate the two currency values (USD 200 = INR 5000) and that should give you the exchange rate on Purchasing Power Parity (PPP) basis (USD 1 = 5000/200 = INR 25)

It is important to understand the use of the PPP rate. For example if very small or insignificant part of that basket is traded between the two countries, then PPP may not have any relation to the “actual” exchange rates between the two countries. What would influence the “actual” exchange rate is the amount of currency flows between the countries i.e. exports, imports and capital flows – which in turn would influence the demand and supply of currencies and thereby the market determined exchange rate. The Purchasing Power of a currency in the domestic market may not (atleast there exists a technical possibility that it will not) influence the exchange rate. It is by this logic that one of the solutions circulated for the current Euro crisis was to have a dual currency system for problem countries – i.e. one currency or one value for domestic transactions and another currency (say Euro) for international transactions.

PPP is more useful in making international comparisons of welfare such as in comparing GDP or Per Capita Income of two or more countries.

**(2) Interest Rate Parity** –

One view is that exchange rates should be influenced by interest rate differentials between two countries. Thus if the Spot USD / INR is 45, then the 90 days forward rate would be calculated as under –

What will be the value of INR 45 if it is kept in an Indian Bank as a Fixed Deposit or some other interest bearing instrument for a period of 90 days, in the interest is – say 12% p.a. So the value of INR 45 after 90 days at 12% p.a. would be INR 46.35.

What will be the value of USD 1 if invested in an American bank at interest rate of 4% p.a. for a period of 90 days? This value would be USD 1.01.

Thus after 90 days INR 45 will be INR 46.35

After 90 days USD 1 will be USD 1.01.

Thus 90 days forward rate would be = 46.35 / 1.01 = 45.89

A related concept is the International Fisher effect.

According to Irving Fisher real interest rates and nominal interest rates are independent of each other. The Real rates are a function of the real returns on capital in the productive sector and thus are independent of the monetary of financial phenomenon. The nominal rate being influenced by the monetary issues, are arrived at by adding the rate of inflation to the real rate of interest.

Thus while estimating the change in exchange rate over time, instead of using prices (as in say, PPP theory) Fisher thought that nominal interest rates would better serve the purpose. This is because the nominal rates of interest are arrived at by adding inflation to real interest rate. Thus Nominal Interest rate contains the effect of inflation within it.

Thus in the above example, if we are considering the nominal interest rate for calculating the Forward rate, it would include the effect of inflation on currency values.

An important implication of the International Fisher Effect is that the changes in exchange rates off-set interest rate differentials. Thus in the above example, an investor investing in USD will earn less interest (4%) however, this will be compensated by the appreciation in exchange rate of USD.

**(3) Asset Approach –**

Here we look at currencies as just another form of asset like say gold, land, shares, etc. Thus holding currency is looked upon in the same way as holding land or shares – i.e. based on the returns that it is likely to give over a period of time. The rate is therefore determined as a part of larger asset market equilibrium. So if Euro is likely to rise faster than say BSE, then people will sell their shares held on BSE and buy Euro. These shifts in demand for Euro from BSE would be a factor in determining the price of Euro. Thus demand and supply of various assets would determine the price of the currencies, when currencies are looked upon as just another kind of asset.

**Inverse and Cross Rates** –

**(1) Inverse Rates / Indirect Quotes** –

USD/INR = 45.50/45.80 is a direct quote

It says – Buy – INR 45.50 for USD 1 and Sell – INR 45.80 for USD 1.

If this is to be converted to inverse quotes – i.e. INR/USD – we will have to answer the following questions –

(1) Buy – How many USD for INR 1?

Step 1 – Note that one buys USD when one Sells INR. So we will use the Sell INR part of the Direct Quote here. i.e. INR 45.80 for USD 1

Step 2 – If INR 45.80 are used to buy USD 1, how many USD will you buy in INR 1 – So – 1/45.80 = USD 0.0218

Sell – How many USD for INR 1?

Step 1 – Note that one Sells USD when one Buys INR. So we will use the Buy INR part of the Direct Quote here. i.e. INR 45.50 for USD 1

Step 2 – If INR 45.50 are got when one sells USD 1, how many USD will you sell to get INR 1 – So – 1/45.50 = USD 0.0219

Thus –

Direct Quote – USD / INR = Bid/Ask

Inverse Quote will be –

INR/USD = Bid = 1/Ask of Direct quote

INR/USD = Ask = 1/Bid of Direct quote

**(2) Cross Rates**

If I had INR and I wanted to convert them into GBP. Suppose if GBP/INR quote is not available. However, USD/INR quotes are available and USD/GBP quotes are available. Then I will have to first convert INR into USD and then convert USD into GBP. This will ultimately give me GBP/INR.

This conversion is done using the following formula –

Suppose X, Y and Z are 3 currencies. If X/Y and Y/Z is given – find X/Z

X/Z Bid = X/Y bid * Y/Z bid

X/Z Ask = X/Y ask * Y/Z ask

Note that if in the above example instead of Y/Z, Z/Y is available, then first convert Z/Y into Y/Z and then use it in the formula. This applies to X/Y and X/Z as well.

Hope this explains. Please feel free to post in case of any doubts.

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