Exchange Rate: Equation

Exchange rates are quoted in terms of number of units of foreign currency bought for one unit of home currency that is $1. The method of quoted foreign exchange can be direct or indirect. The direct quotation method means a rate of exchange quoted in terms of X unit of home currency to one unit of foreign currency. The indirect quotation method means a rate of exchange quoted in terms of Y units of foreign currency per unit of home currency. In London uses the direct quotation method, most other countries use the direct quotation method.

The foreign exchange spot market is a currency market for immediate delivery. in practice, payment and delivery are usually two working days after the transaction date. The forward market involves rates quoted today for delivery and payment at a future fixed date of a specified amount of one currency against another. In the absence of barriers to international capital movements, there is a relationship between spot and forward exchange rate, interest rates and inflation rates. This relationship can be summarized as under:

Notations

So = Spot $ / £ Exchange rate now, Fo = Forward $ / £ Exchange rate now.

i$ = Euro dollar interest rate, i£ = Euro sterling interest rate, r = real return

St = Expected spot $ /£ exchange rate at time t, ft = Expected forward $ /£ exchange rate at time t.

P$ = US price level, P£ = UK price level. ّّp$ = Expected US inflation, ّّّp£ = Expected UK inflation.

Interest Rates and Exchange Rates

Assume that an investor has £1m to invest for a period if 12 months. He has a whole spectrum of investment opportunities he could put the money into Sterling or dollar investment or into yen or into Deutschmarks or whatever the currency markets are quoting the Dollar against sterling at $1.6800 spot and $1.6066 for 12 months. Euro market fixed interest rates are 13% p.a. for 12 months Sterling and 8 1/16% p.a. fixed for US dollars for a similar period.

Notations

i$ = Euro dollar interest rate i£ = Euro sterling interest rate

Fo = Forward $/£ Exchange rate So =Spot $ / £ Exchange Rate

Exchange Rates and Inflation Rates

Just like the above relationship between interest rate and exchange rate there exist a similar hypothesis - related to inflation rate and exchange rates. This relationship is also best approach by a numerical example:

If a commodity sells in the USA at $100 per kg and UK for £250 per kg and the exchange is $1.70 to the pound Stering than a profitable opportunity exit to buy the commodity in the USA, ship to Britain and sell them always assuming that is Gross profit of $25 per kg.

Given by (250*1.70)-400, exceeding shipping at insurance cost from the USA to UK.

The purchasing power parity (PPP) theory uses relative general price changes as a proxy for prices of internationally traded goods and applying the equation.

Thus if inflation is 8% p.a in the USA and 12% p.a in the UK, than applying ppp theory we would expect the pound sterling to fall against the dollar by:

P$ =US price level, P£=UK price level.

PPP theory, itself an approximation since it uses the general price level as a proxy for the price level of internationally traded goods, suggesting that the charges in the spot rate of exchange may be estimated by reference to expected inflation differentials. When looking at Post Exchange rate movements, the hypothesis might be tested reference to actual price level changes.

The precise formulation of the ppp theory:

Interest Rate and Inflation Rates [Fisher Effect]

According to the ‘Fisher effect’, a term coined because it was observed by US economist Irving Fisher, normal interest rates in a country reflect anticipated real returns adjusted for local inflation expectations. In a world where investors are internationally mobile, expected real rates of return should tend towards equally, reflecting the fact that in search of higher real returns investors arbitraging actions will force these returns towards each other, at least there should hold with respect to the free market Euro currency interest rates.

Constraints on international capital mobility create imperfections which, among other things, prevent this relationship from holding in domestic interest rate markets.

So normal Euro currency interest rates may differ for different currencies, but according to the fisher effect only by virtue of different inflation expectations. And these inflation differentials should underpin expected changes in the spot rates of exchange.

The Fisher theorem suggests that local interest rates reflect a real expected return adjusted for inflationary expectations, when money is internationally mobile and market imperfections are eliminated, local interest rates will be equal to the international real return adjusted for domestic inflationary expectations.

The following two equivalences are implied:

Changes in spot rate and the forward discount (Expectation theory)

This is the expectations theory of exchange rates and its implications are summarized below. This hypothesized relationship can be proved by a priori reasoning.

If users of the foreign exchange market were not interested in risk, then the forward rate of exchange would depend solely on what people expected the future spot rate to be.

Interest rate differentials and changes in the spot exchange rate (International Fisher effect)

The hypothesis that differences in interest rate should under the expected movement in the spot rate of exchange is termed the ‘International Fisher effect’. It is sometimes also called ‘Fisher’s open hypothesis”.

‘Agio’ => Means the sum payable for the convenience of exchanging one kind of money For another. The term originally derived from Italian money lending in the middle ages.