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EXPLANATION OF THE OPERATION OF THE FOREIGN EXCHANGE RATE CALCULATOR

This note gives an explanation of the operation of the foreign exchange rate calculator. The note starts by looking at the background and the concept of the trade-weighted rand and then uses an exchange rate forecast that appears once every quarter in The Economist magazine to explain the operation of the calculator.

 BACKGROUND AND CONCEPT OF TRADE-WEIGHTED RAND

 In this section we start of by explaining the concept of the trade-weighted rand and then give the background and the theoretical underpinnings of the foreign exchange rate calculator. 

• Concept of the trade-weighted rand

The trade-weighted rand is a construct that looks at the movement of the rand not only against a single currency but against a basket of currencies. The weights in the basket are determined according to how important a country is in its trade with South Africa. The bigger the share of trade flows a country has with South Africa the larger the weight of its currency in the trade-weighted basket. The trade-weighted basket we use in this calculator use approximately the same weights as that being used by the International Monetary Fund. We have estimated these weights by means of a statistical technique and found that the US dollar, Euro, the British Pound and the Yen explain almost all of the variation of the trade-weighted rand. The reason for only ending up with these four currencies is that the other currencies that make up the basket follow the movement of some of these currencies (mostly the US dollar and the Euro ) and that their own weights should be added to the weights of the four major currencies.

 The table below shows the calculation of the trade-weighted rand.

 In the table we have the movement of the rand against the major currencies. In the case of the US dollar the rand can purchase 6.25% fewer US dollars in the future than what it currently purchase. (This is calculated as follows: {((7.5/8)-1)*100}) The value in the last column is simply the 6.25% multiplied by the weight of the US dollar, which is .262. For each one of the other currencies a similar calculation is made. The trade-weighted rand is simply the sum of the values in the last column. This says that the rand can purchase 8.59% fewer of the basket of currencies in future that what it can purchase today. The change in the trade-weighted rand is simply -8.59%. 

• Background and theoretical underpinning

 The theoretical underpinning to the calculator is revealed by looking at the movement of the rand against the dollar. The movement of the rand against the dollar can come from the general movement of the rand, which is measured by the movement of the trade-weighted rand as well as the movement of the dollar itself against the currencies that make up the trade-weighted basket. (for example, the Euro, the UK Pound and the Yen).

 The calculator allows the user to put it his own assumptions on the movement of the trade-weighted rand as well as the exchange rate of the US dollar against the Euro, UK Pound and the Yen. Given these assumptions the calculator calculates the forecasted value of the rand against the US dollar. Once the forecasted value of the rand against the dollar is calculated it is straightforward to calculate the value of the rand against the Euro, UK pound and the Yen.

 AN EXAMPLE

 To illustrate the working of the calculator, we can use the following example of exchange rate forecasts provided every quarter by The Economist magazine. The table shows the forecasts as provided on 13 August 2003. The exchange rates we are interested in are those of the movement of the US dollar against the Euro, the UK pound and the Yen. We start of by looking at the forecasted exchange rates 12 months in the future and we assume that there is no change in the trade-weighted rand.

 This allows us to calculate the rand per US dollar on the assumption of the movement of the cross rates, but leaving the trade-weighted rand unchanged. This then isolates the effect of cross rate movements from the general movement of the rand. The values calculated by using the calculator is shown in the table titled the first round effect.

 The next step is to calculate the change in the trade-weighted rand. This is done as follows. When there is no change in the trade-weighted rand the rand per US dollar exchange rate is 6.9738 rand per US dollar. This different from the 8.50 rand per US dollar 12 month forecast by JP Morgan Chase. To calculate the change in the trade-weighted rand we simply do the following calculation.

 {((6.9738/8.5)-1)*100}=-17.96%

If we now put in the -17.96% as the change in the trade-weighted rand we get the 12 month forecast as given by JP Morgan. This is now shown under the table showing the second round effect.

 This example has shown how the expected movement of the rand can be broken up in an expected movement of the trade-weighted rand as well as an expected movement in the cross rates of the currencies that make up the trade weighted basis.

 From the example that we have used we can see that JP Morgan takes a very negative view on the change in the trade-weighted rand over the next 12 months of a decline of almost 18%.

 The calculator allows the user to put in his own views regarding the general change of the rand as well as the movements in the cross rates.

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