# What are Cross Rates and Chain Rule

India, buying rates are calculated on the assumption that the foreign exchange acquired is disposed of abroad in the international market and the proceeds realized in US dollars. The US dollars thus acquired would be sold in the local inter-bank market to realize the rupee.

For example, if the bank purchased a DEM 10,000 bill it is assumed that it will sell the DEM at the Singapore market and acquire US dollars there. The US dollars are then sold in the inter-bank market against Indian rupee.

The bank would get the rate for US dollars in terms of Indian rupees in India. This would be the inter-bank rate for US dollars. It would also get the rate for US dollars in terms of Deutsche marks at the Singapore market. The bank has to quote the rats to the customer for Deutsche mark in terms of Indian rupees.

The fixing of rate of exchange between the foreign currency and Indian rupee through the medium of some other currency is done by what is known as ‘Chaos Rule’.

The rate thus obtained is the ‘cross rate’ between these currencies. For example, let us assume that in the inter-bank market dollar is quoted at Rs. 34.50 and at Singapore market the dollar is quoted at DEM 1.6000. With this information, the rate of exchange of Deutsche mark in terms of rupees may be calculate’ as follows:

?Rs. = DEM 1 …(1)

if DEM 1.6000 = USD 1 …(2)

and USD 1 = Rs. 34.50 …(3)

It should be noted that the currency which appears as the second item (right hand side) in the first equation appears as first item (left-hand side) in the next equation. Thus Mark appears on the right-hand side in the first equation and left-hand side in the second equation. US dollar which appears on the right-hand side in the second equation appears on the left-hand side in the third equation.

The rate of exchange between Indian rupee and Deutsche mark can be calculated by dividing the product of the right-hand side by the product of the left-hand side.
(34.50x 1x 1)/(1.6000 x 1 )= Rs.21.5625.

It would be immediately seen that the above calculation involves simply dividing the rupee-dollar rate by the dollar-mark rate.

Note: If rupee-sterling rate is arrived at taking inter-bank rupee-dollar rate and sterling-dollar rate abroad, the rupee-sterling rate is arrived at by multiplying the two rates and not by dividing. This is because the sterling-dollar rate is quoted as GBP 1 = USD ? and not USD 1 = GBP ? as in other currencies.

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