Getting the arithmetic right

The depreciation of the rupee against the dollar has become a hot topic of discussion these days. Many reports and analyses, however, have interpreted the extent of depreciation in percentage terms differently. In some cases, even wrongly.

When the rupee hit the first historic low on August 22, 2013, at Rs. 65.56 intra-day, some wrote that the Indian currency had depreciated by 20-21 per cent since this fiscal (April 2013). The closing rate at the inter-bank foreign exchange market on that day was Rs. 64.55 against the dollar. The closing rate of the rupee on April 2 was Rs. 54.2688. The depreciation since April 2 is only 15.927 per cent, if one takes in to account the closing rates on these two dates. But the dollar has appreciated by 18.945 per cent against the rupee.

If the rupee depreciates against the dollar say by 10 per cent that does not mean the dollar has appreciated by a similar percentage. It only appreciates by 9.09 per cent to be precise.

A simple calculation would help to understand this. Suppose one buys a share of a particular company at Rs. 100 and sells it to Rs. 110. He makes a profit of Rs. 10 in absolute terms and 10 per cent in percentage terms. But if he buys it at Rs. 110 and sells it at Rs. 100, he will lose the same Rs. 10 but in percentage terms it would be (100 divided by 110) 9.09 per cent. On August 27, the Indian currency closed at Rs. 66.24, and its depreciation against dollar since April 2 was 18.072 per cent. But the dollar has appreciated by 22.059 per cent against the rupee.

On August 28, the rupee ended at a new low of 68.80. The depreciation of the rupee since April 2 works out to 21.121 per cent while the dollar has appreciated by 26.776 per cent.

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Printable version | Dec 3, 2021 9:52:17 PM |

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