How to reduce rupee’s depreciation? Just get your calculations right
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Samir Arora, Fund Manager, Helios Capital
On August 7, 2013 Financial Times, London, carried a cover page article mentioning how the rupee had depreciated by 39% in the past two years. On August 18, how foreign investors were bailing out of India as (among other things) "the rupee has lost 57 percent of its value against the US currency since it peaked at 39.40 rupees to the dollar in February 2008".
"Foreign investors, whose investments are denominated in US dollars, have lost close to 20% in the last few months due to currency depreciation," said a managing director of BNP ParibasBSE -1.10 % Securities in an interview reported on August 19. Whether one looks at the past few months, two years or five years, the fact is that the rupee has depreciated a lot. Everyone is scratching their heads as to how far this will go and market participants are discussing as to what India can do to reduce this weakness.
Suggestions have ranged from raising the duty on gold, to opening more sectors to FDI, to selling shares held by SUTI, to removing the ban on ironore exports. Well, I also have one simple suggestion that will definitely help: Calculate the depreciation correctly. All these journalists and highly-paid strategists are making an elementary mistake in calculating how much value the rupee has lost against the US dollar.
Let me explain this with a simple example. Let us suppose that the value of the the dollar was equal to Rs 40 at the start of a period and the same dollar became equal to Rs 50 at the end of the period. Many people, therefore, wrongly calculate that the rupee has depreciated by 25% against the dollar in this period. In fact, what has happened is that the dollar has appreciated by 25% against the Indian rupee in this example.
At the start of the period the holder of one dollar would have got Rs 40 and since he now gets Rs 50 for the same dollar the value of the dollar has appreciated by 25%.
Just because the dollar has appreciated by 25% against the rupee does not mean that the local currency has depreciated by 25% against the dollar.
One way to understand this is to look at the following example: If Salman earns 25% more than Shahrukh, it does not mean that Shahrukh earns 25% less than Salman. When Salman earns 125 and Shahrukh earns 100, Salman earns 25% more than Shahrukh but Shahrukh earns only 20% less than Salman.
Coming back to the calculation on how much the rupee has depreciated against the dollar when $1= Rs 40 became $1 = Rs 50, imagine that you have Rs 100 with you. At the start of the period Rs 100 could have been converted to $2.5. When $1= Rs 50, the same Rs 100 will only fetch you 2 dollars.
Therefore, the rupee has depreciated in value by 20% as it fetches you 20% less dollars. One final way to understand this is to imagine that $1 = Rs 40 at the start of a period has become $1 = Rs 80 at the end of the period. The calculations used by these writers/strategists will imply that the rupee has depreciated by 100% whereas the correct answer would be that dollar has appreciated by 100% and the rupee has depreciated by 50%.
This does not mean that the depreciation of the rupee is not serious or painful over any of these periods. However, the credibility of the person making any suggestion or analysis is seriously threatened when one starts with such an elementary mistake.
On August 7, 2013 Financial Times, London, carried a cover page article mentioning how the rupee had depreciated by 39% in the past two years. On August 18, how foreign investors were bailing out of India as (among other things) "the rupee has lost 57 percent of its value against the US currency since it peaked at 39.40 rupees to the dollar in February 2008".
"Foreign investors, whose investments are denominated in US dollars, have lost close to 20% in the last few months due to currency depreciation," said a managing director of BNP ParibasBSE -1.10 % Securities in an interview reported on August 19. Whether one looks at the past few months, two years or five years, the fact is that the rupee has depreciated a lot. Everyone is scratching their heads as to how far this will go and market participants are discussing as to what India can do to reduce this weakness.
Suggestions have ranged from raising the duty on gold, to opening more sectors to FDI, to selling shares held by SUTI, to removing the ban on ironore exports. Well, I also have one simple suggestion that will definitely help: Calculate the depreciation correctly. All these journalists and highly-paid strategists are making an elementary mistake in calculating how much value the rupee has lost against the US dollar.
Let me explain this with a simple example. Let us suppose that the value of the the dollar was equal to Rs 40 at the start of a period and the same dollar became equal to Rs 50 at the end of the period. Many people, therefore, wrongly calculate that the rupee has depreciated by 25% against the dollar in this period. In fact, what has happened is that the dollar has appreciated by 25% against the Indian rupee in this example.
At the start of the period the holder of one dollar would have got Rs 40 and since he now gets Rs 50 for the same dollar the value of the dollar has appreciated by 25%.
Just because the dollar has appreciated by 25% against the rupee does not mean that the local currency has depreciated by 25% against the dollar.
One way to understand this is to look at the following example: If Salman earns 25% more than Shahrukh, it does not mean that Shahrukh earns 25% less than Salman. When Salman earns 125 and Shahrukh earns 100, Salman earns 25% more than Shahrukh but Shahrukh earns only 20% less than Salman.
Coming back to the calculation on how much the rupee has depreciated against the dollar when $1= Rs 40 became $1 = Rs 50, imagine that you have Rs 100 with you. At the start of the period Rs 100 could have been converted to $2.5. When $1= Rs 50, the same Rs 100 will only fetch you 2 dollars.
Therefore, the rupee has depreciated in value by 20% as it fetches you 20% less dollars. One final way to understand this is to imagine that $1 = Rs 40 at the start of a period has become $1 = Rs 80 at the end of the period. The calculations used by these writers/strategists will imply that the rupee has depreciated by 100% whereas the correct answer would be that dollar has appreciated by 100% and the rupee has depreciated by 50%.
This does not mean that the depreciation of the rupee is not serious or painful over any of these periods. However, the credibility of the person making any suggestion or analysis is seriously threatened when one starts with such an elementary mistake.
vijay
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