## Please get the rupee depreciation math right..

A much needed piece from Samir Arora. There is a need to keep looking at basics.

He says plenty of suggestions are floating to correct rupee depreciation. Apart from  many suggestions, what is irritating is the different figures one gets on rupee depreciation  for even similar periods. He says the problem is with the math:

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.

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 blog itself is guilty of confusing these simple ideas…

In table form it looks like this:

 USD Rupees Rupees USD 1 40 100 2.5 1 50 100 2 USD appreciated by 25 INR depreciated by -20

Based on this, I just calculated value of Rupee depreciation since 2008 and since Apr-13. I used RBI’s reference rate published daily. Obviously this is a point to point calculation and one would be better off taking averages (and other measures) to get a complete picture. Nevertheless it looks like this:

 USD GBP EUR JPY 2008 to 23-Ag-13 -37.9 -21.0 -27.1 -41.2 Apr-13 to 23-Aug-13 -16.0 -17.9 -19.1 -10.3

In terms of absolute values, in Apr-08 we got 2.5\$ for every 100 Rs which has declined to \$1.55 in Aug-13…

Interesting to note..Rupee has depreciated more in terms of JPY than USD from 2008! With GBP it is the least.. Against EUR, one gets lower depre in 2008-till date period but highest from Apr-13 onwards…Even for GBP we see higher depre than USD in Apr-13 till date period..

Thinking about the probable reasons for these trends..

Getting math right is critical.. Thanks Samir for this..

### 2 Responses to “Please get the rupee depreciation math right..”

1. Loknath Rao Says:

What ever is in the denominator, rupee has become a worthless currency anyway.

The only way to correct his anomaly is to verify the sources of incomes of people who are buying gold and land. No registration should be possible on land deals without income tax officials giving a green signal. To reduce red tape, there can be some automatic check based on the transaction details so that the person buying or selling is not harassed mentally

Secondly disincentive ownership of Gold. Its a dead money. This is possible if the state imports a huge amount of Gold and dumps it in the market. These transactions should only be limited through banks. Once prices go down to sub 15K levels, people will start selling their Gold thus dropping the prices further. This will free up lot of cash. Once money supply is good, interest rates will go down and growth can resume

Where will the Dollars come from to buy Gold. Buy by selling Govt. Bonds to Saudi Govt. or borrow more dollars short term. We have screwed it enough already. Nothing more to loose. If the Lungiman delays further, no one will lend him a dime.

2. MacroGoose (@Macromob) Says:

This is essentially siegel’s paradox and nalebuff’s envelope puzzle.

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