Currency Pairs: How to Calculate Depreciation or Appreciation
(This is for information and educational purposes only. This should not be
construed as a recommendation or investment advice even though the author is a CFA
Charterholder. Please consult your financial adviser before taking any
investment decision. Safe to assume the author has a vested interest in stocks
/ investments discussed if any.)
1. Forex market convention
Foreign exchange markets have their own conventions of quoting exchange rates. Exchange rates are quoted as currency pairs.
In
the currency pair USD-INR, US dollar or USD is the base currency, while
Indian rupee or INR is known as quote currency. The USD is kept fixed,
while the quote currency, that is INR, varies.
One year ago, one dollar was quoting at 82.74 rupees and now it is at 83.44 rupees. As you can see, the dollar is kept constant, while the rupee changes.
The value of the base currency (dollar) is expressed in quote currency (rupee), while using direct quotes.
To put differently, the value of one dollar is expressed in terms of rupees.
Direct quotation system: In currency pair USD-INR, USD is the foreign currency and INR is the domestic currency. For example, USD-INR exchange rate closed yesterday at 83.44 -- this is a direct quote because the foreign currency is fixed while the domestic currency varies.
It
is mandatory for banks in India to quote dollar - rupee exchange rate
as a direct quote. In direct quotation system, dollar is fixed while
rupee moves constantly.
Direct quotation system was introduced by Reserve Bank of India, India's central bank, in August 1993. Prior to 1993, India followed indirect quote system.
With indirect quotes, Rs 100 was used to be expressed in US dollars or other foreign currencies -- the domestic currency is fixed, while the foreign currency varies.
For example, at the end of Dec1992, Rs 100 was fetching 3.32 dollars.
Exchange rates are volatile. Let us see how to calculate appreciation and depreciation of one currency against another.
2. Dollar - rupee exchange rate
During March 2020, Indian rupee moved sharply due to the uncertainty and scare surrounding the raging COVID-19 Pandemic across the globe.
Between the end of Feb2020 and Mar2020, Indian rupee moved from 72.20 to 75.60. This was a big change for the currency pair of USD-INR in a month.
When rupee moved from 72.20 to 75.60 versus the dollar, which currency had appreciated and which currency had depreciated?
One dollar was fetching 72.20 rupees at end-Feb2020 and by end-Mar2020, it was fetching 75.60 rupees -- meaning US dollar gained or appreciated versus the rupee. Conversely, rupee depreciated or lost its value against the dollar.
So, dollar appreciated or gained 4.71 per cent [= (75.6 - 72.2)/72.2] against the dollar in Mar2020. What is the depreciation of rupee here?
Movement in a currency pair always results in one currency gaining and another losing.
Many people incorrectly describe this change as rupee depreciated by 4.71 per cent versus the dollar, because it was simple to calculate as shown above. Why is this incorrect?
It becomes more intuitive if you consider the rupee as a commodity, like gold or nickel. It is easy to visualise which currency is appreciating and which one is depreciating, when you think of currencies as commodities.
Calculating rupee depreciation: At the end of Feb2020, the USD-INR exchange rate was 72.2 and it can be converted as INR-USD quote of 0.01385 (=1/72.2), meaning one rupee equalled 0.01385 dollars or 1.385 cents.
Note: here, we converted a direct quote (USD-INR) into an indirect quote (INR-USD).
Likewise, end-Mar2020 USD-INR quote of 75.6 becomes INR-USD 0.01323 (=1/75.6); so one rupee was fetching 0.01323 dollars or 1.323 cents.
In Mar2020, rupee depreciated from 0.01385 to 0.01323 dollars or by 4.5o per cent [= (0.01385 - 0.01323)/0.01385].
Simply put: In Mar2020, the dollar appreciated 4.71 per cent versus the rupee. Conversely, rupee depreciated by 4.50 per cent against the dollar during the month.
3. A simple example
To make matters clearer, let us take another example.
Between the end of Mar2008 and end of Mar2009, rupee moved from nearly 40 to 50 against the dollar, due to negative impact of Global Financial Crisis or GFC. Put differently, USD-INR exchange rate moved from 40 to 50.
So in the financial year 2008-09, the dollar gained 10 rupees (50 - 40) or we can say dollar gained 25 per cent [(50 - 40)/40].
As stated above, many financial market participants incorrectly describe this move as: rupee depreciated by 25 per cent versus the dollar. This incorrect interpretation is widely prevalent.
Why is this incorrect?
Calculating rupee depreciation: Let us convert the USD-INR direct quote into INR-USD indirect quote. One rupee was fetching 0.025 dollars (1/40) or 2.5 cents in Mar2008. By the end of Mar2009, one rupee was worth only 0.020 dollars (1/50) or 2 cents.
So, the rupee depreciated by 20 per cent [(0.025 - 0.020)/0.025] versus the dollar.
4. How to convert USD appreciation to INR depreciation
In general, rupee is a depreciating currency against the dollar. In the past 25 years, rupee gained only in seven calendar years -- the major rupee appreciation years were 2007, 2017, 2003, 2004, 2010 and 2009.
While it is intuitive to calculate dollar appreciation, it is not so for rupee appreciation, because we need to convert USD-INR into an INR-USD quote.
INR-USD is in decimals, it is not easy for many to work with decimals.
One short cut for computing INR depreciation is:
Suppose USD-INR moved from 40 to 50 in 2008-09, as we discussed in the above example. The US dollar appreciated by 25 per cent.
Formula for calculation of rupee depreciation: [x/(100 +x)]
Here, x = USD appreciation
So, INR depreciation = 25/(100 + 25) = 25/125 = 0.20 or 20 per cent.
Note: During episodes of rupee appreciation also, the above formula holds with x value taking minus sign.
5. Major currency pairs
Major currency pairs globally are EUR-USD, GBP-USD, USD-JPY and USD-CAD. Here, EUR is symbol for euro, GBP is symbol for pound sterling, JPY is Japanese Yen and CAD Canadian dollar.
In India, major currency pairs are USD-INR, EUR-INR, JPY-INR and GBP-INR, in addition to global currency pairs such as, EUR-USD, GBP-USD and USD-JPY.
The above formula for calculating depreciation can be used for global currency pairs also.
For example, USD-JPY exchange rate moved from 139 one year ago to 157.3 now. In the past one year, the dollar gained 13.17 per cent [(157.3 - 139)/139] against the yen.
Conversely, the yen lost 11.63 per cent [13.17/(100 + 13.17)] of its value against the dollar.
- - -
-------------------
References and additional data:
Top image: Teak tree canopy, Hyderabad, May2024
Tweet dt 17Feb2016 - mistake of quoting USD appreciation as INR depreciation
Page 208 >
Example of indirect quote system INR-USD: Business India issue of Jan 4-17, 1993 >
-------------------
Read more:
Blog of Blogs Theme-wise
Sensex versus Gold Price
RBI's Record Surplus Transfer to Govt of India
The Little Secret Behind Nifty Next 50 Index's Recent Success
Rapid Rise of India's PMS Industry
NSE Indices Calendar Year Returns: 2006 to 2024
How to Buy Nifty Midcap Index 03May2024
NSE Emerging Indices Comparison 31Mar2024
India Passive Funds and Their Asset Size 29Apr2024
Global Market Data 31Mar2024
Understanding Real Sensex and Currency Debasement
Select Gilt Funds Performance
SEBI Categorization and Rationalization of Mutual Funds
AMFI List of Market Cap: Categorization of Large-, Mid- and Small-Cap Stocks
Disclosure: I've got a vested interest in Indian stocks and other investments. It's safe to assume I've interest in the financial instruments / products discussed, if any.
Disclaimer: The analysis and opinion provided here are only for information purposes and should not be construed as investment advice. Investors should consult their own financial advisers before making any investments. The author is a CFA Charterholder with a vested interest in financial markets.
CFA Charter credentials - CFA Member Profile
CFA Badge
Viewing Options for this blog in different formats:
He blogs at:
https://ramakrishnavadlamudi.blogspot.com/
X (Twitter) @vrk100
No comments:
Post a Comment