View source for Trade-weighted US dollar index

{{Short description|Measure of the relative value of the US dollar}}
[[File:Trade Weighted USD Index.webp|thumb|380px|right|
{{legend|#3C3B6E|outline=#B22234|Trade-weighted US dollar index}}
{{legend-line|#0F64CD solid 3px|[[United States dollar|USD]] / [[South Korean won]]}}
{{legend-line|#810000 solid 3px|USD / [[Japanese yen|Japanese Yen]]}}
{{legend-line|#929292 solid 3px|USD / [[Canadian dollar]]}}
{{legend-line|#006341 solid 3px|USD / [[Mexican peso]]}}
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{{legend-line|#EE1C25 solid 3px|USD / [[Renminbi|Chinese Renminbi]]}}
{{legend-line|#F27200 solid 3px|USD / [[Pound sterling|British Pound Sterling]]}}
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{{Foreign Exchange}}

The '''trade-weighted US dollar index''', also known as the '''broad index''', is a measure of the value of the [[United States dollar]] relative to other world [[currency|currencies]]. It is a [[trade weighted index]] that improves on the older [[U.S. Dollar Index]] by incorporating more currencies and yearly rebalancing.  The base index value is 100 in January 1997.<ref>{{Cite web | title = Trade Weighted U.S. Dollar Index | url = https://fred.stlouisfed.org/series/DTWEXB| accessdate = 2 November 2018}}</ref>  As the U.S. Dollar gains value the index increases.

==History==
The trade-weighted dollar index was introduced in 1998 for two primary reasons.  The first was the introduction of the [[euro]], which eliminated several of the currencies in the standard dollar index; the second was to keep pace with new developments in US trade.<ref name=winter05>{{Cite journal | title = Indexes of the Foreign Exchange Value of the Dollar | last = Loretan | first = Mico | date = Winter 2005 | journal = Federal Reserve Bulletin | volume = 91 | doi = 10.17016/bulletin.2005.91-1-1 | url = http://www.federalreserve.gov/pubs/bulletin/2005/winter05_index.pdf}}</ref>

==Included currencies==
In the older [[U.S. Dollar Index]], a significant weight is given to the euro, because most U. S. Trade in 1973 was with European countries. As U. S. trade expanded over time, the weights in that index went unchanged and became out of date.  To more accurately reflect the strength of the dollar relative to other world currencies, the [[Federal Reserve]] created the trade-weighted US dollar index,<ref>{{Cite web|url=https://www.federalreserve.gov/RELEASES/h10/Summary/|title=The Fed - Foreign Exchange Rates - H.10 - Nominal/Real Indexes|website=www.federalreserve.gov}}</ref> which includes a bigger collection of currencies than the US dollar index. The regions included are:

{{col-begin}}
{{Col-3}}
* Europe (euro countries)
* Canada
* Japan
* Mexico
* China
* United Kingdom
* Taiwan
* Korea
* Singapore
{{Col-3}}
* Hong Kong
* Malaysia
* Brazil
* Switzerland
* Thailand
* Philippines
* Australia
* Indonesia
* India
{{Col-3}}
* Israel
* Saudi Arabia
* Russia
* Sweden
* Argentina
* Venezuela
* Chile
* Colombia
{{Col-end}}
[[File:Broad Index weights by currency.webp|thumb|right|250px|Broad Index weights]]
==Mathematical formulation==

===Based on nominal exchange rates===
The index is computed as the [[geometric mean]] of the bilateral exchange rates of the included currencies.  The weight assigned to the value of each currency in the calculation is based on trade data, and is updated annually (the value of the index itself is updated much more frequently than the weightings).<ref name=winter05/>  The index value at time <math>t</math> is given by the formula:<ref name=winter05/>

:<math>I_t = I_{t-1} \times \prod_{j = 1}^{N(t)} \left( \frac{e_{j,t}}{e_{j,t-1}} \right)^{w_{j,t}}</math>.

where

* <math>I_t</math> and <math>I_{t-1}</math> are the values of the index at times <math>t</math> and <math>t-1</math>
* <math>N(t)</math> is the number of currencies in the index at time <math>t</math>
* <math>e_{j,t}</math> and <math>e_{j,t-1}</math> are the amount of currency <math>j</math> required to purchase one U.S. Dollar at times <math>t</math> and <math>t-1</math><ref>{{Cite journal |last=Beschwitz|first=Bastian von |last2=Collins |first2=Christopher G. |last3=Datta |first3=Deepa D. |date=2019-01-15 |title=Revisions to the Federal Reserve Dollar Indexes |url=https://www.federalreserve.gov/econres/notes/feds-notes/revisions-to-the-federal-reserve-dollar-indexes-20190115.htm |journal=FEDS Notes |language=en}}</ref>
* <math>w_{j,t}</math> is the weight of currency <math>j</math> at time <math>t</math>
* and <math>\sum_{j=1}^{N(t)} w_{j,t} = 1</math>

===Based on real exchange rates===
The real exchange rate is a more informative measure of the dollar's worth since it accounts for countries whose currencies experience differing rates of inflation from that of the United States.  This is compensated for by adjusting the exchange rates in the formula using the [[consumer price index]] of the respective countries.  In this more general case the index value is given by:<ref name=winter05/>

:<math>I_t = I_{t-1} \times \prod_{j = 1}^{N(t)} \left( \frac{e_{j,t} \cdot \frac{p_t}{p_{j,t}}}{e_{j,t-1}\cdot \frac{p_{t-1}}{p_{j,t-1}}} \right)^{w_{j,t}}</math>.

where

* <math>p_t</math> and <math>p_{t-1}</math> are the values of the US consumer price index at times <math>t</math> and <math>t-1</math>
* and <math>p_{j,t}</math> and <math>p_{j,t-1}</math> are the values of the country <math>j</math>'s consumer price index at times <math>t</math> and <math>t-1</math>

==Federal Reserve Bank of St. Louis data==

The Federal Reserve Bank of St. Louis, provides "weighted averages of the foreign exchange value of the U.S. dollar against the currencies of a broad group of major U.S. trading partners" with detailed information. The "broad currency index includes the Euro Area, Canada, Japan, Mexico, China, United Kingdom, Taiwan, Korea, Singapore, Hong Kong, Malaysia, Brazil, Switzerland, Thailand, Philippines, Australia, Indonesia, India, Israel, Saudi Arabia, Russia, Sweden, Argentina, Venezuela, Chile and Colombia."<ref name="FRED_2017">{{citation |url=https://fred.stlouisfed.org/series/TWEXB |publisher=Board of Governors of the Federal Reserve System (US) |title=Trade Weighted U.S. Dollar Index: Broad [TWEXB] |department=Federal Reserve Bank of St. Louis (FRED)|date=April 27, 2017 |accessdate=April 28, 2017}}</ref>

This table shows some highs and lows of the Trade Weighted U.S. Dollar Index: Broad [TWEXB] from 2002 to April 2017.<ref name="FRED_2017" /> 

{| class="wikitable"
|+ Sample of trade weighted averages of foreign exchange value USD (highs/lows ) DMY <ref name="FRED_2017" />
! 20-02-2002 !! 09-04-2008 !!  23-07-2011 !! 27-07-2011 !! 18-03-2015 !! 03-06-2015 !! 17-02-2016 !! 04-05-2016 !!26-08-2016 !! 23-11-2016 !!04-01-2017 !!19-04-2017 
|-
| 129.3639  || 95.6084 ||  102.1682 || 94.0323 || 117.4927 || 115.5347 || 123.7823 || 118.6478 || 120.2955 || 127.2899 || 128.5246 ||124.0479
|}

==References==
{{Reflist}}

==External links==
*[https://fred.stlouisfed.org/series/TWEXB Trade weighted dollar indexes at St. Louis Fed]

[[Category:Economic indicators of United States currencies]]