The DXY Basket Weights, Quote Conventions, and Base-Level Constant
Summary
The document explains the structure of the U.S. Dollar Index as a weighted geometric basket of six foreign currencies. Its currency exponents correspond to fixed component weights based on bilateral trade, while the leading coefficient sets the index’s historical level to 100 at the start of its reference period. The answer also distinguishes DXY from trade-weighted variants whose weights are periodically updated.
Quote conventions explain why the euro and pound exchange rates have negative exponents: those rates express dollars per unit of foreign currency, whereas the other components are quoted as foreign currency per dollar. The basket changed when the euro was introduced, replacing several European currencies, so commonly available series begin around that transition. The document describes the formula’s construction and historical context, but does not provide a derivation of the coefficient beyond its role as the normalization factor or discuss later methodology changes.
Key ideas
- DXY combines six currencies using a weighted geometric basket.
- The component exponents represent fixed currency weights tied to bilateral trade.
- The leading coefficient normalizes the index to its historical reference level.
- Exchange-rate quote direction accounts for the differing exponent signs.
- The basket was revised when the euro replaced several European currencies.
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Full text
# Where does the 50.14348112 coefficent in the US Dollar Index formula come from?
# Where does the 50.14348112 coefficent in the US Dollar Index formula come from?
The formula for the US Dollar Index (DXY) that every resource on the internet provides is: $$DXY = 50.14348112 × EURUSD^{-0.576} × USDJPY^{0.136} × GBPUSD^{-0.119} × USDCAD^{0.091} × USDSEK^{0.042} × USDCHF^{0.036}$$ Some also mention that DXY is the weighted geometrical mean of these exchange rates. So by calculating the weighted geometric mean in Excel I found that its actually the same as the above formula but without the 50.14348112 coefficent. So my question is where does it come from?
## Answer by Dimitri Vulis (score 5, accepted)
https://quant.stackexchange.com/a/53180
The US Dollar Index is the ratio of the US dollar (USD) to a geometric basket of six major foreign currencies – the Euro (EUR), the Japanese yen (JPY), the pound sterling (GBP), the Canadian dollar (CAD), the Swedish kroner (SEK) and the Swiss franc (CHF). The countries that use these currencies constitute the bulk of international trade with the United States, and also have well-developed foreign exchange markets, with rates freely determined by market participants.
The exponents that you write as superscripts come the constant weights of each component currency in the index:
EUR: 57.6%;
JPY 13.6%;
GBP: 11.9%;
CAD: 9.1%;
SEK: 4.2%;
CHF: 3.6%.
The weights add up to 100%. The Federal Reserve created this index in March, 1973, when the Bretton Woods Agreement fell apart and the main currencies began to be freely quoted relative to each other. They weights were set based on bilateral trade. There is are also trade-weighted version of this index, where the weights are updated periodically.
The first factor, 50.14348112, is the historical value of the index to 100 on the date that the reference began.
GBP and EUR rates have negative exponents because by market convention they are quoted "cable" against USD, as the amount of USD needed to buy 1 unit of foreign currency. Conversely the quotes for the other currencies are the amount of foreign currency needed to buy 1 USD.
The calculation formula has changed once in connection with the creation of the Euro. Prior to the Euro, the index contained the Deutsche Mark, the French Franc, the Italian Lira, the Dutch Guilder and the Belgian Franc. For this reason the time series usually begin in 1999.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.