As there appears to be much discourse around the status of the dollar as "the world reserve currency", it seems interesting to me that the standard measure of the dollar's strength is not weighted in this way.

Here I am attempting to reconcile the standard dollar index ( DXY ), which measures the strength of the USD against a basket of other currencies (see below), with the dollar's presence within the IMF's World Currency Reserves (see below). I have chosen to call this the "True Dollar Index" ( TDI )
To do so, I have first taken the ratio of the Dollar's IMF weight against each currency and multiplied it by the dollar denominated exchange rate. Then I attempt to normalize the value by dividing it by the average of the 9 dollar denominated exchange rates.

The equation I used for the 2022 TDI is as follows(*):
( USDEUR * (58.81/20.64) + USDJPY * (58.81/5.57) + USDGBP * (58.81/4.78) + USDCNH * (58.81/2.79) + USDCAD * (58.81/2.38) + USDAUD * (58.81/1.81) + USDCHF * (58.81/0.2) + USDSGD * (58.81/1.505) + USDHKD * (58.81/1.505)) / (( USDEUR + USDJPY + USDGBP + USDCNH + USDCAD + USDAUD + USDCHF + USDSGD + USDHKD )/9)

(*) This is in standard TradingView equation format and can be directly copy/pasted into the search bar - though values will convert to decimal

As the weighting of the IMF World Currency Reserves is shuffled and reported at the end of the year, this should only be taken to be valid as of Q1 2022.

For comparison, I have included the DXY in Orange. Note that I have adjusted the DXY by 41.0351, this is the difference in their starting values on Dec 31, 2021.
This should allow us to capture deviation from this starting point. I chose this action as opposed to adjusting the existing equation to for simplicity, though one could easily drag the TDI down by subtracting the same amount.

I make no claims to the accuracy of this chart as a measure of the strength of the dollar. I am not an economist, and I am happy to hear suggestions on how to improve this model.

DXY Geometric Weightings:
  • Euro (EUR), 57.6% weight
  • Japanese yen (JPY) 13.6% weight
  • Pound sterling (GBP), 11.9% weight
  • Canadian dollar (CAD), 9.1% weight
  • Swedish krona ( SEK ), 4.2% weight
  • Swiss franc (CHF) 3.6% weight

Currency composition of official IMF foreign exchange reserves:
  • Dollar (USD), 58.81%
  • Euro (EUR), 20.64%
  • Japanese yen (JPY), 5.57%
  • Pound sterling (GBP),4.78%
  • Chinese renminbi, 2.79%
  • Canadian dollar (CAD), 2.38%
  • Australian dollar (AUD), 1.81%
  • Swiss franc (CHF), .2%
  • Other, 3.01%*

    *To account for this ambiguity, I have opted for a 50/50 split of the Hong Kong Dollar ( HKD ) and the Singapore Dollar (SGD). These are roughly equal in their use as a global payment currency at the time of writing and are the only top payment currencies not already included in the weighting.

    Sources:
  • https://en.wikipedia.org/wiki/U.S._Dolla...
  • https://data.imf.org/regular.aspx?key=41...
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