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Hi,

I am trying to understand what Geometric Progression Weighted Average (GPWA) is in the context of the calculation of the US Dollar Index (USDX). I understand what a weighted average is but don’t understand what a GPWA is and when one should use it.

The following equation shows how the USDX is calculated using GPWA. In simple terms, the exchange rates of the US dollar with six major currencies are raised to a power value and the product of these terms is multiplied with an offset (50.14) to get the USDX. The power by which an exchange rate is raised represents the % of total US trade with that country. You can read more about http://www.akmos.com/forex/usdx/".

Note that my formula looks a bit different from the formula given in the article, but both formulae give the same answer. The term EUR / USD represents how many Euros can be purchased using one US dollar.

I am trying to understand the advantage of using trade weights as powers (i.e Ex. rate ^ weight) over simply using the weights as multiplying factors (i.e. Ex rate × weight). I know that using the weights as factors would result in a smaller number, but that is not a strong argument for using GPWA as one can always increase the magnitude of the offset to get a large value.

I have calculated the USDX below using exchange rates as of Dec 30, 2008.

EUR / USD 0.7099

JPY / USD 90.36

GBP / USD 0.6924

CAN / USD 1.2185

SEK / USD 7.7565

CHF / USD 1.0575

USDX = 51.1435 × 0.821 × 1.845 × 0.957 × 1.018 × 1.090 × 1.002 = 82.44

Thanks,

MG.

I am trying to understand what Geometric Progression Weighted Average (GPWA) is in the context of the calculation of the US Dollar Index (USDX). I understand what a weighted average is but don’t understand what a GPWA is and when one should use it.

The following equation shows how the USDX is calculated using GPWA. In simple terms, the exchange rates of the US dollar with six major currencies are raised to a power value and the product of these terms is multiplied with an offset (50.14) to get the USDX. The power by which an exchange rate is raised represents the % of total US trade with that country. You can read more about http://www.akmos.com/forex/usdx/".

Note that my formula looks a bit different from the formula given in the article, but both formulae give the same answer. The term EUR / USD represents how many Euros can be purchased using one US dollar.

I am trying to understand the advantage of using trade weights as powers (i.e Ex. rate ^ weight) over simply using the weights as multiplying factors (i.e. Ex rate × weight). I know that using the weights as factors would result in a smaller number, but that is not a strong argument for using GPWA as one can always increase the magnitude of the offset to get a large value.

**USDX = 50.14348112 × EUR / USD ^ 0.576 × JPY / USD ^ 0.136 × GBP / USD ^ 0.119 × CAD / USD ^ 0.091 × SEK / USD ^ 0.042 × CHF / USD ^0.036**I have calculated the USDX below using exchange rates as of Dec 30, 2008.

EUR / USD 0.7099

JPY / USD 90.36

GBP / USD 0.6924

CAN / USD 1.2185

SEK / USD 7.7565

CHF / USD 1.0575

USDX = 51.1435 × 0.821 × 1.845 × 0.957 × 1.018 × 1.090 × 1.002 = 82.44

Thanks,

MG.

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