(Redirected from Trade Weighted US dollar Index)

The trade-weighted US dollar index, also known as the broad index, is a measure of the value of the US dollar relative to other world currencies. It is similar to the US dollar index in that its numerical value is determined as a weighted average of the price of various currencies relative to the dollar, but different currencies are used and relative values are weighted differently.

## 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.[1]

## Included currencies

In the standard US dollar index, a significant weight is given to the euro. To more accurately reflect the strength of the dollar relative to other world currencies, the Federal Reserve created the trade-weighted US dollar index,[2] which includes a bigger collection of currencies than the US dollar index. The regions included are:

 Europe (euro countries) 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 Colombia

## 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).[1] The index value at time $t$ is given by the formula:[1]

$I_t = I_{t-1} \times \prod_{j = 1}^{N(t)} \left( \frac{e_{j,t}}{e_{j,t-1}} \right)^{w_{j,t}}$.

where

• $I_t$ and $I_{t-1}$ are the values of the index at times $t$ and $t-1$
• $N(t)$ is the number of currencies in the index at time $t$
• $e_{j,t}$ and $e_{j,t-1}$ are the exchange rates of currency $j$ at times $t$ and $t-1$
• $w_{j,t}$ is the weight of currency $j$ at time $t$
• and $\sum_{j=1}^{N(t)} w_{j,t} = 1$

### Based on real exchange rates

In order to account for countries whose currencies experience differing rates of inflation from that of the United States the real exchange rate is a more informative measure of the dollar's worth. 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:[1]

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

where

• $p_t$ and $p_{t-1}$ are the values of the US consumer price index at times $t$ and $t-1$
• and $p_{j,t}$ and $p_{j,t-1}$ are the values of the country $j$'s consumer price index at times $t$ and $t-1$