Learns Forex: November 2010

The trade weighted dollar index was introduced in 1998 for two primary reasons. The first being the introduction of the euro, which eliminated several of the currencies in the standard dollar index; the second being to keep pace with new developments in US trade

Included currencies

Europe (euro countries)
Canada
Japan
Mexico
China
United Kingdom
Taiwan
Korea
Singapore

Israel
Saudi Arabia
Russia
Sweden
Argentina
Venezuela
Chile
Colombia

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]

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