Trade-weighted US dollar index

From Wikipedia, the free encyclopedia
  (Redirected from Trade Weighted US dollar Index)
Jump to: navigation, search

The trade-weighted US dollar index, also known as the broad index, is a measure of the value of the United States dollar relative to other world currencies. It is similar to the U.S. 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[edit]

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[edit]

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:

Mathematical formulation[edit]

Based on nominal exchange rates[edit]

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[edit]

The real exchange rate is a more informative measure of the dollar's worth since it accounts for countries whose currencies experience differing rates of inflation from that of the United States. 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

References[edit]

External links[edit]