What do you Know About Trade Weighted US dollar Index?

The Trade Weighted US dollar Index, which is also referred to as the broad index, is a measure of the value of the US Dollar relative to other world currencies. It is identical to the US Dollar Index in a way that its numerical value is determined as a weighted average of the price of various currencies relative to the dollar, however it differs from the US Dollar Index in a way the currencies are used and how their relative values are weighted.

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History of Trade Weighted US dollar Index

In 1998 the trade weighted dollar index was introduced. There were two primary reasons due to which it was introduced. The first reason was the introduction of the euro, by which elimination of several of the currencies in the standard dollar index takes place; the second reason was to keep pace with new developments in US trade.

Included Currencies

A significant weight is given to the euro in the standard US Dollar Index. the Federal Reserve created the Trade Weighted US Dollar Index in order to more accurately reflect the strength of the dollar relative to other world currencies. The Trade Weighted US Dollar Index includes a bigger collection of currencies than the US Dollar Index.

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Mathematical Formulation

Based on nominal exchange rates

The index is computed as the geometric mean of the bilateral exchange rates of the currencies that are included in it. Trade data is the base to which the weight is assigned to the value of each currency in the calculation, and it is updated annually (the value of the index itself is more frequently updated than the weightings). The index value at time t is given by the formula:

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

here,

I_t and I_{t − 1}indicates the values of the index at times t and t − 1

N(t) indicates the number of currencies in the index at time t

e_j,t and e_{j,t − 1} indicates the exchange rates of currency j at times t and t − 1

w_j,t indicates the weight of currency j at time t

and $sum_{j=1}^{N(t)} w_{j,t} = 1$

Based on real exchange rates

There are some countries whose currencies experience differing rates of inflation from that of the United States. Then in order to account for such countries the real exchange rate is a more informative measure of the dollar’s worth. By adjusting the exchange rates in the formula using the consumer price index of the respective countries this is compensated. In this more general case the index value is given by:

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

here,

p_t and p_{t − 1} indicates the values of the US consumer price index at times t and t − 1

and p_j,t and p_{j,t − 1} indicates the values of the country j‘s consumer price index at times t and t − 1

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