USDINR and Dollar Indices, Part I

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The St. Louis Fed publishes a number of economic and financial series on its Federal Reserve Economic Data (FRED) database. It is a treasure trove of information for quants. There are a number of currency related time-series in the database. In this post, we will plot the USDINR exchange rate with the trade-weighted indices available on FRED to explore any relationships that there might be between them.

Trade-weighted indices

A trade-weighted dollar index is simply the weighted average of the foreign exchange value of the U.S. dollar against the currencies of a group of U.S. trading partners. The FRED publishes the following such indices:

  1. DTWEXB: Includes the Euro Area, 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 and Colombia.
  2. DTWEXM: Includes the Euro Area, Canada, Japan, United Kingdom, Switzerland, Australia, and Sweden.
  3. DTWEXO: Includes Mexico, China, Taiwan, Korea, Singapore, Hong Kong, Malaysia, Brazil, Thailand, Philippines, Indonesia, India, Israel, Saudi Arabia, Russia, Argentina, Venezuela, Chile and Colombia.

Additionally, they also publish the DEXINUS series that is the USDINR exchange rate.

These series go back to the mid-70’s and mid-90’s. However, India was a closed economy with a managed currency for the most parts. So for the rest of this post, we will consider data only from 2005 onward.

Here is how the time-series looks:
FRED DEXINUS-DTWEXB-DTWEXM-DTWEXO indices

Beta between USDINR and the rest

What we are interested in is the relationship between USDINR and the rest of the trade-weighted averages. DTWEXB and DTWEXO have India exposure with the latter made up predominantly of emerging markets. So we should expect a high beta between USDINR and those.

To calculate the beta, we will fit a linear model through USDINR and each of the trade-weighted indices in turn. Also, we will force the intercept to be zero to force the fit.

Here are the betas with a 20-day look-back:
20-day beta between USDINR and trade-weighted indices

Here are the betas with a 50-day look-back:
50-day beta between USDINR and trade-weighted indices

The 20-day chart shows that the beta oscillates within a tight band for the most part. This insight can be used to build a mean-reversion model for USDINR.

In Part II, we will explore the spread between USDINR and all three of the indices. Stay tuned!

Code and charts are on github.

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