# Correlation Patterns in Foreign Exchange Markets

## TL;DR

This paper develops transformation equations for means and covariances of log returns when changing the numeraire in foreign exchange markets, and empirically shows that partial correlations remain invariant under such changes, revealing hidden relationships.

## Contribution

It introduces transformation formulas for means and covariances under numeraire change and demonstrates the invariance of partial correlations empirically in FX markets.

## Key findings

- Partial correlations are invariant under numeraire change.
- Partial correlations reveal hidden asset relationships.
- Empirical validation across numerous FX assets.

## Abstract

The value of an asset in a financial market is given in terms of another asset known as numeraire. The dynamics of the value is non-stationary and hence, to quantify the relationships between different assets, one requires convenient measures such as the means and covariances of the respective log returns. Here, we develop transformation equations for these means and covariances when one changes the numeraire. The results are verified by a thorough empirical analysis capturing the dynamics of numerous assets in a foreign exchange market. We show that the partial correlations between pairs of assets are invariant under the change of the numeraire. This observable quantifies the relationship between two assets, while the influence of the rest is removed. As such the partial correlations uncover intriguing observations which may not be easily noticed in the ordinary correlation analysis.