Journal of Risk
ISSN:
1465-1211 (print)
1755-2842 (online)
Editor-in-chief: Farid AitSahlia
Converting a covariance matrix from local currencies to a common currency
Need to know
- A new formula for converting a covariance matrix estimated in local currencies into a covariance matrix expressed in a common currency is proposed.
- This process uses simple matrix multiplications.
- We solve a long-standing problem in the calculation of risk exposures.
Abstract
This short paper demonstrates how a covariance matrix estimated using log returns of multiple assets in their respective base currencies can be converted directly into a covariance matrix in a single common currency by using basic matrix multiplication. This approach eliminates the need to convert returns into a common currency, simplifying the estimation process. In addition to describing the conversion process, this note also addresses the conversion of covariances between two currencies. By applying the proposed methodology, asset managers can efficiently analyze the covariance between assets denominated in diverse currencies, saving time and resources. It is thus a valuable tool for asset managers seeking to optimize portfolio allocation across different currencies.
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