Aggregating Bond Yields Across Currencies and a Portfolio

Summary

The document outlines a two-step approximation for reporting yield across a bond portfolio denominated in multiple currencies. First, to express a bond’s yield in another currency, it proposes matching the bond’s cash flows with one leg of a cross-currency swap, then solving for the yield on the other currency’s flows. The cross-currency basis is part of that swap pricing.

Second, it suggests calculating the portfolio figure as a weighted average of the individual bond yields. It notes that differing coupon or payment frequencies may need normalization before averaging. The response gives no worked example, weighting convention, or treatment of portfolio cash flows, and describes more elaborate approaches as possible. Consequently, the weighted average is a practical simplification rather than a universal measure of portfolio yield; the chosen currency and yield definition should be made explicit.

Key ideas

• A cross-currency swap can translate a bond’s cash flows into another currency for yield calculation.
• The swap pricing should account for the cross-currency basis.
• A portfolio yield can be approximated by weighting the individual bond yields.
• Yields with different payment frequencies may need normalization before aggregation.

Tags

# How do you calculate the YTM of a multi-currency portfolio?


# How do you calculate the YTM of a multi-currency portfolio?












I would like to know how to calculate the aggregate YTM of a portfolio with bonds of different currencies

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/80074

There are two parts to this question.

- yield in a different currency: Suppose you have a bond denominated in ccy1. To get its ccy2 yield, taking into consideration the cross-currency basis, price a cross-currency swap whose ccy1 cash flows match the bond. Solve for the yield of the ccy2 flows of the swap.

- yield of a portfolio of bonds: just use the weighted average of individual yields. It's possible to do more complicated calculations, but probably not worth it. If some bonds have different frequencies, you may want to normalize their yields to the same frequency.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.