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Measuring Fixed-Income Diversification with Factor Risk Models

Article Quant Q&A · Author: rrg
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Summary

The document asks how to reward diversification in a fixed-income portfolio whose holdings vary by currency, yield, tenor, and class. It raises portfolio-weighted correlation and the Herfindahl index as possible ingredients, but does not develop either into a complete investment metric.

The response suggests using a linear multi-asset factor model to separate systematic from specific risk, then calculating specific risk through established risk-model methods. Another contribution points to comparing standalone bond or portfolio VaR with overall portfolio VaR to observe diversification effects, and asks how the variance-covariance matrix was estimated, including whether it used daily price changes. These are possible approaches rather than a tested recommendation. The discussion supplies no model specification, estimation guidance, numerical evidence, or treatment of how diversification should be rewarded under Solvency II.

Key ideas

  • A linear multi-asset factor model can distinguish systematic risk from specific risk in fixed-income portfolios.
  • Portfolio correlation and concentration measures such as HHI are proposed but not fully specified.
  • Comparing standalone and aggregate VaR may help reveal portfolio diversification effects.
  • The usefulness of a variance-covariance matrix depends on how its inputs and observation frequency are chosen.
  • The discussion offers suggestions rather than a validated metric or empirical comparison.

Tags

Fixed incomePortfolio constructionRisk managementStatistics
Full text
# Diversification investment metric for a FI portfolio


# Diversification investment metric for a FI portfolio












What is a good investment metric to reward diversification within a portfolio. Suppose we have a fixed income universe and prefer stable currency, mid yield and mid tenors. Our stressed spread var covar matrix suggests that we have correlation factor amongst each currency & fixed income class.

A simple metric would be weighted-portfolio for correlation Possibly the HHI Herfindahl index weights

This is in the context of Solvency II but would apply much more broadly. Any suggestions or solutions?

## Answer by pyCthon (score 2)

https://quant.stackexchange.com/a/33733

This extends to not just FI but multi asset class (MAC) as well. You can use a linear MAC factor model to compute specific\unsystematic risk.

Here's are several examples of such a model:

- https://www.msci.com/documents/1296102/5025433/PRESENTATION_FixedIncomeRoadshow.pdf

- https://www.jpmorgan.com/jpmpdf/1158651692009.pdf

You would compute specific risk the same way you normally would: How to calculate unsystematic risk?

## Answer by AK88 (score 0)

https://quant.stackexchange.com/a/30639

Also intrested in this question. A more qualitative approch is presented here.

Can you tell how did you get your variance-covariance matrix? Did you use daily price changes?

Somebody suggested using VaR if you have multi-currency FI portfolio. So you'd have VaR measures for specific bonds and for overall portfolio. And from there maybe you be able to see the difersification effect?

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.