Choosing Bond Spread Curves for Relative-Value Analysis

Summary

The document explains that the right bond comparison measure depends on the task. For an indicative price on an illiquid bond, it describes interpolating between observable bonds that mature earlier and later. For amortizing bonds, weighted average life may be a more suitable reference than stated maturity, and interpolating spreads over observable risk-free rates can help make the basis for the quote explicit.

For rich-cheap analysis, the answer favors comparing spreads, such as Z-spreads or option-adjusted spreads, rather than raw yields, because a fixed-coupon yield includes a risk-free component that may obscure bond-specific value. It suggests fitting a Nelson-Siegel curve or splines instead of relying on linear interpolation for this purpose. For credit-risky bonds, it recommends considering default probabilities and loss given default, since rate-based spread methods alone do not represent credit risk fully. These are context-dependent guidelines, not a single universal valuation rule.

Key ideas

• Choose a bond valuation or comparison method based on the intended use.
• Linear interpolation between nearby observable bonds can support transparent indicative quotes.
• Weighted average life may be more relevant than maturity for amortizing bonds.
• Spread measures can isolate bond-specific relative value better than raw yields.
• Credit comparisons may need default probability and loss-given-default analysis.

Tags

# Relative value of bonds


# Relative value of bonds












Is it best to measure the relative value of bonds on a z-spread curve or by modified duration?

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/84090

This is an extremely broad question, and, as @alper suggested, it depends on what you're trying to do. For example, if you need to come up with a transparent and explainable indicative quote for an illiquid bond without an observable quote, then the "industry standard" would be a linear interpolation of the observable quotes of bonds maturing before and after yours. You'd need to justify doing anything different. But sometimes something slightly different is better, e.g. if some bonds amortization, then weighted average life may work better than maturity. It would make more sense to interpolate just some spreads over observable risk-free rates, but you'd need to explain it.

If you're trying to build a rich-cheap comparison, and I've seen literally hundreds of bad ones, then Z-spreads or option-adjusted spreads or some other spread makes more sense than yields simply because a fixed-coupon bond yield contains a risk-free rate that has little to do with the bonds' idiosyncrasies. Nelson-Siegel or splines make more sense than linear interpolation. But if these are credit-risky bonds, then looking at their probabilities of default and loss given default looks much better than any methodology treating the bonds as rates-only.

Related Interpolating a yield from two yields (giving more weight to one of the two)

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