How Default Probability and Recovery Shape Bond Prices
Summary
A defaultable bond’s market price reflects interest rates, the probability of default, and the value expected after default, represented by recovery or loss given default. The relative influence of these factors changes with credit quality: interest rates tend to matter more for investment-grade debt, while recovery expectations can become more important as default risk rises.
The explanation uses a simplified one-period payoff model to show how survival and recovery values combine in a price. It also points to distressed sovereign bonds that traded at different prices because investors expected different post-default collateral value, despite the bonds sharing default risk. Contract terms such as collective action clauses may also affect distressed bond values. The model is illustrative; actual bond pricing uses more complex assumptions and methods, so a quoted price does not imply a single universal recovery assumption.
Key ideas
- Defaultable bond prices depend on rates, default probability, and expected recovery value.
- Recovery assumptions have little influence when survival is highly likely, but gain importance as default risk rises.
- Distressed bonds from the same issuer can trade differently when investors expect different post-default values.
- Bond contract terms, including collective action clauses, may affect valuation in distressed situations.
- The simple payoff model illustrates the factors but does not capture the full complexity of bond pricing.
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Full text
# Does bond market trading price has recovery assumption in mind?
# Does bond market trading price has recovery assumption in mind?
We all know fixed income seucirties have default risk which can be generated from CDS market. However, I am curious if the market trading price of a bond (say, $105) imposing any recovery assumption?
Using recovery of 0 or 40%, the bond price could diff by more than 10 bucks. What is the real meaning out there from what we see on the screen or bid/ask of this $105? Should I price it without recovery assumption?
## Answer by Dimitri Vulis (score 5)
https://quant.stackexchange.com/a/55826
The price of a defaultable bond is driven by 3 things:
- the observable interest rates
- the probability of default
- the price of the bond after a default (or, equivalently, the loss given default)
The price of an investment-grade bond reacts mostly to interest rates. Further into junk, the interest rates affect the price less, and the thoughs of what might happen after a default begen to affect the price more. For example, a few years ago, before Venezuela defaulted on its USD sovereign bonds, one of the bonds was much more expensive than the others - not because it was less risky (they all defaulted at the same time) but because traders thought it was better collateralized and would be more valuable after the imminent default.
Similar bonds might also trade differently because some have collective action clause (CAC) and others don't. For an IG bond it should not matter, but for junk, it may play a role.
Greatly oversimplying, imagine that the price of a defaultable bond that pays 1 with survival probability $p$ and alternatively pays recovery $R<1$ with probability $1-p$ is $$\frac{1}{1+r} p + (1-p) R,$$ where $r$ is the interest rate. (People use much more complicated models but this is the general idea.) Clearly if $p$ is close to 1, then $R$ doesn't matter and $r$ drives the price. But as $p$ decreases and approaches 0, $r$ matters less, $R$ matters more, and eventually the price expresses the expectation of what the bond will be worth after the default.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.