# 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?

## 1 Answer

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.

• Can I ask in general how we get the recovery rate? Also, from different vendors, I can see most of them do not impose a loss model or recovery input even when I run a HY bond. Does that mean the calculation and all analytics are based on 0 recovery with implied spread which basically contains default, liquidity and recovery risk? That sounds too bad. Isn’t it? Another thing I found is that one bond I looked at trade at around 85. If I implied default p from cds market and input a 40% recovery, I will get price of 95. If I implied a recovery, it is super small (around 2%). How can that be? – HoldBreath Jul 22 '20 at 1:16
• No one knows the recovery exactly until after the fact. But it's also not very useful until the credit event is near. Moody's has some service that predicts recovery, AFAIK not very popular or credible. For vanilla CDS, you only see CDS spread in the market. You use some standard recovery assumption, usually 40%, sometimes 70% or 25%.. to get risk-neutral surival probability, which for HY names depends a lot on the recovery assumption. – Dimitri Vulis Jul 22 '20 at 3:17
• Thanks Dimitri! Mind I ask in practice, what recovery you use for valuing HY bond? As you mentioned that it makes no much sense until we get very close to a credit event. Does that mean, if a HY bond trade at 90 today on market, people generally value it with 0 recovery assumed? Since I guess any non-zero value would be too arbitrary and embed a model risk for your valuation and in worse case scenario, place yourself in a bad position when trading with counterparties. – HoldBreath Jul 22 '20 at 17:30
• Generally, it's not common to use any physical recovery assumption to calculate a fair price of a HY bond because it is so uncertain. I once build a bond rich-cheap tool which aimed to calculate a bond-CDS basis for some bonds, where the CDS spread was observable (it is not for most credits). I used "standard" recovery (25% for emerging markets, 40% for others) to get risk-neutral survival curve. Then I got a (pretty useless) "fair price" of the bonds using the same recovery that I assumed for the CDS, except that I override the recovery to 70% for some bonds known to be highly collateralized, – Dimitri Vulis Jul 22 '20 at 18:39
• (continued) and I also overrode the recovery 0 for subordinated bonds (but I assumed the same probability of default as senior, which might not be correct). As I said this "fair price" is useless, but the process allows me to solve for - how much does the observable CDS spread need to be shifted in order to explain the observable bond price? This "bond-CDS basis" (which depends little on the recovery assumption) is not very useful either, but you can examine it over time to see, for example, whether it reverts to mean. – Dimitri Vulis Jul 22 '20 at 18:42