Newbie here. I should say upfront that I'm not a quant, just someone trying to broaden his knowledge of fixed income investing. I apologise in advance if I'm mangling some terminology.

Imagine a rational investor who's trying to select from a set of risky bonds, all of which have the same maturity date yet different credit qualities. My question is, is it possible to say in advance which bond will have the highest expected return if held to maturity ? Will it be the bond with the highest yield, the one with the lowest yield - or is it impossible to generalise ?

I know that riskier bonds have a higher YTM, reflecting their increased rate of default. But AIUI, the existence of this "default premium" doesn't necessarily influence the expected return from the bond. Yes, a poor quality bond will trade at a lower price but you have a smaller chance of receiving the promised cashflows. In a perfect world I'd expect the two effects to balance out, and I therefore wouldn't think there's a strong reason for a rational investor to prefer the highest-yielding bond over the lowest-yielding, or vice versa (?)

I have read that there's also a credit risk premium, which (AIUI) represents the extra compensation that risk-averse investors demand for the stress and uncertainty of holding a bond that may or may not default. It's not a direct function of default probabilities or anything like that; it's purely a psychological/market-driven phenomenon (I've read papers debating whether this risk premium actually exists, but let's assume for a sec that it does)

Putting this all together, I think the rational approach is to select the bond that has the highest credit risk premium (CRP). The size of the default premium by itself isn't directly relevant (except in the sense that you need it in order to back out the CRP). This leads me to the conclusion that there is no easy way to choose between the bonds merely by looking at them.

Is my thinking basically correct here, or am I hopelessly mixed up ? thanks !

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    $\begingroup$ You are correct that 1) higher YTMs of riskier bonds doesn't imply higher expected returns, 2) it is not straightforward to evaluate the expected return. Theoretically you would prefer bonds with best expected returns relative to risk (beta). $\endgroup$
    – fes
    May 2, 2022 at 7:56
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    $\begingroup$ My professor used to say that the YTM should really be called the PYTM (the Promised Yield to Maturity, i.e. assuming that there is no default). The expected return taking prob of default into account is presumably lower, although as fesman said not straightforward to calculate. Clearly buying the bond with the highest PYTM thinking it is the best return is a fallacy. $\endgroup$
    – nbbo2
    May 2, 2022 at 15:26
  • $\begingroup$ There were several papers in the 1990s by Bielecki and by Duffie and Singleton, discussing how a fair value of a risky bond could be computed, similar to pricing a credit default swap, out of probability of default, and loss given default (both of which should ideally have term structure). Any day, with probability PD on that day, the bondholder receives 1-LGD on that day; else, with probability 1-PD, he receives the promised payments. Discount with the cost of financing, and sum up to get fair dirty price. If you have Bloomberg, "VCDS<Go>" does this. But you need cash flows, not just yield. $\endgroup$ May 3, 2022 at 22:50

1 Answer 1


I'll mark this closed shortly, the comments from nbbo2 and fesman were both very helpful (and thanks also to Dimitri V). If anyone else finds this topic interesting, I subsequently found a paper that attempts to separate out the "actuarial" default premium to arrive at estimates of the CRP. There are similar papers, but I found this one the clearest : papers.ssrn.com/sol3/papers.cfm?abstract_id=2173148. Thanks all.


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