I have the price of a bond and would like to convert it to spreads. Is this possible by just having dollar duration?

Secondly, if I just care about the relative spreads of multiple bonds, is it enough to consider their prices and dollar durations? Would I simply divide the price by the dollar duration to get relative spreads?


1 Answer 1


Unless I misread your question, NO: Spread calculation (calibration) is a root-finding exercise. In the simplest case (flat rate curves), given market price $P$ and reference yield $r$ (e.g. treasury rate), which spread level $s$ ensures that

$$ s:PV(r,s,t,T)\equiv\sum_{i}c_ie^{-(r+s)(T-t_i)}\stackrel{!}{=}P $$

In root-finding, we can employ Newton's method and iterate towards the correct spread level $s$ given some initial guess $s_0$

$$ s_{n+1}=s_n-\frac{PV(r,s_n,t,T)-P}{\left.\frac{\partial PV(r,s,t,T)}{\partial s}\right|_{s=s_n}}=s_n+\frac{PV(r,s_n,t,T)-P}{\mathrm{Dollar\ Duration(DV01)}} $$

The last equality is true as:

$$ dPV/dy = dPV/dr = dPV/ds = -\sum_{i}(T-t_i)c_ie^{-(r+s)(T-t_i)} $$

i.e. $\mathrm{DV01=CS01}$. Yet, given only the bond price and its duration is not sufficient - We also need the reference rate level, $r$. But if we know $r$, we have $s=y-r$ and we do not need the value or the duration in the first place.


  • $\begingroup$ What if I don’t care about the absolute level of spread; but just want to compare a relative level of spreads? Would it be enough to have prices and dollar duration? $\endgroup$
    – Nickpick
    Mar 22, 2022 at 7:47
  • $\begingroup$ Assuming equal times-to-maturity and coupons across bonds then, yes, price levels are sufficient to rank spreads: Lowest price = largest spread. I'd say the case with different maturities and coupons require some more analysis. $\endgroup$ Mar 22, 2022 at 7:58
  • $\begingroup$ Would the duration be enough to compensate for time to maturity as it’s a proxy for that? $\endgroup$
    – Nickpick
    Mar 22, 2022 at 8:17
  • $\begingroup$ Hi, at this point I'd say: Please update your initial post so that it better reflects your ideas and questions, ok? $\endgroup$ Mar 22, 2022 at 8:24
  • $\begingroup$ Added second part to the question $\endgroup$
    – Nickpick
    Mar 22, 2022 at 8:26

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