1
$\begingroup$

Suppose we have the PV of a bond, as well as two separate streams of cash flows, say, $C_a$ and $C_b$ that make up the total annual cash flows $C$ (i.e. $C=C_a+C_b$). In other words, suppose we have,

\begin{equation} PV(bond)=\frac{C^{(1)}}{(1+YTM)}+\frac{C^{(2)}}{(1+YTM)^2}=\frac{C^{(1)}_a+C^{(1)}_b}{(1+YTM)}+\frac{C_a^{(2)}+C_b^{(2)}}{(1+YTM)^2}. \end{equation} noting that $C^{(1)}\ne C^{(2)}$. I have been assigned with the task of breaking down the YTM according to the individual $YTMs$, which I cannot figure out. Would appreciate it, if someone could explain this to me.

Thanks.

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ I don't quite understand - are you trying to attribute yield to credit risk-free yield, credit spread and various other spreads? Or are you trying to attribute the yield to single cash flows or tenor buckets? I'm not sure if you can decompose the yield itself by tenor bucket very meaningfully. It may make more sense to decompose by tenor the instrument's sensitivity to a yield change (interest rate risk) . $\endgroup$
    – Dimitri Vulis
    Commented Apr 26, 2022 at 12:39

1 Answer 1

Reset to default
0
$\begingroup$

I think I understand. You are trying to calculate the IRR of the a-cash flows and the b-cash flows individually ? But there are multiple solutions: you can partition the PV into PV(a) and PV(b) and solve for IRRs of a and b separately with only the constraint that PV= PV(a)+PV(b).

Improve this answer
$\endgroup$
5
  • $\begingroup$ That is what I thought initially as well. But the part I do not get, is that $PV(a)$ and $PV(b)$ are obtained by discounting by the same rate as $PV$, so wouldn't then $YTM(A)=YTM(B)=YTM$? $\endgroup$
    – Carl
    Commented Apr 26, 2022 at 17:28
  • $\begingroup$ There is a unique partition of the PV which satisfies that, yes. But maybe a) and B) have different riskiness or some other reason to discount them at different rates. $\endgroup$
    – dm63
    Commented Apr 26, 2022 at 17:51
  • $\begingroup$ In other words, what is the point of the question if a and b must be discounted at the same rate ? $\endgroup$
    – dm63
    Commented Apr 26, 2022 at 19:59
  • $\begingroup$ Without adding at least a constraint on $PV(a)$ or $PV(b)$, this question is ill-posed, I'd say. $\endgroup$
    – Kermittfrog
    Commented Apr 26, 2022 at 20:53
  • $\begingroup$ This reminds me of analysis (not very useful) we used to try on Brady bonds. Part of the bond's cash flow was guaranteed by US Treasury. Discouting the guaranteed cash flows with treasury, we can calculate PV(guaranteed). Subtracting that from the observed dirty price (PV), we get PV(not guaranteed flow) and solve for the yield of not guaranteed flows. But it was not very useful, and does not seem to be what you want. $\endgroup$
    – Dimitri Vulis
    Commented Apr 27, 2022 at 16:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.