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Say have a basket of coupon bonds $B_i$ with $i \in \{1, ..., n\}$. Those bonds have different characteristics one from another. For example they differ in maturity, face value and coupon outstanding. But they are in same currency.

The problem I am facing is quite theoretical: how can I come up with a benchmark index of those bonds. In particular, I want to find the "yield" of the index which is composition of all $n$ bonds.

The most trivial thing I could think of is the following ($P_i$ is the $i$-th bond price in 100s, $F_i$ its outstanding face):

  1. For each bond I calculate YTM$_i$
  2. I define weights as: $w_i = \frac{F_i \cdot P_i}{\sum_{i = 1}^nP_i}$
  3. I define YTM of the index as YTM$_I = \sum_{i = 1}^n$YTM$_i \cdot w_i$

Basically a weighted average of YTM. To me, this doesn't have so much theoretical background and may lead to misleading results. Does anybody have any idea on a way to find YTM of the basket of bond (possibly computationally efficient).

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    $\begingroup$ Index yield is non-intuitive. Take a look at research.ftserussell.com/products/downloads/… section 2.4. $\endgroup$ Commented Jul 1, 2021 at 22:01
  • $\begingroup$ This actually helps a lot! Can you recommend other similar sources (maybe more detailed ones, with some theoretical background)? $\endgroup$ Commented Jul 1, 2021 at 22:05
  • $\begingroup$ Can also be interesting to know different weights mechanism available out there! $\endgroup$ Commented Jul 1, 2021 at 22:07
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    $\begingroup$ As I recall, Citi/YieldBook had a good writeup on the theoretical underpinnings of a bond index yield, so so did Merrill Lynch, but I don't see either one posted online, and don't actually have them. $\endgroup$ Commented Jul 1, 2021 at 22:11
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    $\begingroup$ Not sue of this is one of the docs mr. vulis is referring to financedocbox.com/75903663-Mutual_Funds/… $\endgroup$
    – nbbo2
    Commented Jul 2, 2021 at 15:45

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