# Different methodologies of building indices

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).

• Index yield is non-intuitive. Take a look at research.ftserussell.com/products/downloads/… section 2.4. Commented Jul 1, 2021 at 22:01
• This actually helps a lot! Can you recommend other similar sources (maybe more detailed ones, with some theoretical background)? Commented Jul 1, 2021 at 22:05
• Can also be interesting to know different weights mechanism available out there! Commented Jul 1, 2021 at 22:07
• 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. Commented Jul 1, 2021 at 22:11
• Not sue of this is one of the docs mr. vulis is referring to financedocbox.com/75903663-Mutual_Funds/… Commented Jul 2, 2021 at 15:45