Building a Duration-Weighted Yield Index for Comparable Bonds

Summary

The document addresses how to construct a benchmark yield from bonds grouped by similar risk, maturity, and duration. The investor has calculated each bond’s yield to maturity and wants a representative index from a group of bonds considered comparable to bonds suspected of being manipulated. The proposed method assigns each constituent a weight proportional to its market value multiplied by its duration, then normalizes those quantities so the weights sum to one.

The index yield is calculated as the weighted average of constituent yields to maturity using those duration-adjusted market value weights. This gives greater influence to bonds with both larger market value and greater duration. The response supplies formulas for the weights and index yield, but no worked numerical example or evidence that this benchmark reliably estimates an individual bond’s “real value.” It also does not discuss data quality, outlier treatment, constituent selection, or whether this weighting is appropriate for the user’s intended comparison; the result should be understood as a specified weighted yield measure.

Key ideas

• Assign each bond a weight proportional to its market value multiplied by its duration.
• Normalize the duration-adjusted market values by their total to obtain constituent weights.
• Calculate the index yield as the weighted average of constituent yields to maturity.
• The method defines a benchmark yield but does not establish an individual bond’s fair value.
• The document provides no worked example or guidance on outliers and constituent selection.

Tags

# How I can calculate index bond market


# How I can calculate index bond market












I know that some of the bonds on the market have been manipulated by investment funds. I could identify these bonds. I have classified similar bonds in terms of risk, maturity and Duration. I have calculated YTM for all bonds. Next, I would like to estimate their real value these bonds using the bond index. My problem is I don't know how to make an index for each category and calculate the YTM index. To understand more accurately: My papers are divided into 30 categories according to the features. And, for example, in the first batch there are 2 manipulated bonds and 25 similar ones and not manipulated. I want to make index using 25 bonds' YTM that could represent these value these 2 bonds. But I don't know how to make this index better? i have 25 bonds. i calculate YTM for each them. now i don't know how i can make a index for in 25 bonds.

## Answer by Atlas (score 0, accepted)

https://quant.stackexchange.com/a/47466

To calculate the average YTM of the index, you need to use the duration-adjusted market value weight ($mv_{wd}$) for any bond $i$:

$$mv_{wd;i} = \frac{mv_i \cdot d_i}{\sum_{i=1}^n mv_i \cdot d_i}$$

, where $d_i$ denotes the duration of a bond $i$ and $mv_i$ the market value.

The average index YTM, $Ind_{YTM}$, is than calculated by:

$$Ind_{YTM} = \sum_{i = 1}^n mv_{wd;i} \cdot YTM_i$$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.