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I am trying to make an index for the bond market in my country, which will be modified daily. For simplicity, suppose that I only have three bonds.

Additionally, suppose that I am interested in establishing the weights of each asset by their nominal debt value, and that they will be rebalanced monthly. Suppose also that I am interested in finding the weighted average coupon payed by the securities. Finally, suppose that one of the bonds expire somewhere during this month.

So as long as no bonds expire, we will have no problems for finding this weighted average. However we encounter a problem when the bond reaches its maturity and we do not modify the vector of weights $(\alpha_1, \alpha_2, \alpha_3)$, in the sense that the average coupon will decrease. How do indexes overcome this situation?

Thanks in advance.

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    $\begingroup$ In my personal opinion, if a bond matures in February 2020, it should have been removed from the index at the previous rebalancing on 31 January (and replaced by another bond with more than 1 month of maturity left, if available). That is how I would run a monthly rebalanced bond index. $\endgroup$ – noob2 Feb 18 at 20:19
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    $\begingroup$ this is in agreement with @noob2 <theice.com/publicdocs/data/ice-treasury-methodology.pdf? $\endgroup$ – Vrun Feb 18 at 22:49
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Major indicies, like Bloomberg Barclays, publish two versions of the index. One is rebalanced daily and the other monthly.

Returns are always compared against the monthly rebalanced index. Bonds with less than a month to maturity are typically excluded due to index rules.

However, calls and other redemptions still happen mid month. These bonds are replaced with a cash plug record until the next month’s rebalance.

Even though the index is rebalanced monthly, I would not worry about shifting index level statistics mid month. You’ll have duration changing, interest rates resetting on FRNs, and redemptions happening on a daily basis. Index providers still publish daily returns and both bond and index level statistics on the monthly rebalanced benchmarks for this very reason.

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