# Rebalancing Bond Indexes

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?