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Let's say there are about 100 illiquid EM bonds. I would like to construct a Price Index of these bonds to see the overall performance of these instruments. I have their issue volume (number of bonds x face value) that will be used to find each bond's weight. However, after some time some of the bonds will mature or will be excluded if their rating falls. Also, there will be some new issues which will qualify for inclusion to the Index. Can anybody tell how can I effectively account for such events?

As per my findings there are two basic types of Price Index construction approaches - Paasche and Laspeyres. But thus far I have not encountered them in some of the bond index construction methodologies.

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    $\begingroup$ A bond index has to be Investable, meaning you know in period t the portfolio weights to hold from t to t+1. That's not possible in Paasche index, which uses the quantities for period t+1 as weights. Therefore it is always a Laspeyeres type index that is used. $\endgroup$ – noob2 May 10 '17 at 20:17
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As @noob2 pointed out, a Laspeyeres type index is the way to go, so I'll focus on other parts of your question.

Nearly all bond indices are rule-based and rebalanced monthly. At the end of each month, based on a pre-determined set of rules (countries, credit rating range, maturity range, minimum par amount, etc.), you select a basket of bonds. This basket is known as the "returns universe" and is used to compute the daily returns for the next month.

As the month progresses, some of the bonds may be disqualified (perhaps due to a credit event or maturity being too short) and other bonds may qualify. These subtractions and additions result in a forward-looking "statistical universe," but have no impact on the current "returns universe." In other words, these events do not change the bonds you use to calculate returns for the current month.

At the end of the month, the statistical universe replaces the old returns universe as the new returns universe, and the cycle starts again.

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